PHYS.192 Manual

Physics for engineers PHYS192

Academic year 2011-20112

University of Qatar Math & Physics Department-----------------------------------------------------------------------------------------------------------------------

ContentsPage No. 4444444788810101111111313141517171719List of ExperimentsWhy Do We Make Experimental Measurements?The Physics LaboratoryLab OrganizationLaboratory NotebookNotes for Physics Lab Reporting1.2.Grading:Experimental Uncertainty and Data AnalysisTypes of Experimental UncertaintyAccuracy and PrecisionSignificant FiguresComputations with Measured ValuesRounding OffGraphical Representation of DataError BarsStraight-Line GraphsLinear Regression and Method of Least SquaresThe Goodness of the Fit:Data Analysis with Microsoft Excel1. Tables with Excel2. Plotting with ExcelSafety in the Physics LabPreparing Your ReportMarking the ReportPhysics for engineers PHYS1922Academic year 20011/2012

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------

List of ExperimentsExperiment (1)Experiment (2)Understanding of Motion using Motion SensorDetermination of the Acceleration of Gravity using theFree fallExperiment (3)Experiment (4)Experiment (5)Experiment (6)Experiment (7)Verification of Newton‘s Second LawTransforming Gravitational Potential Energy to Kinetic EnergyVerification of Hook‘s LawVerification of (Work – Kinetic energy) theoremDetermination of the Acceleration of Gravity using theSimple PendulumExperiment (8)Experiment (9)Determination of the Coefficient of ViscosityDetermination of the speed of sound in air usinga resonance tubeExperiment (10)Experiment (11)Experiment (12)Determination of the Mechanical Equivalent of HeatStatic EquilibriumDetermination of Specific Heat Capacity of a solid4754576441442730323639Page No.20References…………………………………………………..…………………………….66Physics for engineers PHYS1923Academic year 2008/2009


The Physics LaboratoryWHY DO WE MAKE EXPERIMENTAL MEASUREMENTS?When you can measure what you are speaking about and express it in numbers, you know something about it; butwhen you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager andunsatisfactory kind. LORD KELVINThe main purpose of laboratory experiments is to augment and supplement the learning andunderstanding of basic physical principles while introducing laboratory procedures, techniques,and equipment. Introductory physics laboratory in particular provide ―hands-on‖ experiences ofvarious physical principles. In so doing, one becomes familiar with laboratory equipment andprocedures and with the scientific method.Lab organizationStudents usually work in pairs, but each student is expected to record his/her results as well asperform their analysis and drawings separately. However, discussion about the practical andtheoretical aspects of each experiment is highly encouraged.Laboratory notebookA laboratory notebook record must be kept for all experimental work during the lab period. Aformal laboratory report will then be required. This could be hand written or typeset, in English.Typed reports with data plotted using a computer are encouraged but are not compulsory.Organization of write-upsAll notes, sketches, readings and data points must be recorded in a laboratory notebook. No loosepieces of paper are allowed. The notebook must be signed by the lab instructor, at the end of thelab. A copy of data may be stored on the computers available in the laboratory in a sub-directorywith the STUDENT name under the LAB192 folder. Those computers may also be used forplotting or data analysis if there is sufficient time, a preliminary analysis must be discussed withthe demonstrator. A mark is assigned to this. The final write up must be presented no later than thefollowing week.

Notes for Physics Lab ReportingThe Laboratory Report1. Preparing your ReportThe purpose of a laboratory report is to communicate the aim, process and outcome of aninvestigation to an outside audience. It is a record of your direct (―hands-on‖) experience in thelaboratory. In most cases, a scientific investigation is considered to be incomplete without a report.By putting together thePhysics for engineers PHYS1924Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------different aspects of your laboratory experience in a structured and coherent report, the essence ofyour investigation becomes clearer in your own mind. In the process, you develop your skills ofreasoning and ability to communicate in writing.There are many acceptable ways of presenting a scientific/laboratory report, but, almost all reportswill include the components outlined below.Components of a laboratory reportTitle page should include:Author‘s name(Partner‘s name/s)Course detailsExperiment titleDateThe title must be short but factual and descriptive. It must summarize the major aspects to be dealtwith in the report. The key words will often come from the laboratory task that has been set andyou need to identify these. These words help clarify the requirements of the task and also alert thereader as to what the report is about.Introduction and aim:The introduction puts the report into perspective by giving the reader relevant backgroundinformation about the phenomenon being investigated. This is in order to prepare the reader forwhat he or she is about to read. This background may include some historical information ordevelopments, the theory or law governing the phenomenon being investigated. These introductoryremarks must be kept brief to avoid obscuring the main point of the investigation. Yourintroduction must state the aim of your investigation. The integration of the aim into theintroduction allows for the smooth transition from general information to the specific goal of theinvestigation.Apparatus and method:Present a clear, concise and step-by-step description of the apparatus, techniques and proceduresused. List and name the apparatus with brief descriptions of the main parts as well as the functionsthereof. A neatly sketched and labeled diagram is essential and can save you paragraphs of tediouswritten descriptions. Briefly describe the procedures that you followed in the investigation.Wherever appropriate, give a reason for each step you took in a procedure. Sometimes more thanone section is required for this material. e.g. If two techniques were used i.e. Technique No.1,Technique No.2, etc. then a brief explanation of each of these techniques must be given. Do notomit any significant steps. A description of method helps you to recall the problems that wereassociated with experimental procedures such as precision of measurements, strengths andweaknesses of certain techniques, recording of observations etc.This will help you when you have to summarize your conclusions and recommendations at the endof your report.Physics for engineers PHYS1925Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Data and results:The main parts of this section are your tables of results and graphs. You must have a consistentway of recording your observations and calculations. Data are normally summarized and displayedin tables and graphs. Each table and graph is usually referenced by a number and should benumbered in sequence e.g. Table 1, Table 2; Figure 1, Figure 2 etc. Each table is accompanied by atitle and each graph by a caption, which describes the purpose for which it has been presented. (e.g.―Table 1: Measurements of the width of the cylinder‖ and ―Graph 3: To determine the viscosity ofthe sample of oil‖).Tables and figuresThose must be referred to in the text e.g. ―The apparatus was arranged as shown in Figure 1‖; ―Thedata gathered were recorded as shown in Table 1 below‖ or ―The data in Table 1 were used to plotthe graphs in Figure 1, 2 and 3.‖ These brief statements help to link the different parts of the report.This section does not contain your judgment of the data. It is a straightforward presentation of yourreadings or measurements.Analysis, interpretation and discussion:In this section examine and extract important aspects of the data and use these to explain variousrelationships or derive other useful quantities (such as means, standard deviations, uncertainties,etc.). For example, what is the shape of your graph and what does it suggest in terms of therelationship between the variables? If it is a straight line, what is the value of the slope? Rememberto quote slopes, means or other derived quantities with the appropriate significant figures and thecorresponding uncertainties. How do an expected value compare with your own and what reasonscan you give for this? You may give tentative explanations for your data but be careful not to mixfacts with opinions.Conclusion and recommendations:This is normally a section in which you say what the investigation has shown and to what extentthe problem or claim stated in the introduction has been resolved. Remember that any conclusionsmust be supported by evidence from your data. Always quote any final results, together with theiruncertainties in your conclusion. Avoid making vague statements such as ―This was a successfulexperiment.‖ You may also need to discuss sources of systematic error and any improvements thatcould be made to the apparatus (and measurements). Again, avoid meaningless phrases such as ―itwas caused by human error.Writing a report allows you to reflect critically on the whole experiment and check yourunderstanding of the purpose of the investigation as well as produce an accurate record of it. Notethat any physics practical is not a set of procedures designed to reproduce some ―correct‖ answer.It is a problem that has been posed that requires an experimental solution, which may includemaking measurements, implementing different procedures and techniques and then the formulationof a suitable report.Whether you graduate and leave with a B.Sc. to work in industry or whether you carry on at auniversity to become a post-graduate student, you will find that report writing will remain as one ofthe most important activities in your career.Physics for engineers PHYS1926Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Scientific StyleVery often, in reports of this kind, writers prefer to use the passive construction or impersonal styleto report procedures followed in conducting experiments. For example:Five measurements were taken, instead of: We took five measurements. However, both styles areacceptable, but passive style is encouraged.2. Marking the reportWhen marking your reports a lot of feedback will be given that is relevant to your individualreport. More feedback of a general nature is given at a formal session to the whole class. All thefeedback you get is intended to help you consider ways of improving your report. The assessmentof reports is largely a subjective exercise on the part of the markers but criteria are used asguidelines for giving feedback and marks.Marks will be given for your data collection and processing (which includes your method, tables,graphs and calculations) as well as the overall coherence of the report as a piece of writing. Thereport should have nearly all of these elements present:1. The aim of the report is clearly stated.2. The relevant theory is competently discussed.3. The results of the experiment are clearly discussed and interpreted In relation to aim of the report.4. A definite conclusion, which is ideally supported by the final results, is stated and clearly related to the aim of the report.5. The significance of the final results is thoroughly discussed.6. Recommendations are made and clearly linked to the method of the experiment and/or the aim.7. Sentences within and across sections are linked together effectively with the use of cohesive ties.8. The reading process is uninterrupted as there is few grammar or spelling errors.9. The report should be neat and well-structured, with appropriate headings.

Grading: Final grades will be determined by the following components:ReportsEfficiency in lab and preparationMidterm examFinal examTOTAL30%5%30%35%100%Physics for engineers PHYS1927Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Experimental Uncertainty and Data AnalysisNo reading of a physical quantity is exact. All readings have some uncertainty. This uncertaintymay be small, but it is never zero. It is important to be able to estimate how large the uncertainty is.This uncertainty has many causes resulting in several types.Types of experimental uncertainty:1. Random errorsRandom errors (also called statistical or indeterminate errors) result from unknown andunpredictable variations that arise in all experimental measurement situations. The termindeterminate refers to the fact that there is no way to determine the magnitude or sign (+, toolarge; -, too small) of the error in any individual measurement. Conditions in which random errorscan result include:a/ Unpredictable fluctuations in temperature or voltageb/ Mechanical vibrations of an experimental setupc/ Unbiased estimates of measurement readings by the observerRepeated measurements with random errors give slightly different values each time. The effect ofrandom errors may be reduced and minimized by improving and refining experimental techniques.However, the key point is that random or statistical errors can be estimated by repeating ameasurement several (perhaps many) times. In general,experimental result is of little or no use if the size of its uncertaintycannot be estimated. (One should not only report a result but alsogive some indication of its reliability.Here is a key point: Statistical errors can, in general, be estimatedin only one way: by repeating the measurement several times.Therefore, in all your work in this lab, you must repeatmeasurements to determine the statistical error.2. Systematic errorsSystematic errors (also called determinate errors) are associatedwith particular measurement instruments or techniques, such as animproperly calibrated instrument or bias on the part of theobserver. The term systematic implies that the same magnitude andsign of experimental uncertainty are obtained when the meas-urement is repeated several times. Determinate means that themagnitude and sign of the uncertainty can be determined if theerror is identified. Conditions from which systematic errors canresult include:Fig. 1 An improperly “zeroed”instrument gives rise to systematicerror.1. An improperly ―zeroed‖ instrument, for example, an ammeter as shown in Fig. 1.2. A faulty instrument, such as a thermometer that reads 101ºC when immersed in boiling water at standard atmospheric pressure. This thermometer is faulty because the reading should be 100ºC.Physics for engineers PHYS1928Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------3. Personal error, such as using a wrong constant calculation or always taking a low reading of a scale division. Other examples of personal systematic errors are shown in Fig. 2. Reading a value from a scale generally involves lining up something, such as a mark at the scale. The alignment and hence the value of the reading can depend on the position of the eye (parallax).Avoiding systematic errors depends on the skill of the observer to recognize the sources of sucherrors and to prevent or correct them.Here is a key point: Statistical errors can, in general, be estimated in only one way: by repeating themeasurement several times. Therefore, in all your work in this lab, you must repeatmeasurements to determine the statistical error.Temperature measurementLength measurementFig. 2 Examples of personal error due to parallax in reading scales.Accuracy and Precision: Accuracy and precision are commonly used synonymously, but inexperimental measurements there is an important distinction. The accuracy of a measurementsignifies how close it comes to the true (or accepted) value, that is, how correct it is.Precision refers to the agreement among repeated measurements, that is, the ―spread‖ of themeasurements or how close they are together. The more precise a group of measurements, thecloser together they are. However, a large degree of precision does not necessarily imply accuracy.Obtaining greater accuracy for an experimentalvalue depends in general on minimizing systematicerrors. Obtaining greater precision for anexperimental value depends on minimizing randomerrors.Significant Figures:The significant figures (sometimes called significantdigits) of an experimentally measured value includeall the numbers that can be read directly from theinstrument scale plus one doubtful or estimatednumber or fraction of the smallest division (Fig. 3).Physics for engineers PHYS1929Fig.3 Significant figures. The edge of the objectis reported to be at the 10.45cm position of themeter stick. This reading has four significantfigures, with the last 5 being the estimated or Academic yeardoubtful (least significant) figure. 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Computations with measured values:Calculations are often performed with measured values,and error and uncertainty are propagated by themathematical operations (that is, error is carried throughto the results by the mathematical operations). Thedivision of 374/29 = 13 is shown in Fig. 4 as done on ahand calculator. The result must be rounded off to twosignificant figures. (Why?) Reporting more figures wouldimply greater significance than given by themeasurements, and a result cannot be made moresignificant by a mathematical operation.Rounding offThe non-significant figures are dropped from a result ifthey are to the right of the decimal point or are replacedby zeros if they are to the left of the decimal point. Thelast significant figure retained should be rounded off.The procedure for doing this is as follows:Rules for Rounding Off NumbersLocate the first number to the right of the appropriate number of significant figures, which is thefirst digit of those to be removed. (For example, in rounding off 5.247 to two significant figures,this is the 4.) If this digit isFig. 4 The calculator shows the result ofthe division operation 374/29. Since thereare only two significant figures in the 29,the result can have no more than thisnumber, and the calculator display valueshould be rounded off to 13.1. less than 5, then the preceding digit remains the same (e.g., 5.247 rounds to 5.2), or2. Equal to 5 or greater than the preceding digit is increased by 1 (e.g., 2.257 rounds to 2.3)For multiple operations, rounding off to the proper number of significant figures should not bedone each step because rounding errors may accumulate. It is usually suggested that one or twoextra insignificant figures be carried along, or if a calculator is being used, rounding off may bedone only on the final result of the multiple calculations.Graphical Representation of DataIt is often convenient to represent experimental data in graphical form, not only for reporting, butalso to obtain information.Graphing ProcedureQuantities are commonly plotted using rectangular Cartesian axes (X and Y). The horizontal axis(X) is called the abscissa, and the vertical axis (Y), the ordinate. The location of a point on thegraph is defined by its coordinates x and y, written (x, y), referenced to the origin 0, theintersection of the X and Y axes.When plotting data, choose axis scales that are easy to plot and read.Physics for engineers PHYS19210Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Graphs should have:1. Each axis labeled with the quantity plotted.2. The units of the quantities plotted.3. The title of the graph on the graph paper (commonly listed as the y coordinate versus the xcoordinate).As a general rule, it is convenient to choose the unit of the first major scale division to the right orabove the origin or zero point as 1, 2, or 5 (or multiples or submultiples thereof, e.g., 10 or 0.1) sothe minor (intermediate) scale divisions can be easily interpolated and read.The graph in figure 5 shows an example of graphs that are too small. Scales which are too smallbunch up the data, making the graph too small, and the major horizontal scale values make itdifficult to read intermediate values. Choose scales so that most of the graph paper is used. Figure6 shows the data in table 1 plotted with more appropriate scales.Also note in figure 5 that scale units on the axes are not given. Scale units should always beincluded as shown in figure 6.Displacement (cm)0.160.751.001.351.632.002.75Force (N)2.406.9012.0016.3019.1025.0032.10d1.951.871.201.761.991.821.68Physics for engineers PHYS19211Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------8060Force4020002468DisplacementFig. 5 Poor graphing An example of an improperly labeled and plotted graph.Error BarsYou must account for the statistical error on your measured points by representing theseuncertainties as error bars on your plots. In nearly every lab here, you are varying some quantity,X, and the measuring the impact on some quantity, Y. Measure the statistical error on Y. Then plotY vs. X with error bars on Y that are statistical errors. This is what a physicist means by error bars.You must show such a plot in your lab report. A plot without error bars is just plain wrong.STRAIGHT-LINE GRAPHSTwo quantities (x and Y) are often linearly related; that is, they have an algebraic relationship ofthe form y = mx + b, where m and b are constants. When the values of such quantities are plotted,the graph is a straight line.The m in the algebraic relationship is called the slope of the line and is equal to the ratio of theintervals Δy/Δx. Any set of intervals may be used to determine the slope of a straight-line graph.However, in practice, points should be chosen relatively far apart on the line. For best results,points corresponding to data points should not be chosen, even if they appear to lie on the line.The b in the algebraic relationship is called the y-intercept and is equal to the value of the Ycoordinate where the graph line intercepts the Y axis. Notice from the relationship thatY = mx + b, so that when x = 0, then Y = b. If the intercept is at origin (0, 0), then b = 0.Physics for engineers PHYS19212Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------504030Force (N)20100012Displacement (cm)34Fig.6 Proper graphing. An example of a properly labeled and plotted graph.LINEAR REGRESSION AND METHOD OF LEAST SQUARESWhen the data points are plotted, draw a smooth line described by the points. Smooth means thatthe line does not have to pass exactly through each point but connects the general areas ofsignificance of the data points, with an approximately equal number of points on each side of theline. This gives a "curve of best fit."The resulting equations and the procedure for determining the slope and intercept of the best fittingstraight line can be computed automatically by some hand calculators and by computers with theappropriate software.The straight line of "best fit" for a set of data points on a graph can be determined by a statisticalprocedure called linear regression, using what is known as the method of least squares. Thismethod determines the best-fitting straight line by means of differential calculus.In cases where several determinations of each experimental quantity are made, the average valueis plotted and the mean deviation or the standard deviation may be plotted as error bars. ForPhysics for engineers PHYS19213Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------example, the data in Table 1 are plotted in Fig. 6. A smooth line is drawn so as to pass within theerror bars. (You may want to use a French curve at this point.)The goodness of the fit:Once you have done a best fit, however, you need to address the following question: is the best fita good fit. In other words, does the model fit the data to within the uncertainties prescribed by theerror bars? This is the critical question for the experimental physicist. Your goal is not tomeasure a number. Your goal is not even to measure the "right" number. Really, your goal isto determine if the physical model is supported by the data. In my opinion, if you take thisnotion to heart, you will understand the soul of experimental physics. To do this you mustnumerically answer the question: "Does the data fit the model to within the statistical uncertaintieson the measurements?"In order that you answer the question: "is this a good fit?" numerically, you should calculate thechi-squared of the data relative to the model. No matter how you have done your fit, be sure tocalculate the chi-square. By dividing the number of degrees of freedom (usually N-2 for a linear fitto N points) you end up with a number called the reduced chi-square. Be sure you understand thefollowing:The expected value for the reduced chi-square is 1 (unity) in the case that the data aredescribed by the model with given statistical uncertainties. If you get a reduced chi-squarenear 1.0 this usually means that within your error bars you appear to have a good fit to themodel.If, on the other hand, the reduced chi-square is significantly larger than 1.0, this indicatesthat either the model does not fit the data (new physics!) OR your estimates for your errorbars are too small (this should not happen if you measured them by repeated measurements)OR there is some sort of systematic error that remains unaccounted for in your model.If, on the other hand you get a value that is significantly less than 1.0, then either you arevery lucky (maybe too lucky) or (more likely) you have somehow overestimated the size ofyour statistical errors. Again, this should not happen if you estimate your errors fromrepeated measurements.The reduced chi-square is the experimentalist's universal criteria for comparing data with models.If you learn to use the chi-square, you will have gained a powerful tool for evaluating the meaningof nearly any new experimental result in any field.What is “least squares” Fitting?The following situation is common in experimental physics. You have taken some data on the waya quantity (y) varies with changes in another quantity (x). You now wish to plot the variation on agraph and extract the slope and the intercept of the "best fit" straight line. The data points have asmall random uncertainty associated with them and so you draw a "best fit" straight line throughthe points. You decide on this line using good judgement. You then estimate the slope and interceptof the line to which you believe that your data conform.Aside from "good judgement", there are other ways of estimating the slope and intercept of the bestfit straight line. These other techniques are useful because they are numerical, and don't involvedrawing graphs. Because of this, the fitting of the data can be done by a computer, based onobjective mathematical criteria, rather than the "good judgement" that you are used to using.Physics for engineers PHYS192Academic year 2008/200914

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------There are many possible criteria that may be used to decide which line gives the best fit to the data,but by far the most commonly used is the Least Squares criterion. This says that:The best fit line to some data is the one which minimises the sum of the squares of all thedifferences between the data points and the line.I think we need some pictures to see what this means. Here are some data points. In this case thereare 9 of them: (X1,y1)(X2,y2)... (Xi,yi)... (X9,y9).The graph below shows three possible lines A, B and C, that could be fitted to the data. Some linesseem more appropriate than others.Using your innate good judgement of these matters, you will spot that line B is a better fit to thedata than lines A or C. Each of the three lines has an equation of the form...Y = mx + cPhysics for engineers PHYS19215Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------where m is the slope of the line, and c is the intercept on the y-axis. What we are looking for is anobjective way of deciding which line best fits the data i.e. the choice of values for m and c that is insome sense "optimal".Notice that none of the lines pass through all the points. In fact, even the best fit line B goesthrough only one point. For each data point, the difference between the y-value, yi and what thefitted line would lead us to expect, is called a residual, i.Clearly we would like the residuals to be as small as possible. However adjusting the slope andintercept of the line to reduce one residual can cause another residual to be larger. However, if mand care chosen So that the sum of the residuals is small, then m and c are likely to represent a linewhich is a "good fit" to the data.It is however, not quite that simple. This is because we do not mind whether a residual is positiveor negative, we just want its magnitude to be as small as possible. Thus the Least Squares criterionchooses m and c such that the sum of the squares of the residuals is minimised. The square of anumber, positive or negative, is always positive. Thus minimising the squares of the residuals,results in a line which minimises the sum of the "distances" between the data points and the line.More technically, if the residual from the ith data point is i then m and c are chosen such that thequantity Q given byis minimised.Q: Why does this technique minimise the sum of the squares of the residuals, and not the sum ofthe residuals themselves?We should next do some mathematics to see how to pick the values of m and c which satisfy the"Least Squares" criterion.Physics for engineers PHYS19216Academic year 2008/2009


Data analysis with Microsoft Excel3. Tables with ExcelInitiate Excel by clicking on the Excel shortcut on the computer‘s desktop. If you want to changethe width and height of cells, highlight the cells and then use FORMAT, ROW, HEIGHT andFORMAT, COLUMN, WIDTH to change their sizes. To add headings (and units) to the columnsclick on the cell and type, as you would normally do. Unfortunately one can‘t produce superscriptsand subscripts in Excel so one needs to use the ^ sign to indicate power of the unit. Your data isentered the same way — just click on the cell and enter the value.If you want to get Excel to do a calculation just click on the cell where you want the answer to go,and type = followed by the required mathematical expression. For example, if the value in theparticular cell is obtained by multiplying the value in cell C3 by that in D3 just type = C3*D3. (Infact you can just type = then click on cell C3 and hit the Enter key, type *, click on D3 and hit theenter again.) In Excel the * symbol is used to indicate multiply, the / symbol for divide and the ^symbol for ―raise to the power‖. It is very easy to apply the same formula to the rest of the cells inthe column, just select the cell with the formula in it, then click on the bottom right hand cornerand drag it down the column.Remember to take care to display the correct number of significant figures in your data. SinceExcel calculates the answer to as many places as can fit in the cell you often need to adjust thenumber of decimal places in columns to reflect the correct number of significant figures.Decreasing the number of decimal places in a number is easiest achieved using the button marked,increasing the number of decimal places by that marked. To add gridlines or borders to your tableuse the button marked.

4. Plotting with ExcelWhen you are ready for Excel to plot your data you need to highlight the two columns of data youwish to plot and use INSERT, CHART to call up the chart (plotting) procedure. Choose the XY(SCATTER) option and then select the chart sub-type option that allows you to plot the pointswithout lines. Then click on NEXT, and NEXT again until you bring up the CHART OPTIONSwindow. You can use the TITLE option to write a title and label the X- and Y-axes, theGRIDLINE option to switch off the gridlines and the LEGEND option to switch off the ―showlegend‖. Having done this click on FINISH.Move your plot into the desired position by clicking just inside the borders and dragging it towhere you want it positioned. Expand it by pulling on the small black squares in the middle of theborders. To draw the best straight line through your points click somewhere inside your graph toselect it, then click on CHART > ADD TRENDLINE and select the LINEAR option. If you needto know the slope and intercept of this straight line click on OPTIONS and check the DISPLAYEQUATION ON CHART box. Before plotting your graph it will probably be best to remove thegrey background — easiest done by clicking twice somewhere on the background and eitherchoosing the color white, or choosing none.The final alteration you may wish to attempt is to change the origin of the plot so that your graphPhysics for engineers PHYS19217Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------covers most of the page. To change the scale on the x-axis, click on the axis to select it. Next clickon FORMAT, SELECTED AXIS and choose the SCALE option to change the minimum for yourx-axis. Repeat exercise for the y-axis if desired.ConclusionThese procedures will lead you to a useable graph. It is then up to you how far you gowith resizing the labels and general prettifying. Excel is astonishingly powerful – but only if wetell it what to do using our vast experience does it become astonishingly useful.10 Steps to making your Excel graphs look more professional1. Create your chart as a separate chart rather than having it drawn over the top of your data. This makes it much easier to see the effects of changing font sizes, etc.2. Double click on the axes and adjust the number format so that it makes sense –often scientific notation with 2 decimal places.3. Double click on the axes and adjust the scales so they are what you would choose rather than what Excel often bizarrely thinks you want.4. When you have a trendline with an equation double click on the equation and set it so that there ARE both automatic borders and background of white.5. Get your trendline to extrapolate along by inserting a row into your data and entering a value in the x-axis column which stretches the line. Note that you should NOT insert anything in the y- axis column.6. Double click on the plot area and set the background to none.7. Remove the legend (almost always!)8. Insert text boxes by clicking on insert/picture/autoshapes at the top of the screen. Drag a box shape and use it to insert your conclusions. If necessary change the font size of the text.9. Use a speech or thought bubble to point towards key features. Click on the text box and drag the yellow spot to move the point of the bubble.10. Format superscripts and subscripts in your axis labels, etc. by selecting the text and clicking on format at the top of the screen.Note: You may import your excel graphs into your MS Word document if you are word processingyour reports using MS Word. The same applies to tables.Physics for engineers PHYS19218Academic year 2008/2009


Safety in the Physics LabGeneral lab practice:Eating and drinking in the lab is not allowed. When you leave the lab, all apparatus must bereturned to its original position and the lab left as it was. Please do not leave litter behind. Allapparatus must be treated as delicate.High voltage:Safety is a priority. No student may open any equipment driven by mains voltage or high voltage.Glass equipment:Such as thermometers, mirrors, lenses, etc. should be handled with extra care as they representfragile items; basic common sense and knowledge are required. In case of breakage please report tolab instructor immediately.Mercury:Mercury is used in thermometers and some pressure experiments; this is a poisonous material thatmust be handled with great caution.Hot plates:Hot plates are used in some experiments. Those get very hot and must not be touched by hand.Avoid letting paper and plastic stationary or bags touch them.Physics for engineers PHYS19219Academic year 2008/2009


Experiment (1)Understanding Motion (1): Position and Time (Motion Sensor)INTRODUCTIONWhen describing the motion of an object, knowing where it is relative to a reference point, howfast and in what direction it is moving, and how it is accelerating (changing its rate of motion) isessential. A sonar ranging device such as the PASCO Motion Sensor uses pulses of ultrasound thatreflect from an object to determine the position of the object. As the object moves, the change in itsposition is measured many times each second. The change in position from moment to moment isexpressed as a velocity (meters per second). The change in velocity from moment to moment isexpressed as acceleration (meters per second per second). The position of an object at a particulartime can be plotted on a graph. You can also graph the velocity and acceleration of the objectversus time. A graph is a mathematical picture of the motion of an object. For this reason, it isimportant to understand how to interpret a graph of position, velocity, or acceleration versus time.In this activity you will plot a graph of position in real-time, that is, as the motion is happening.EQUIPMENT NEEDED1-Motion sensor 2-Base and support RodFor your Safety:Follow all safety instructions.Keep the area clear where you will be walking.

What Do You Think?What is the relationship between the motion of an object – YOU – and a graph of position and timefor the moving object?Physics for engineers PHYS19220Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------For You to Do This activity is easier to do if you have a partner to run the computer while you move.For this activity, you will be the object in motion. Usethe Motion Sensor to measure your position as youmove in a straight line at different speeds. UseDataStudio or ScienceWorkshop to plot your motion on a graph of position and time.The challenge in this activity is to move in such a way that a plot of your motion on the same graphwill ―match‖ the line that is already there.1. Computer setup1.Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn onthe computer.2.Connect the stereo phone plugs of the Motion Sensor to Digital Channels 1 and 2 on theinterface. Connect the yellow plug to Digital Channel 1 and the other plug to Digital Channel2.3.••••Open the file titled as shown: DataStudio --P01 Position and TimeThe DataStudio file has a Workbook display. Read the instructions in the Workbook.The ScienceWorkshop document has a Graph display of Position versus Time.The Graph shows Position and Time values that were entered into the Graph.Data recording is set to stop automatically at 10 seconds. In the DataStudio file there is athree-second ‗countdown‘ before data recording begins.Physics for engineers PHYS19221Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------2. Sensor Calibration and Equipment SetupYou do not need to calibrate the Motion Sensor.1.Mount the Motion Sensoron a support rod so that itis aimed at yourmidsection when you arestanding in front of thesensor. Make sure that youcan move at least 2 metersaway from the MotionSensor.2.Position the computermonitor so you can see thescreen while you moveaway from the MotionSensor.You will be moving backwards for part of this activity. Clear the area behind you for atleast 2 meters (about 6 feet).Physics for engineers PHYS19222Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------3. Data Recording1.2.••Enlarge the Graph display until it fills the monitor screen.Study the plot of Position versus Time in order to determine the following:How close should you be to the Motion Sensor at the beginning?How far away should you move?_______ (m)_______ (m)•3.How long should your motion last?When you are ready, stand in front of the Motion Sensor._______ (s)WARNING: You will be moving backward, so be certain that the area behind you is free of obstacles.4.•When everything is ready, start recording data.In DataStudio, click ‗Start‘. There is a three-second countdown before data recording begins.The ‗cursor‘ on the vertical axis of the Graph will move up and down as you move forwardand backward relative to the sensor. Use the feedback from ‗cursor‘ to find your best startingposition.••In ScienceWorkshop, click ‗REC‘. Data recording will begin almost immediately.The Motion Sensor will make a faint clicking noise.5. Watch the plot of your motion on the Graph and try to move so the plot of your motionmatches the Position versus Time plot already there.If the Motion Sensor is having difficulty picking up the echo, use a notebook as a reflector. Holdthe notebook at the same height as the sensor.6.Repeat the data recording process a second and a third time. Try to improve the matchbetween the plot of your motion and the plot already on the Graph.The Graph can show more than one run of data at the same time.23Academic year 2008/2009Physics for engineers PHYS192

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Analyzing the data1.Determine the slope of the best-fit line for the middle section of your best position versustime plot. You may want to resize the graph to fit the data.•The slope of this part of the position versus time plot is the velocity during the selectedregion of motion.Questions1.In the Graph, what is the slope of the line of best fit for the middle section of your plot?2.What is the description of your motion? (Example: “Constant speed for 2 seconds followedby no motion for 3 seconds, etc.”)What would be the physical meaning of a steeper slope on the graph?What would be different about the motion if the slope were negative?3.4.Physics for engineers PHYS19224Academic year 2008/2009


Understanding Motion (2): Velocity and Time (Motion Sensor)In this second experiment of motion, first and second parts are same as first section but the thirdpart will be:3. Data Recording1.2.Enlarge the Graph until it fills the monitor screen.Study the Velocity versus Time plot in order to determine the following:Which direction (positive or negative) should you go at the beginning?What is the maximum speed (positive or negative) you must achieve?How long should your motion last?______________ (m/s)_______ (s)•3.When you are ready, stand in front of the motion sensor.WARNING: You will be moving backward, so be certain that the area behind you is free of obstacles.4.5.6.When everything is ready, start recording data. Data recording will begin almostimmediately. The motion sensor will make a faint clicking noise.Watch the plot of your motion on the Graph, and try to move so that the plot of your motionmatches the Velocity versus Time plot that is already there.Repeat the data recording process a second and a third time. Try to improve the matchbetween the plot of your motion and the plot that is already on the Graph.The Graph can show more than one run of data at the same time.Physics for engineers PHYS19225Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Analyzing the data1.Determine how well your best plot of velocity versus time matches the velocity versus timeplot that was already on the Graph. You may want to resize the graph to fit the data.•In DataStudio, check the „Match Score‟ calculation in a Digits display.Physics for engineers PHYS19226Academic year 2008/2009


Experiment (2)Free-Fall AccelerationAIM OF THE EXPERIMENTTo determine the free fall acceleration (g) due to the gravity.INTRODUCTIONAn object thrown upward and one thrown downward will both experience the sameacceleration as an object released from rest. Once they are in free-fall, all objects have anacceleration downward, equal to the free-fall acceleration. Since positive Y is upward, theacceleration (g) is negative and given by: (-g).When object dropped, they fall toward the earth with nearly constant acceleration due togravity and it is denoted by the sample: (g).The free-fall acceleration or the acceleration due to gravity (g) is directed downward thecenter of the earth. At the surface of the earth, the value of g is approximately 9.8 m/s² or 980 cm/s²or 32 ft/s².EQUIPMENT NEEDEDTwo photo-light sensors connected to digital timer, holder, small ball, battery or power supply(6 volts).EXPERIMENTAL PROCEDURE1. Connect the circuit shown in fig (1). Take a distance (x) between the two sensors of about80 cm.2. Throw the small ball in a way that will pass the gap between the 2 sensors. When the ballpasses throw the first sensor, its digital timer starts counting the time where the secondsensor stops the timer when the ball passes from it.Physics for engineers PHYS19227Academic year 2008/2009

University of QatarMath & Physics Department----------------------------------------------------------------------------------------------------------------------- 3. Record the time (t) shown to you from the digital timer and record the distance (x) between2 sensors. Repeat step 2 many times at this distance and take the average time.4. Repeat steps 2, 3 for different distances and record your data in a table.5. Plot the relationships between the time (t), along X-axis, and the velocity (x/t), along the Y-axis. Evaluate the slope from this relation.6. From the slope, calculator the free-fall acceleration (g) as following.v = v0 + (1/2) g tWherev: the velocity at time t and v = x/t,v0: the velocity at time t = 0 at can be deducedfrom interception of the line with the Y-axis,g: the free-fall acceleration due to gravityt:time of fall.DistancebetweensensorsX (cm)Timer(1)(2)t(s)(3)Average Timer t (s)Velocity V=x/t (cm/s)Physics for engineers PHYS19228Academic year 2008/2009


BallPowerSupplyDigitalTimerHolderPlasticBasketPhysics for engineers PHYS19229Academic year 2008/2009


Experiment (3)Application of Newton's LawsAIM OF THE EXPERIMENTTo determine the acceleration and the force applied to the cart by hanging mass.Introduction:There's nothing obvious about the relationships governing the motion of objects. In fact, ittook around 4,000 years of civilization and the genius of Isaac Newton to figure out thebasic laws. Fortunately for the rest of us, hindsight is a powerful research tool. In thisexperiment you experimentally determine Newton's second law by examining the motion ofcart under the influence of a constant force. The constant force will be supplied by theweight of a hanging mass that will be used to pull the cart (figure 1.).EQUIPMENT NEEDED:Photogate timer with Accessory Photogate (or two Photogate Timers)PulleyTrack &cartMassesPhysics for engineers PHYS19230Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Procedure:1. Set up the system as shown in the figure 1.2. Determine the total mass of your cart and record it as m.3. Place a mass of approximately 5-25 grams on the weight hanger. Record the totalmass (hanger "5g" plus added mass) as ma.4. Take a distance x between the two sensors of about 50 cm.5. Set you Photogate timer to PULSE mode.6. Choose a starting point xo for the cart, near the end of the track. Mark this pointwith pencil so that can always start the cart from this same point.7. Press the RESET buttons.8. Hold the cart steady at xo, and then release it. Measure and record t, the time it takesthe cart to pass between the Photogates. Repeat this measurement three more timesand record the average of these measurements as t in the table 1.9. Vary the distance x , and repeat step 9. Try at least five different values for x .10. Plot the relationships between the time t, along X-axis, and the velocity x t , alongthe Y-axis.x vo t 1 2at 2

x vo 1 2att11. Determine F, the force ( F ma g 980cm / s 2 ).appliedtothecartbythehangingmass.Table 1.(cm)t1

t2

t3

tavg. (sec)(cm/sec)Physics for engineers PHYS19231Academic year 2008/2009


Experiment (4)Transforming Gravitational Potential Energy to Kinetic EnergyAIM OF THE EXPERIMENTTo determine if energy is conserved, by measuring the gravitational potential energy lost by thefalling mass and the kinetic energy gained by platter and falling mass.INTRODUCTIONIn this activity, a falling object applies a constant net torque to a rotating disk. As the object falls,its gravitational potential energy decreases and its translational kinetic energy increase. At thesame time, the rotational kinetic energy of the disk increases. How does the decrease ingravitational potential energy compare to the increase in translational and rotational kineticenergy?THEORYThe gravitational potential energy of an object depends on its weight and its vertical distance, h,relative to a reference point (usually the Earth‘s surface). The gravitational potential energy is:GPE = mghWhere m is the mass of the object and g is the acceleration due to gravity. The kinetic energy of arotating object depends on its rotational inertia, I, and its angular speed, rotational kineticenergy is:RKE = ½ Іω².As the object falls, it has translational kinetic energy:KE = ½ mv²Where m is the mass of the object, and v is its speed.Physics for engineers PHYS19232Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------NoteFor this activity you need to know the rotational inertia of the disk that is part of the RotationalAccessory.Equipment NeededRotary Motion Sensor (CI-6538)Balance (SE-8723)Base and Support Rod (ME-9355)

Qty Equipment Needed111Mass and Hanger Set (ME-9348)Rotational Accessory (CI-6691)Thread (inc. w/ CI-6691)

Qty111m

COMPUTER SETUP1.Connect the ScienceWorkshop interface to thecomputer, turn on the interface, and turn on thecomputer.2.Connect the Rotary Motion Sensor‘s stereophone plugs into Digital Channels 1 and 2 on theinterface.3.From the sensor list chose "Smart Pulley" :The Data studio file has a Workbook display, a Table display, and a Graph display.Physics for engineers PHYS19233Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------PROCEDURE1.Mount the Rotary Motion Sensor on a support rodso the step pulley is on top. Use the bubble level tolevel the apparatus.Use a piece of thread about 10 cm longer than thedistance from the Super Pulley to the ground. Tie oneend of the thread to the edge of the medium groove onthe step pulley on the Rotary Motion Sensor. Drape thethread over the Super Pulley.Attach the other end of the thread to a mass hanger.Adjust the angle of the Super Pulley so the thread istangent to the step pulley and in the middle of thegroove on the Super Pulley.Remove the thumbscrew from the step pulley on top ofthe Rotary Motion Sensor. Place the disk on the pulleyand attach the disk with the thumbscrew.Measure r, the radius of the smallest spindle. Attach apiece of the thread to the step pulley and wind it up on the smallest of the three spindles.Attach the mass hanger to the thread, high enough on the thread so masses will not hit thefloor at the lowest part of their fall. Add masses to the holder, so the total mass isapproximately 160g. Record the total mass as m in the data table. Measure and record H =(h1 – h2).Select GRAPH DATA from the main menu to move to the graphing program, and the VELOCITY VS TIME for a velocity-time graph.Examining the graph, you should note that there is a point of maximum velocity,corresponding to the point where the gravitational potential energy reached a minimum andthe rotational kinetic energy reach a maximum. Press RETURN, and then choose DISPLAYTABLE OF DATA to see a table of the data. Determine the maximum velocity of the platter,given in m\sec. Record this value as (v max) in the table.Repeat your measurements at least three times, keeping h1 constant. Repeat more times if your data shows any inconsistencies between trials.Repeat steps 6-9, but change the mass to 170, 180, till 200g. Repeat the same steps for different spindles.Calculate (½ І platter ω² max), (mgh), (½ m falling v² max).2.3.4.5.6.7.8.9.10.The angular speed, ω, of the rotating disk is related to the linear speed, v, of the falling object:v where r is the radius of the step pulley on the Rotary Motion Sensor.rPhysics for engineers PHYS19234Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------11. DataRunMass (g)V maxV max

ωmax=v/ r

GPERKEKERKE+KEaverage123Rotational inertia, I, of the disk (9.2 x 10-3 kg m2 )12. Compare GPE and RKE+KE. Is energy conserved?

Questions1.Is the rotational kinetic energy equal to the gravitational potential energy of the fallingobject?2.How does the total kinetic energy compare to the gravitational potential energy of the fallingobject?Physics for engineers PHYS19235Academic year 2008/2009


Experiment (5)Study of Hook’s Law and simple harmonic motionUsing a helical springTHEORYAn elastic material tends to return to its original form or shape after beingstretched. Hence, elasticity implies a restoring force that can give rise tovibrations or oscillations. For many elastic materials, the restoring force is pro-portional to the amount of deformation, if the deformation is not too great.This is best seen for a coil spring. The restoring force F exerted by a stretched (orcompressed) spring is proportional to the stretching (compressing) distance x, orF x. In equation form, we have what is known as Hook’s lawF = - kx(1)Where x is the displacement of one end of the spring from its un-stretched (x = 0)position, k is a positive constant of proportionality, and the minus sign indicatesthat the displacement and force are in opposite directions. The constant k is calledthe spring constant and is a relative indication of the ―stiffness‖ of the spring.When the motion of an object is repeated in regular time intervals or periods, it is called periodicmotion. Examples include the oscillations of a pendulum. This motion is called simple harmonicmotion (SHM) — simple because the restoring force has the simplest form and harmonic becausethe motion can be described by harmonic functions (sines and cosines). A particle or object inmotion under the influence of a linear restoring force such as that described by Hook‘s lawundergoes simple harmonic motion (SHM).This periodic oscillatory motion is one of the common types found in nature. The period ofoscillation of an object in simple harmonic motion is related to the constant of proportionality inHook‘s law.T 2(2)mkIn this experiment, Hook‘s law will be investigated along with the parameters and description ofsimple harmonic motion (i.e using static and dynamic methods).After performing this experiment and analyzing the data, you should be able to:1. Tell how Hook‘s law is represented graphically, and cite an example of an elastic object that does not follow Hook‘s law.2. Explain why simple harmonic motion (SHM) is simple and harmonic.Physics for engineers PHYS19236Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------3. Better understand how the period of a weight oscillating on a spring varies with the weight‘s mass and the spring constant.EQUIPMENT NEEDEDCoil spring,supports,clamps,Slotted weights and weight hanger,Meter stickStop watchEXPERIMENTAL PROCEDURE1/ Spring Elongation1. Hang a coil spring on a support and suspend a weight hanger from it.2. Add an appropriate weight to the weight hanger (e.g., 500-4000 g)3. Record the total suspended weight (m1g) in a Table. [It is convenient to leave g the acceleration due to gravity in symbolic form, that is, if m1 = 500 g or 0.500 kg, then weight = m1g = (0.500 kg) g N.]. Note: Be careful not to confuse the symbol for the acceleration due to gravity, g, and the abbreviation for gram(s), g.4. Fix a meter stick vertically alongside the weight hanger and note the position of the bottom of the weight hanger (or a pointer) on the meter stick.5. Record this in the data table.6. Add appropriate weights to the weight hanger one at a time (e.g., 500 g), and record the total suspended weight and the position of the bottom of the weight hanger on the meterstick after each elongation.7. The weights should be small enough so that seven or eight weights can be added without over- stretching the spring. Note: Choose appropriate mass increments for the spring stiffness.8. Plot the total suspended weight force versus elongation position (F=mg versus x), and draw a straight line that best fits the data points.9. Determine the slope of the line (the spring constant k) and record in the data table.2/ Period of Oscillation1. On the weight hanger suspended from the spring, place a mass just great enough to prevent the spring from oscillating too fast and to prevent the hanger from moving relative to the end of the spring during oscillations when it is pulled down (e.g., 5 to 10cm) and released. Record the total mass in a Table.2. Using a stopwatch, release the spring weight hanger from the initial displacement and determine the time it takes for the mass to make a number (5 to 10) of complete oscillations or cycles. The number of cycles timed will depend on how quickly the system loses energy or is damped.Physics for engineers PHYS19237Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------3. Make an effort to time enough cycles to get a good average period of oscillation. Record the total time and the number of oscillations in the data table.4. Divide the total time by the number of oscillations to determine the average period.5. Repeat procedure 2 for four more mass values, each of which is several times larger than the smallest mass, and record the results in the Data Table.6. The initial displacement may be varied if necessary. (This should have no effect on the period. Why?)7. Plot a graph of the average period squared (T2) versus the mass (m) and draw a straight line that best fits the data points. Determine the slope of the line and compute the spring constant k from Equation 2. Note that k is not simply equal to the slope8. Compare this value of k with that determined from the slope of the spring elongation graph by computing the percent difference.Physics for engineers PHYS19238Academic year 2008/2009


Experiment (6)Work - Kinetic Energy TheoremINTRODUCTIONWe know that energy is found in many different forms, such as chemical, thermal, electrical,solar, mechanical, etc. It is convenient to reduce these to only two forms: the energy of motion (Kinetic energy, KE) and the energy of position (potential energy, PE).Chemical energy is thus dueto the position of molecules in a material, while thermal energy can be thought as dependent uponthe motion of the molecules in that material ( the kinetic energy ). Mechanical energy consists ofboth KE and PE. One of the most basic laws of physics states that energy is conserved in anisolated system. (An isolated system is one in which no work and no heat is added to the system).Within this isolated system, we can certainly have transformations or conversions of energyfrom one form to another, as from potential energy into kinetic energy, or from chemical energyinto thermal energy. But energy does not appear from nowhere, or disappear, so that total energyremains the same.THEORY For an object with mass m that experiences a net force Fnet over a distance d that is parallel tothe net force, the work done is:W Fnet dIf the work changes the object‘s vertical position, the object‘s gravitational potential energychanges. The work done on a rigid body by a net force changes the energy of the body. However,if the work changes only the object‘s speed, the object‘s kinetic energy changes as follows:W KE f KEi 2 mv f 2 mvi1212

where W is the work, vf is the final speed of the object and vi is the initial speed of the object.So, The theorem can be defined as the change in the kinetic energy of a particle during adisplacement is equal to the work done by the resultant force on the particle during thisdisplacement.Physics for engineers PHYS19239Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------In this experiment, we will investigate the conservation of mechanical energy in a systemconsisting of a ruler, a marble and steelier, and book (to give the ruler an incline on a table).EQUIPMENT NEEDEDLong ruler.Marble balls with different sizes and masses.A book or a piece of wood (to give the ruler an incline on a table).Styrofoam cups.EXPERIMENTAL PROCEDURE1- Take the masses for the given marble balls2- Place one of the glass marble on the end of ramp as shown.3- From three different heights or positions, let the ball roll to the bottom on the ruler and thenmeasure its velocity for a fixed distance on the table .(What type of energy does it have??).Determine if the mass of the ball and the height affects the time it takes the ball to get to thebottom.Discuss, what type of energy did the marble possess at the top of the ruler?What type of energy did the marble possess at the half way of the ruler?What type of energy did the marble possess at the bottom?4- Using the Styrofoam cup with the small opening in it, let the marble roll down the ruler from 3different positions and into the cup.5- Measure how far the cup moves on the table.6- Calculate the force applied to the cup..7- Then deduce the coefficient of friction (µ).Physics for engineers PHYS19240Academic year 2008/2009


Experiment (7)Determination of the Acceleration of GravityUsing the Simple PendulumTHEORYA pendulum consists of a "bob" (a mass) attached to a string that isfastened so that the pendulum assembly can swing or oscillate in aplane (Fig. 1). For a simple or ideal pendulum, all the mass isconsidered to be concentrated at a point at the center (of mass) of thebob.Some of the physical properties or parameters of a simple pendulum are(1) the length L of the pendulum, (2) the mass m of the pendulum bob,(3) the angular displacement through which the pendulum swings, and(4) the period T of the pendulum, which is the time it takes for thependulum to swing through one complete oscillation.From physical principles and advanced mathematics, the theoreticalexpression for the period of a simple pendulum oscillating in a plane is

T 2(1.1)Lg

9

1 1 sin 2 64 sin 2 ...422

where g is the acceleration due to gravity and the terms in parenthesesare part of an infinite series. In calculating T for a given angulardistance , the more terms of the series that are evaluated, the greaterthe accuracy of the theoretical result.For small angles (20o), the terms in the series are small compared tounity (i.e., «1), and in this case, to a good approximation,Fig. 1 The simplependulum.

T 2Lg(1.2)(This is called the first-order approximation. If the second term in the series is retained, theapproximation is to second order, and so on.)Notice that even without an approximation (Eq. 1.1), the period is theoretically independent of themass of the pendulum bob. Also, within the limits of the small-angle approximation (Eq. 1.2), theperiod is independent of the displacement angle.Physics for engineers PHYS19241Academic year 2008/2009

University of QatarMath & Physics Department----------------------------------------------------------------------------------------------------------------------- It is sometimes helpful to visualize a physical system as a "black box" with inputs andoutputs. The black box is the relationship connecting the input and output parameters. The termparameter refers to anything in the physical system that can be measured. The input parameters are the physical variables that may control or influence the behavior ofthe output parameters (the physical quantities that are measured and that describe the resultingbehavior of the system). The input parameters are often called independent variables becausethey can (and should) be varied independently of each other. The output parameters, on the otherhand, may be called dependent variables because their values depend on the inputs. In any givensystem, some of the inputs may have little or no effect on the outputs.You may find drawing black box diagrams helpful in understanding the physical systems to beinvestigated in later experiments.EQUIPMENT NEEDEDString, Meterstick, Three or more pendulum bobs of different masses, Laboratory timer orstopwatch, Pendulum clamp (if available), Protractor, graph paperEXPERIMENTAL PROCEDURE1. Set up a simple pendulum arrangement. Make sure that the string is secure and does not slip on the arm.2. Measure and record the pendulum length. The length should be measured to the center of the pendulum bob.3. Determine the pendulum period for the several lengths measured [Rather than timing only one oscillation, time several (e.g., four or five) and determine the average period. Timing is generally more accurate if you start the pendulum oscillating before the timing begins. Also, it is usually best to take the timing reference point as the lowest point of the swing.]4. Experimentally investigate whether the period is independent of the mass of the pendulum bob. Using the three masses provided, determine the periods of a pendulum with each mass as the bob (keeping length L and the small angle of oscillation constant). Record your results in a Table and draw a conclusion from the data.5. Experimentally investigate the relationship between the length and period of a pendulum. Using different lengths, determine the average period of a pendulum of each length (keeping mass and the small angle of oscillation constant). Record the data in a Table.6. Compute the error in the experimental values of the period for each pendulum length and record in a Table. Draw conclusions about the validity or applicability of Eq. 1.2.7. The object of the preceding experimental procedures was to determine the validity or applicability of Eq. 1.2, that is, whether the experimental results agree with the theoretical predictions as required by the scientific method. Once found acceptable, a theoretical expression can then be used to determine experimentally other quantities occurring in the expression. For example,Eq. 1.2 provides a means for experimentally determining g, the acceleration due to gravity, by measuring the pendulum parameters of length and period as was done previously.Physics for engineers PHYS192Academic year 2008/200942

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------8. Squaring both sides of Eq. 1.2, we have

T 2Lg

42

T2 L gThis can be plotted as a straight line with the general form y = mx by letting T2 = y and x = L.The line will have a slope of m.9. Plot T2 versus L from the experimental data, determine the slope of the best straight line that fits the data in the graph, and compute the experimental value of g. Record this in the Laboratory Report and compute the percent error of the result.10. Show the error bars on the graph.Physics for engineers PHYS19243Academic year 2008/2009


Experiment (8)Determination of the Coefficient of Viscosity of engine oil byStokes methodTHEORYViscosity is that property of a fluid that indicates its internal friction. The more viscous a fluid, thegreater the force required to cause one layer of fluid to slide past another. Viscosity is whatprevents objects from moving freely through a fluid or a fluid from flowing freely in a pipe. Theviscosity of gases is less than that of liquids, and the viscosity of water and light oils is less thanthat of molasses and heavy oils. Your experience with liquids such as motor oils and syrups, tellsyou that viscosity increases with decreasing temperature. Thus, it is hard to restart a car engine insubzero weather when the oil is thick and flows slowly, but it is easy to start the same car on a hotsummer day when the oil is warm and flows readily.An object moving through a fluid experiences a resistive force, or drag, that is proportional to theviscosity of the fluid. If the object is moving slowly enough, the drag force is proportional to itsspeed v. If the object is a sphere of radius r, the force is

F 6vo rwhere is the coefficient of viscosity.Vo is the terminal velocity of fall of a spherical particle in a viscousmediumr is the radius of the particle This equation is known as Stokes' law, after Sir George Stokes(1819-1903), who first conceived it in 1845. Stokes' law can be usedto relate the speed of a sphere falling in a liquid to the viscosity ofthat liquid.Consider a solid sphere of radius r dropped into the top of a columnof liquid (see figure). At the top of the column, the sphereaccelerates downward under the influence of gravity. However thereare two additional forces, both acting upward: the constant buoyantforce and a speed dependant retarding force given by stokes‘ law.When the sum of the upward forces is equal to the gravitationalforce, the sphere travels with a constant speed vt, called the terminalvelocity.To determine this speed, we write the equation for the equilibrium of forces:Physics for engineers PHYS19244Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Fgrav = Fbouyant + Fdrag

The gravitational force: 4Fgrav r 3 s g 3The buoyant force is equal to the weight of the displaced liquid, which has a densityL : 4Fbuoyant r 3 L g 3Hence:4 34 r s g r 3 L g 6rvt334 3r g s L 6rvt3vt EQUIPMENT NEEDED1m long glass tube of about 3cm diameter closed at the bottom and open at the top filled withvehicle engine oil.MicrometerMeter stickThermometerBall bearings of various diametersMagnetStop watchColoured sticky tape2 s L g 2 r 9(1)Physics for engineers PHYS19245Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------EXPERIMENTAL PROCEDURE1. Using the sticky tape mark two points A an B on the glass tube. Mark A towards the top of thetube should be sufficiently well down the tube to ensure that the sphere acquires its terminalvelocity before passing A.2. Take the times of descent between marks A and B of several spheres of the same diameter andcalculate their average velocity.3. Use the micrometer to determine the diameter of the ball bearings.4. Repeat the experiment for balls of different diameters.5. Plot a graph o the squared radius as a function of terminal velocity.6. Use equation (1) to determine the viscosity of the oil.Physics for engineers PHYS19246Academic year 2008/2009


Experiment (9)Determination of the speed of Sound in AirUsing a resonance tubeTHEORYSound WavesWhen the diaphragm of a speaker vibrates, a sound wave is produced that propagates throughthe air. The sound wave consists of small motions of the air molecules toward and away from thespeaker. If you were able to look at a small volume of air near the speaker, you would find that thevolume of air does not move far, but rather it vibrates toward and away from the speaker at thefrequency of the speaker vibrations.This motion is very much analogous to waves propagating on a string. An important differenceis that, if you watch a small portion of the string, its vibration motion is transverse to the directionof propagation of the wave on the string. The motion of a small volume of air in a sound wave isparallel to the direction of propagation of the wave. Because of this, the sound wave is called alongitudinal wave.Another way of conceptualizing a sound wave is as a series of compressions and rarefactions.When the diaphragm of a speaker moves outward, the air near the diaphragm is compressed,creating a small volume of relatively high air pressure, a compression. This small high pressurevolume of air compresses the air adjacent to it, which in turn compresses the air adjacent to it, sothe high pressure propagates away from the speaker. When the diaphragm of the speaker movesinward, a low pressure volume of air, a rarefaction, is created near the diaphragm. This rarefactionalso propagates away from the speaker.In general, a sound wave propagates out in all directions from the source of the wave.However, the study of sound waves can be simplified by restricting the motion of propagation toone dimension, as is done with the Resonance Tube.Physics for engineers PHYS19247Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Standing Waves in a TubeStanding waves are created in a vibrating string when a wave is reflected from an end of thestring so that the returning wave interferes with the original wave. Standing waves also occur whena sound wave is reflected from the end of a tube.A standing wave on a string has nodes—points where the string does not move—andantinodes—points where the string vibrates up and down with a maximum amplitude.Analogously, a standing sound wave has displacement nodes—points where the air does notvibrate—and displacement antinodes—points where the amplitude of the air vibration is amaximum.Pressure nodes and antinodes also exist within the waveform. In fact, pressure nodes occur atdisplacement antinodes and pressure antinodes occur at displacement nodes. This can beunderstood by thinking of a pressure antinodes as being located between two displacementantinodes that vibrate 180° out of phase with each other. When the air of the two displacementantinodes are moving toward each other, the pressure of the pressure antinode is a maximum.When they are moving apart, the pressure goes to a minimum.Reflection of the sound wave occurs at both open and closed tube ends. If the end of the tube isclosed, the air has nowhere to go, so a displacement node (a pressure antinode) must exist at aclosed end. If the end of the tube is open, the pressure stays very nearly at room pressure, so apressure node (a displacement antinode) exists at an open end of the tube.ResonanceAs described above, a standing wave occurs when a wave is reflected from the end of the tubeand the return wave interferes with the original wave. However, the sound wave will actually bereflected many times back and forth between the ends of the tube, and all these multiple reflectionswill interfere together.In general, the multiply reflected waves will not all be in phase, and the amplitude of the wavepattern will be small. However, at certain frequencies of oscillation, all the reflected waves are inphase, resulting in a very high amplitude standing wave. These frequencies are called resonantfrequencies.Physics for engineers PHYS19248Academic year 2008/2009

University of QatarMath & Physics Department----------------------------------------------------------------------------------------------------------------------- In Experiment 1, the relationship between the length of the tube and the frequencies at whichresonance occurs is investigated. It is shown that the conditions for resonance are more easilyunderstood in terms of the wavelength of the wave pattern, rather than in terms of the frequency.The resonance states also depend on whether the ends of the tube are open or closed.For an open tube (a tube open at both ends), resonance occurs when the wavelength of the wave(l) satisfies the condition:L = nl/2, n = 1, 2, 3, 4…where L = tube length.These wavelengths allow a standing wave pattern such that a pressure node (displacementantinode) of the wave pattern exists naturally at each end of the tube.Another way to characterize the resonance states is to say that an integral number of halfwavelengths fits between the ends of the tube.For a closed tube (by convention, a closed tube is open at one end and closed at the other),resonance occurs when the wavelength of the wave (l) satisfies the condition:L = nl/4, n = 1, 3, 5, 7, 9…These wavelengths allow a standing wave pattern such that a pressure node (displacementantinode) occurs naturally at the open end of the tube and a pressure antinode (displacement node)occurs naturally at the closed end of the tube. As for the open tube, each successive value of ndescribes a state in which one more half wavelength fits between the ends of the tube.NOTE: The first four resonance states for openand closed tubes are diagramed below. The firstresonance state (n = 1) is called the fundamental.Successive resonance states are called overtones. Therepresentation in each case is relative displacement.Physics for engineers PHYS19249Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------The formulas and diagrams shown above for resonance in a tube are only approximate, mainlybecause the behavior of the waves at the ends of the tube (especially at an open end) dependspartially on factors such as the diameter of the tube and the frequency of the waves. The ends ofthe tubes are not exact nodes and antinodes.It can be a useful experiment to investigate the wave behavior at the ends of the tube using themicrophone. The following empirical formulas give a somewhat more accurate descriptionof the resonance requirements for standing waves in a tube.For an open tube:L + 0.8d = nl/2, n = 1, 2, 3, 4,….where L is the length of the tube and d is the diameter.Physics for engineers PHYS19250Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------For a closed tube:L + 0.4d = nl/4, n = 1, 3, 5, 7, 9,….where L is the length of the tube and d is the diameter.NOTE: When using the microphone to investigate thewaveform within the tube, be aware that the microphoneis a pressure transducer. A maximum signal, therefore,indicates a pressure antinode (a displacement node) and aminimum signal indicates a pressure node(displacement antinode).EQUIPMENT NEEDED1- PASCO Resonance Tube2- Function Generator3- Frequency Counter (if your function generator does not accurately indicate frequency)4- Oscilloscope (recommended, but not necessary)IntroductionFor any given tube length, there are a variety of resonant frequencies—frequencies at whichstanding waves will be formed in the tube. Likewise, for a given frequency, there are avariety of tube lengths at which a standing wave will be formed. In this experiment you willexamine the series of tube lengths which will resonate with a set frequency.Procedure1. Set up the Resonance Tube, oscilloscope, and function generator as shown in Figure 3.1.Move the piston to a position very near the end of the tube. Set the signal generator toapproximately 800 Hz and turn the amplitude up until the speaker is clearly heard. Recordthis frequency. If you use the oscilloscope, trigger on the speaker output.Physics for engineers PHYS19251Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------2. Slowly push the piston further into the tube, until you hear the sound from the speakerbeing amplified by the tube, indicating that you have produced a standing wave in the tube.Adjust the piston position carefully until you find the point which produces the loudestsound as well as the largest signal on the oscilloscope screen. Record this position.3. Now continue moving the piston into the tube until you reach a new position where astanding wave is produced. Record this new position. Continue moving the piston until youhave found all of the piston positions along the tube which produce standing waves.4.SPEAKER INPUT.1 W MAX

Repeat the procedures above for as many different frequencies as your instructor directs.WARNING: You can damage the speaker by overdriving it. The sound from the speakershould be clearly audible, but not loud. Note also that many signal generators becomemore efficient and thus produce a larger output as the frequency increases, so if youincrease the frequency, you may need to reduce the amplitude.Physics for engineers PHYS19252Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------AnalysisUse the data that you have recorded to sketch the wave activity along the length of your tubewith the piston in the position furthest from the speaker. How do the successive piston positionsthat produced a standing wave relate to this sketch? Is the apparent spacings of nodes andantinodes consistent with the wavelength of your sound waves as calculated from V/,=where V = speed of sound?Table 3.1 Closed Tube ResonancesFrequency:…………….nL (m)Frequency:…………….nL (m)Physics for engineers PHYS19253Academic year 2008/2009


Experiment (10)Determination of the Mechanical Equivalent of HeatTHEORYThe Joule and calorie are both units of energy. However they are defined such a way that therelation between them can be established only experimentally. The simplest method to find thisrelation is to analyze energy which is delivered by an electric current to a resistor (this energy iscalled a Joule's heat) from electric and thermodynamic points of view.Energy E which is delivered by the source of current to the resistor R in a short time t is equal toE = V I t = I2 R t = V2 t/R(1)where V and I are the voltage and current on this resistor.If we deal with DC voltage, and consequently a constant current, then the energy E which isdelivered in an arbitrary time t is given by (1).In our experiment the energy which is delivered from the source of current to the resistor heats thewater and internal cup of calorimeter rising their temperature. Therefore the amount of heat Qwhich is delivered to the system can be expressed as followsQ = cw mw (Tf - Ti) + cc mc (Tf - Ti)(2)where cw, cc, mw, mc are specific heats andmasses of water and calorimeterrespectively. Ti and Tf are initial and final(after the time t) temperatures of thesystem.Of course E and Q represent the sameenergy expressed in joules of work andcalories of heat. THEREFORE THERATIO E/Q TELLS US HOW MANYCALORIES ARE EQUIVALENT TO 1JOULE. This is known as the mechanicalequivalent of heat.Physics for engineers PHYS19254Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------EQUIPMENT NEEDEDCalorimeter with heater,two digital multimeters,stop watch,thermometer,connecting wires,voltage supply 25 V DC,EXPERIMENTAL PROCEDURE1. WITHOUT PLUGGING THE VOLTAGE SUPPLYIN AND SWITCHING IT ON arrange the circuitshown in Fig. 1. Use the top bench multimeter as theammeter with the range up to 10 A. Set the rheostat toabout 15 V.AskTHEINSTRUCTORTOCHECKTHISARRANGEMENT.Physics for engineers PHYS19255Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------2. Prepare 190 - 200 g of water with temperature Ti in a cup.3. Weigh the cup with water, put it into the calorimeter, and insert the heater and thermometer.4. Switch the voltage supply on DC current and at the same time start the stop watch.5. With the help of the rheostat slider (or potentiometer) set up the current as close to 1A.6. Stir the water frequently to make sure its temperature is homogenous.7. Read the voltage on the voltmeter.8. Determine the time required for the temperature to raise 5ºC from the initial temperature.9. Use equations 1, and 2 to calculate the mechanical equivalent of heat.Physics for engineers PHYS19256Academic year 2008/2009


Experiment (11)Static EquilibriumINTRODUCTIONStatic equilibrium refers to objects that are not moving. If an object is in static equilibrium, thereare two very specific things the object is not doing that are important to understand. It is neithertranslating nor is it rotating. The first condition, no translation, requires that the net force (meaningthe sum of all forces) acting on the object must be zero. The second condition, no rotation, requiresthat the net torque or moment also be zero:ΣF=0AndΣτ=0WHAT IS TORQUETorque is a measure of how much a force acting on an object causes that object to rotate. Theobject rotates about an axis, which we will call the pivot point, and will label "O".We will call the force "F". The distance from the pivot point to the point where the force acts iscalled the moment arm, and is denoted by "r". Note that this distance, "r", is also a vector, and pointsfrom the axis of rotation to the point where the force acts. (Fig.1).Physics for engineers PHYS19257Academic year 2008/2009

University of QatarMath & Physics Department -----------------------------------------------------------------------------------------------------------------------Torque id defined asτ = " Lever Arm" times the " Force"τ=rxF= (Component of the Force perpendicular to Lever Arm) x ( Lever Arm- the distance between thepivotal axis and the point where the force is applied) = Fp ι-The more exact definition is that the torque is that the torque is the cross product ofthe lever arm with applied force (see appendix).-The torque's direction is perpendicular to both the direction of the lever arm and thedirection of the force. The direction can be found using the right hand rule (seeappendix).Imagine pushing a door to open it. The force of your push (F) causes the door to rotate about itshinges (the pivot point, O). How hard you need to push depends on the distance you are form thehinges (r) ( and several other thing, but let's ignore them now). The closer you are to the hinges (i.e the smaller r is), the harder it is to push. This is what happens when you try to push open a dooron the wrong side. The torque you created you created on the door is smaller than it would havebeen had you pushed the correct side ( away from its hinges).* Note that the force applied, F, and the moment arm, r, are independent of the object.Furthermore, a force applied at the pivot point will cause no torque since the moment arm wouldbe zero (r=0) ( Fig. 2).FFFFFig. 2Physics for engineers PHYS19258Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Let the force acting on an object be broken up into its tangential ( F tan) and radial ( F rad)components ( Fig. 3). ( Note that the tangential component is perpendicular to the moment arm,while the radial component is parallel to the moment arm). The radial component of the force hasno contribution to the torque because it passes through the pivot. So, it is only the tangentialcomponent of the force which affects torque ( since it is perpendicular to the line between the pointof action of the force and the pivot point).

rF tanF radPivot Point

FFig. 3 Tangential and radial components of force FA given force F will produce the same torque on a system if it is applied anywhere along a straightline. Here the perpendicular distance lp between the line of action of the force and the center ofrotation will be the same (Fig.4).

τ = (Force) x (Lever Arm) x sin (angle between the two) = F l sin (θ)Physics for engineers PHYS19259Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Fp=F sin ( θ)FFpAxis of rotationlplFrLp = l sin (θ) Fig. 4Note that Forces that lie along the same line have the same perpendicular lever arm lp(Fig. 5).FFFFlpFig. 5There may be more than one force acting on an object, and each of these forces may act ondifferent point on the object. Then, each force will cause a torque. The net torque is the sum ofthe individual torques.Physics for engineers PHYS19260Academic year 2008/2009

University of QatarMath & Physics Department----------------------------------------------------------------------------------------------------------------------- Rotational Equilibrium is analogous to translational equilibrium, where the sum of the forces isequal to zero. In rotational equilibrium, the sum of the torques is equal to zero. In otherwords, there is no net torque on the object.

Στ=0 Note that the SI unit of torque is a Newton-meter, which is also a way of expressing a Joule(the unit for energy). However, torque is not energy. So to avoid confusion, we will use the unitsN.m, and not J. The distinction arises because energy is a scalar quantity, whereas torque is avector.Our experiment consists of one ruler of length L which can rotate around one axe from one endand fixed to a thread at the other end. One holder of mass can move along the ruler and its distance to the pivot point O is named x.The force of the thread is called T and the angle between the direction of force and the direction ofthe ruler is θ.

L0

θTxWAt static equilibrium, Σ τ = 0 SoThen- Mg x + T L sin θ = 0T L sin θ = Mg xMg x_______L sin θAt lastT=Physics for engineers PHYS19261Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Apparatus:- Stand- Ruler- Thread- Holder of mass and masses- Motion sensor- ComputerExperimental Procedure1. Set the experiment as given by the instructor.2. Fix the mass (m) so that the total mass M = m + mh where mh is the mass of the holder.3. Vary the position (x) of the holder and take the tension (T) of the thread for each position using the motion sensor.4. Plot the relation between T as y-axis and x as x-axis.5. Calculate the slope of your graph and determine the angle (θ) between the thread and the ruler.6. Calculate the percentage of error.AppendixVector (or Cross) Product : À x BThe magnitude of the cross product is equal to the area of a parallelogram formed using the vectorsas the sides of parallelogram.AÀθArea=A B sin θBBThe direction of the cross product is perpendicular to the plane formed by the two vectors andfollows the right hand rule.Physics for engineers PHYS19262Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------ÀxBAArea= |AxB|BRight hand ruleUsing the right hand rule, we can find the direction of the torque vector. If we out our fingers in thedirection of r, and curl them to the direction of F, then the thumb points in the direction of thetorque vector (Fig.3)The torque‘s direction is perpendicular to both directions (of the lever and the force).Right Hand RulePhysics for engineers PHYS19263Academic year 2008/2009


Experiment (12)Determination of Specific Heat Capacity of a solidINTRODUCTIONThe specific heat capacity of a solid or liquid is defined as, the heat required to raise a unit mass ofsubstance by one degree of temperature. The relationship between heat and temperature change isusually expressed in the form shown by the following equation:

Q mcTWhere,ΔQ= Heat supplied to substance,m= Mass of the substance,c= Specific heat capacity,ΔT= Temperature rise.The relationship does not apply if a phase changeis encountered, because the heat added orremoved during a phase change does not changethe temperature.Calorimeters are designed to be well-insulated, sono heat is gained from or lost to the surroundings. If no heating element is used to introduce heat inthe system, the total heat transferred (Q) for the entire calorimeter system must equal zero. Thetotal heat can be split into heats for each component in the system.THEORYImagine an experiment in which hot balls are dropped into a calorimeter containing water at roomtemperature. The balls will lose heat, which will be absorbed by the calorimeter and water.Because no heat enters or leaves the system from the calorimeter, the heat balance for thisexperiment isQballs Qcalorimeter Qwater

The basic strategy in calorimeter is to use a temperature change and a heat capacity to determine aheat. In this experiment, all substances have the same final temperature (Tf), but not all substanceshave the same initial temperature. The balls are initially at temperature Tballs while the calorimeterand water are initially at temperature Ti.Physics for engineers PHYS19264Academic year 2008/2009

University of QatarMath & Physics Department-----------------------------------------------------------------------------------------------------------------------Qballs mballs Cmetal (T f Tballs )Qcalorimeter mcalorimeter CCu (T f Ti )Qwater mwater Cwater (T f Ti )The heat capacity of the calorimeter must be known. The specific heat capacity of water is alsoknown (4.184 J oC-1), and the temperatures Tballs, Ti, and Tf can be measured experimentally. Themasses of the balls and water (mballs and mwater) can also be measured experimentally. The onlyunknown property in the above equations is the specific heat capacity of the metal balls.Cmetal (mwater Cwater mcalorimeter CCu )(T f Ti )mballs (T f Tballs )(1)EQUIPMENT NEEDEDHotplateBoilerBalanceSmall metal ballsCalorimeterWater or OilThermometersBalanceEXPERIMENTAL PROCEDURE1.2.3.4.5.6.7. Using the boiler, heat the balls up to water boiling point (100ºC). Determine the values for the masses of the calorimeter mcalorimeter and water mwater. Determine the initial temperature of the calorimeter and water Ti. Determine the initial temperature of the balls Tballs. Drop the balls into the water inside the calorimeter. Stir to obtain equilibrium then measure the final temperature of the system Tf. Perform the calculations necessary to determine the specific heat capacity of the balls material Cmetal according to equation (1).8. You may repeat the experiment several times using different metal balls and various liquids to find the specific heat capacity of the material they are made of.Physics for engineers PHYS19265Academic year 2008/2009


References1- Introductory Physics Laboratory Manual, Physics for Engineering students1052192, Spring 2005, Dr.Ilham AL-Qaradawi.2- Instruction Manual and Experiment Guide for the PASCO scientific, 1999 &1988.3- ―PHYSICS: For Scientists and Engineering, with Modern Physics by Serway.4- http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Work/WorkEngergyTheorem.html.5- Static equilibrium by Dr. Shokry Al-Ameen.Physics for engineers PHYS19266Academic year 2008/2009

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