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DAS 12703 – LABORATORY MANUAL

TABLE OF CONTENT

Contents i

Introduction ii

Laboratory Safety ii

Laboratory Rules and Regulations iv

Laboratory Report and Assessment v

Experiment 1 : Oxidation Reaction of Potassium Permanganate 6

Experiment 2 : Measurement of Reaction Rate 9

Experiment 3 : Electrochemistry – Voltaic Cell 13

Experiment 4 : Projectile Motion I 17

Experiment 5 : Centripetal Force 22

Experiment 6 : Simple Harmonic Motion 28

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INTRODUCTIONThe Technical Science laboratory work is related to topics discussed in the DAS 12703 Technical Science II Diploma subject. It consists of seven topics, designed to enhance students understanding of the subject. Each student is given a manual at the beginning of the semester. Students are required to read and make a summary of the work prior to each laboratory session. Each session will lasts for three hours. Students are required to write a short report in the laboratory sheet provided. The report must be handed to their respective instructors at the end of each session.

A Head of laboratory is responsible for the management of activities in the laboratory. The head is supported by senior laboratory assistant and laboratory assistants for the daily operation. Academic staffs’ role is as instructor for the laboratory sessions and for assessing the students’ laboratory reports. For safety reasons, students are required to follow strictly the laboratory rules and regulations.

Laboratory Safety

1. Students must dress appropriately to the laboratory. Bare feet, sandals, or other opentoed shoes are not permitted in the laboratory. Long hair should be tied back and headscarves should be tucked under your lab coat. Playing of radios, tapes, CDs is not permitted. This includes small portable devices used with earphones or headsets. Lab coats are required to be worn. Failure to observe these requirements will result in your removal from the laboratory.

2. Know the location and operation of the emergency eye washes and fire extinguishers in the laboratory. In the case of spill onto a person or clothing, the immediate action should be to flush with lots of water. Use the safety showers and/or eye washes in case of emergency. The fire extinguishers should only be used for real emergencies since the chemicals might cause considerable damage. Report accidents to your instructor or laboratory assistant immediately.

3. Become familiar with all of the exits from the laboratory. A repeating siren is the building evacuation signal. If this alarm goes off while you are in the lab, turn off any open flames, grab your valuables, and leave the building as quickly as possible.

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4. Never attempt any unauthorized or unassigned experiments. Follow the experimental procedures explicitly; identify all reagents before you use them. There are potentially hazardous combinations of chemicals present in the laboratory.

5. Never return unused reagents to their storage container. If you take more than you need, dispose of the excess in the appropriate manner. Use the reagents sparingly as they are expensive and timeconsuming to prepare. When taking the reagents, transfer the amount you need to a clean beaker or other suitable container. Never insert a pipette or any other object into a liquid reagent container.

6. Clean up spills immediately. The next person to come along has no way of knowing if the clear liquid or white powder on the lab bench is innocuous or hazardous.

7. Do not pick up hot objects. Ensure that your apparatus is cool before picking it up.

8. Do not point the open end of a test tube or other vessel containing a reaction mixture toward yourself or anyone else. If the procedure calls for you to observe the odor of the contents of a vessel, hold it upright in front of you, gently fan some of the vapors toward your nose and sniff cautiously. Most chemical vapors are at least irritating, and many are quite toxic. Please do not taste any chemicals.

9. Do not eat and drink in the laboratory. Eating and drinking is strictly prohibited.

10. Keep your backpacks and other nonessential materials away from the area where people are working. Lockers are available at the back of the laboratory.

11. Wash hands frequently when working in the lab, and always wash thoroughly before leaving. Please bring along a good morning towel for every lab session.

12. Use the fume cupboard for evaporation of anything other than water. The vapors from the procedure of the experiments could combine to create a hazard.

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13. Do not leave a Bunsen burner or other heated apparatus unattended. The person working next to you may not know what is involved with your setup and may be working with a flammable material. Turn off open flames if you must leave your area.

14. If in doubt, please ask your instructors or laboratory assistant.

Laboratory Rules and Regulations

1. Due dates of the Lab Reports. The lab reports are due the same day of the lab session. All work done during the lab session and data manipulation must be reported in the lab sheet provided. You are given approximately one and a half hours to carry out the experiment and another one and a half hours to write the report. All reports must be submitted to your instructors at the end of each lab session. Failure to do so will result in zero marks.

2. Punctuality. Be punctual for the lab sessions. If you are late without any valid reasons, you will not be allowed to do the experiment and will be given zero marks.

3. Inability to Attend a Lab session. Only a verifiable illness (with medical certificate from the Students Health Centre), official involvement in student activities or prior permission of the instructor count as excused absences. In an event that you are not able to attend the lab session, inform your instructor or lab assistant in advance (at least 3 days before the lab). You should produce a letter of exemption. If you are ill or in case of an emergency and not able to attend the lab, please call the lab (07 – 4537096 / 7097) to inform your instructor or lab assistant. Unexcused or failure to attend lab session will receive a grade of zero.

4. Lab Partners. For those experiments where students are to work in pairs or in groups, lab partners will be assigned randomly as announced by the instructor at the beginning of the semester. You may not exchange lab partners. The lab partners must be present for the entire experiment.

5. Plagiarism. All lab reports are to be your own. Lab partners are to independently produce their lab reports. In the event of copying, all students involved will receive a grade of zero; therefore do not give a copy of your lab report to another student.

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6. MakeUp Labs. There will be no makeup labs. However, makeup labs will be arranged for those with valid reasons (mentioned in (3) above).

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LABORATORY REPORT AND ASSESSMENT

The Laboratory Report is the means whereby you convince the instructor that you conducted the experiment thoughtfully and learned something in the process. Below are the elements that will be assessed in your laboratory report:

1. Data: Observations and data must be recorded in the lab sheet provided. Whenever possible, data for an experiment should be presented in an organized table. All observations and data should be recorded in the lab manual while the work is in progress. The quality of the experimental data is taken into account in giving the grades for your laboratory report. Your data and observation must be verified by your instructor.

2. Calculations: All calculations from your data used to obtain your results must be shown in your lab sheet. These should be presented in a readable manner. Good data manipulation, correct calculations, good graph (where appropriate), use of proper units and tidiness will result in a better grade for your laboratory report.

3. Results: Results from the experiments that had been done must be clearly indicated. Use a table if appropriate.

4. Answers to Questions: Be sure to show the method of calculation, if applicable.

5. Marks allocations:

Your laboratory report will be due on the same day of the laboratory session.

Your lab reports contribute 20% of your coursework marks.

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(a) 6 laboratory report 100%


EXPERIMENT 1

OXIDATION REACTION OF POTASSIUM PERMANGANATE

OBJECTIVE1. To prepare a solution of iron (II) ammonium sulphate from

its salts.2. To prepare a solution of KMnO4 by dilution method3. To carry out titration of KMnO4 and iron (II) ammonium sulphate in acidic

medium. 4. To determine the stoichiometry of the reaction.

INTRODUCTIONOxidation is a process of removing electrons from a substance. Reduction on the other hand is a process of adding electrons to a substance. When reduction occurs, there must also be an oxidation and vice versa. This process is known as the reductionoxidation reaction (or redox reaction). In a redox reaction, there will be an oxidizing and reducing agent. The oxidizing agent is the substance that causes an oxidation by accepting one or more electrons from a substrate and it will be reduced in the reaction. The reducing agent on the other hand is the substance that cause reduction by donating one or more electrons to a substrate and therefore it will be oxidized in the reaction.

For example :Fe(s) + Cu2+

(aq) Fe2+ (aq) + Cu(s)

From the above reaction, Fe donates two electrons to Cu2+ to form Cu, while Fe lost two electrons and therefore it is oxidized. On the other hand, Cu2+ gained two electrons from Fe and therefore it is being reduced. The substance, which is oxidized, is the reducing agent whereas the substance, which is reduced, is the oxidizing agent.

An aqueous solution of potassium permanganate, (KMnO4) consists of MnO4 anion is a

strong oxidizing agent. This substance is a strong oxidizing agent because elements become more electronegative as the oxidation states of their atoms increase. The oxidizing reaction of KMnO4 may take place in an acidic, neutral or basic medium. In an acidic medium, the permanganate ion (oxidation number of Mn = +7) is reduced to Mn2+

ion (oxidation number +2). In a basic or neutral medium, a brown precipitate of MnO2 is formed (oxidation number of Mn = +4).

One of the uses of redox reaction is in chemical analysis. For example, if the stoichiometry of a redox reaction is known, then the concentration of the other substance

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can be determined. In this experiment, potassium permanganate is titrated into iron (II) solution in a conical flask.

aMnO4(aq) + bFe2+(aq) + cH+(aq) → aMn2+(aq) + bFe3+(aq) + dH2O(ℓ)

Before the endpoint, formation of Mn2+, which is colourless, causes the purple coloration of permanganate to disappear. Initially, the rate of reaction is slow (as shown by the slow disappearance of the purple coloration) but later increases due to the presence of Mn2+ ions, which act as a catalyst. When all of the Fe2+ ions are oxidized to Fe3+ ions, addition of one drop of permanganate will turn the colour of solution to light purple. At the endpoint, a permanent purple coloration forms.

Coefficient b is determined from the following equation

bVM

aVM bbaa =

Va = average volume of permanganate solution

Vb = volume of Fe(II) solution

Ma = molarity of permanganate solution

Mb = molarity of Fe(II) solution.

a = stoichiometric coefficient of permanganate

b = stoichiometric coefficient of Fe (II)

The value of b is determined based on the assumption that a = 1.

APPARATUS

1. Beaker, 50 mL 2. Beaker, 100 Ml3. Beaker, 250 mL 4. Amber burette with retort stand, 50 mL 5. Measuring cylinder, 25/50 mL 6. Filter funnel

7. Beaker, 50 mL 8. Beaker, 100 Ml9. Beaker, 250 mL 10. Amber burette with retort stand, 50 mL 11. Measuring cylinder, 25/50 mL 12. Filter funnel

CHEMICALS1. Potassium permanganate solution, KMnO4 solution, 0.05 M

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2. Iron (II) ammonium sulphate salts, FeSO4(NH4)2SO4.6H2O

3. Sulphuric acid, H2SO4 , 1 M

PROCEDURE1. Pipette 20 mL 0.05 M KMnO4 solution into a 100 mL volumetric flask.

Add distilled water to the graduation mark.

Place the stopper and mix thoroughly.

2. Carefully transfer the diluted KMnO4 solution (from 1) to an amber burette using a filter funnel.

Record the initial burette reading.

3. Place a dry 100 mL beaker on the electronic balance.

Press “Tare”.

Ensure that the display on the electronic balance is 0.000.

4. Weigh accurately 1.40 – 1.60 g iron(II) ammonium sulphate, FeSO4(NH4)2SO4.6H2O in a dry beaker.

Dissolve the salts in approximately 30 mL of distilled water.

5. Using a glass rod and filter funnel, transfer the solution quantitatively to a 100 mL volumetric flask.

Rinse the glass rod and filter funnel with distilled water and add the rinsing to the volumetric flask.

Finally, add distilled water to the graduation mark. Place the stopper and mix thoroughly.

6. Pipette 20 mL iron(II) ammonium sulphate solution that you have just prepared in step 5 into a 250 mL conical flask.

Add 20 mL of 1 M H2SO4 using a measuring cylinder into the conical flask (make sure that the solution is clear).

7. Titrate the iron solution with the diluted KMnO4 solution (from steps 1 & 2) and shake the flask homogenously.

Stop addition of KMnO4 when there is a permanent colour change from colourless to pale purple.

Record the final burette reading.

8. Repeat steps 6 and 7 twice.

Reminder:

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1. Wash pipette and burette with water and rinse with distilled water before use.2. Formation of brown precipitate during titration indicates that you did not add in

the acid or the amount of acid added is not enough.

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EXPERIMENT 2

MEASUREMENT OF REACTION RATE

OBJECTIVE1. To study the effect of concentration, temperature and catalyst on the rate of reaction

between persulphate, S2O82– and iodide, I− ions.

2. To plot graphs of temperature and percent concentration of reactant B versus time.

INTRODUCTIONChemical kinetics is the area of chemistry concerned with the speed or rates at which a chemical reaction occurs. The progress of a reaction can be determined by monitoring either a decrease in concentration of the reactant or the increase in concentration of products. The rate of reaction is defined as the changes in the concentration of a reactant or a product (M) with time.

For a reaction represented by a general equation :

A + B C Reactants Product

This equation tells us that during the course of a reaction, reactants are consumed while products are formed. The rate expression for the reaction is given by the equation

[ ] [ ] [ ]

A B Ct t t

= = −∆ ∆ ∆= − = +∆ ∆ ∆

concentration changeRate

time change

Where ∆[A] and ∆[B] are the changes in concentration (molarity) over a period of time ∆t.

A chemical reaction is either homogeneous or heterogeneous. In a homogeneous reaction, the reactants and products are in the same phase, whereas in a heterogeneous reaction they are in different phases for example gas and solid.

Several factors can affect the rate of a reaction such as types of reaction, type and structure of reactants, concentration of reactants, temperature and the presence of catalyst. Because the concentration of A decreases during the time interval, ∆[A] is a negative value. The rate of reaction is a positive value, thus a minus sign is required in the rate expression to make the rate negative. On the other hand, the rate of product formation does not require a minus sign because

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∆[B] is a positive value (the concentration of B increases with time). These rates are average rates because they are averaged over a certain time period, ∆t.

Effect of temperature, concentration and catalysts on reaction rates

Reactions usually require collisions between reactant molecules or atoms. The formation of bonds requires atoms to come close to one another. New bonds can form only if the atoms are close enough together to share electrons. Some collisions are not successful. These are called ineffective collisions. The particles simply hit and then rebound. Collisions that lead to products are called effective collisions. An effective collision must happen with a great enough speed, energy and force to break bonds in the colliding molecules.

Effect of temperature on reaction rate

The rate of a reaction increases with an increase in temperature of the reactants. An increase in temperature will increase the kinetic energy of reactant molecules, causing the molecules to collide and increase the collision frequency. A 10°C increase in temperature will increase the reaction rate twofold.

Effect of concentration on reaction rate

Reaction rates can be increased if the concentration of reactants is raised. An increase in concentration produces more collisions. The chance of an effective collision goes up with the increase in concentration. The exact relationship between reaction rate and concentration depends on the reaction mechanism. In general, doubling the concentration of one of the reactants would increase the amount of the reactant molecules. This consequently doubles the number of collisions and thus the reaction rate.

Effect of catalyst on reaction rate

The reaction energy path controls the speed of the reaction. The molecules follow the path of least resistance, but this path may still require a lot of energy. The activation energy for the path may be high and then the reaction will be slow. A reaction pathway can be altered by adding nonreacting compounds to the reaction mixture. These molecules can sometimes alter the pathway so the energy needed for reaction is lowered. When this happens the reaction rates are faster. A material that lowers the activation energy is called a catalyst. The catalyst is unchanged at the end of the reaction.

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This experiment studies the effect of temperature, reactant concentration and the presence of catalyst on the reaction rate between iodide ions, −I and persulphate (peroxydisulphate) ions, S2O8

2–. The equation for the reaction is

S2O82–(aq) + 2 −I (aq) 2SO→ 4

2–(aq) + I2(aq)

The reaction rate will depend on the concentration of S2O82 and −I ions and given by the rate

equationrate = k [ S2O8

2– ]m [ −I ]n

where k = rate constant

m = order with respect to [S2O82–]

n = order with respect to [ −I ]

[S2O82–] = concentration of persulphate ions

[ −I ] = concentration of iodide ions

Iodine, I2 formed during the reaction will react immediately with thiosulphate, S2O32– ions until all

of the ions are used up.

2S2O32–(aq) + I2(aq) S→ 4O6

2–(aq) + 2 −I (aq)

The excess I2 will react with starch solution to form a dark blue complex.

APPARATUS

1. Glass rod2. Beaker, 250 mL3. Stopwatch

4. Thermometer5. Pipette, 10 mL6. Boiling tubes7. Water bath (set at different temperatures)

CHEMICALS

1. Solution A : 50 g potassium iodide (KI) + 25 g sodium thiosulphate (Na2S2O3) + 10 mL 8% starch solution in 1 litre solution

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2. Solution B : Sodium persulphate, Na2S2O8, 0.4 M

3. Copper (II) sulphate solution, CuSO4 , 0.1 M

4. Iron (II) sulphate solution, FeSO4, 0.1 M

PROCEDURE

1. Effect of temperature on reaction rate 1.1 Using a pipette, transfer 5 mL solution A and 5 mL solution B into two separate

boiling tubes.

1.2 Place both tubes in a water bath set at 70oC.

1.3 Once the temperature of both solutions reaches 70oC, mix the two solutions and start the stopwatch.

1.4 Record the time taken for the appearance of a dark blue coloration.

15 Repeat steps 1.1 to 1.4 at temperatures of 60oC, 50oC, 40oC and 30oC.

2. Effect of concentration on reaction rate 2.1 Prepare different concentrations of solution B as in the table below :

Boiling tube Volume of distilled H2O (mL) Volume of solution B (mL)

1 8 2

2 6 4

3 4 6

4 2 8

5 0 10

2.2 Mix the solution well using a glass rod.

2.3 Pipette 10 mL solution A into 5 separate boiling tubes.

2.4 Mix solution A and solution B in boiling tube 1 and immediately start the stopwatch.

2.5 Record the time taken for the appearance of a dark blue coloration.

2.6 Repeat steps 2.3 to 2.5 with solutions in boiling tubes 2, 3, 4 and 5.

3. Effect of catalyst on reaction rate3.1 Pipette 10 mL solution A into a boiling tube and add one drop of catalyst (catalyst

solution is made up of equal volumes of 0.1 M FeSO4 and 0.1 M CuSO4).

3.2 Pipette 10 mL solution B in a separate boiling tube.

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3.3 Mix solutions A and B, immediately start the stopwatch and record the time taken for the appearance of a dark blue coloration.

3.4 Compare your results with boiling tube 5 from section 2.

Reminder :

Make sure all boiling/test tubes are clean and free of contaminants by cleaning the tubes using the test tube brush provided and rinse with distilled water before use.

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EXPERIMENT 3

ELECTROCHEMISTRY –VOLTAIC CELL

OBJECTIVE1. To set up a, Zn – Cu, Mg – Zn and Sn – Zn voltaic cell and measure the cell voltage.

2. To measure cell voltage of Zn – Zn concentration cell and compare the measured value with the value calculated using the Nernst equation.

INTRODUCTION

Chemical reactions that involve a change in the oxidation state of chemical species are called the redox reaction (an abbreviation of reductionoxidation reaction). Redox reactions are reactions in which there are changes in oxidation numbers. Every redox reaction can be divided into two halfreaction; one that involves a gain of electron (reduction) and one that involves the loss of electron (oxidation). Redox reactions in which electrons are completely lost by one species and completely accepted by another are very useful because the two halfreactions can be physically separated. The electrons that are transferred may then be allowed to flow through external wires in a circuit and be made to do useful work. Electrochemistry is the study of redox reactions that either produce or utilize electrical energy (moving electrons and/or ions) in devices called electrochemical cells.

Voltaic cell also known as galvanic cell is a device to generate electricity through a spontaneous redox reaction. Oxidation and reduction reactions occur in each compartment simultaneously with the transfer of electron through an external wire.

A voltaic cell is made up of two parts of electrode known as halfcells. A halfcell consists of an electrode immersed in a solution of its ions known as the electrolyte. For example, a zinc metal immersed in Zn2+ solution and copper metal immersed in Cu2+ solution. A salt bridge connects the two solutions, and the electrodes are joined by a piece of wire in an arrangement shown in Figure 8. The electrons flow through an external circuit from the Zn to the Cu electrode. Therefore, zinc electrode is the anode at which oxidation occurs. At the cathode compartment, electrons are received by the copper ions and reduced to copper. The two halfcell reactions can be written as follows: Anode (oxidation) : Zn(s) → Zn2+(aq) + 2 e−

Cathode (reduction) : Cu2+(aq) + 2 e− → Cu(s)

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Figure 3 : Zn – Cu Voltaic Cell

A voltmeter measures the electromotive force, emf (E) or cell voltage, which is produced by the redox reaction. The cell voltage depends not only on the nature of the electrodes and the ions, but also on the concentrations of the ions and the temperature at which the cell is operated. The redox or cell reaction is the sum of two halfcell reactions given by

Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)

A short notation known as a cell diagram or cell notation can represent a voltaic cell. For Zn – Cu voltaic cell, the cell diagram is

Zn(s) Zn2+(aq) Cu2+(aq) Cu(s)

Standard cell potential, oE cell is the cell potential measured under standard state conditions (temperature = 25°C, pressure =1 atm and the concentration of electrolyte =1 M).

ocellE = o

anodeocathode EE

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Concentration Cell

The dependence of electrode potential on ion concentration can be studied by constructing a concentration cell, a cell with the same electrode but of different ion concentration. For an example, a zinc electrode immersed in one compartment of 0.1 M zinc sulphate solution and the other in a 1.0 M solution.

According to Le Chatelier’s principle, the tendency for the reduction of Zn2+ to Zn increases with increasing concentration of Zn2+. Therefore, reduction should occur in the more concentrated compartment and oxidation should take place on the more dilute side. Cell diagram for this process can be written as follows:

Zn(s) Zn2+ (0.10 M) Zn2+ (1.0 M) Zn (s)

The halfreaction for each half cell is

Oxidation : Zn(s) → Zn2+ (0.10 M) + 2e−

Reduction : Zn2+ (1.0 M) + 2e− → Zn(s)

Overall reaction : Zn2+ (1.0 M) → Zn2+ (0.1 M)

The cell potential can be calculated by using Nernst Equation:

where n = the number of moles of electron involved in the overall redox equation

Q = +

+

2

2

]dilute[Zn[Zn ]

conc ; oE cell = 0 (same electrode).

In this experiment, you will construct, Zn – Cu, Mg – Zn and Sn – Zn voltaic cells and measure the cell voltage. The effect of concentration on cell voltage is studied by measuring the cell voltage of Zn – Zn concentration cell.

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= −o 0.0592log

cellcellE Q

nE


APPARATUS

Beaker, 50 mL

Voltmeter

Dropper

CHEMICALS

Magnesium chloride, MgCl2Zinc sulphate, ZnSO4

Tin chloride, SnCl2Copper nitrate, Cu(NO3)2

Sodium nitrate, NaNO3

Copper, Cu metals

Magnesium ribbon, Mg

Tin, Sn metal

Zinc, Zn metal

PROCEDURE

1. Determination of cell voltage

1.1 Polish the strips of metal (Mg, Zn, Sn, and Cu) provided with sand paper.

1.2 Place 30 mL 1 M electrolyte solutions of MgCl2, ZnSO4, SnCl2 and Cu(NO3)2 into 50 mL clean and dry beakers separately. Make sure each beaker is labelled correctly.

1.3 Set up a voltaic cell of Zn – Cu as in Figure 3. Connect the halfcells with strips of filter paper saturated with sodium nitrate that act as a salt bridge. Ensure that all connections are correct (voltmeter reading in positive direction). If not, reverse the connection.

1.4 Record the cell voltage.

1.5 Repeat step 1.3 for Mg – Zn and Sn – Zn voltaic cells (make sure that you replace the strips of filter paper for each setup of voltaic cells).

2. Concentration Cell

2.1 Prepare two pieces of polished Zn metals.

2.2 Prepare 0.02 M ZnSO4 electrolyte solution by diluting the 1 M ZnSO4 solution from part 1.

2.3 Using procedure 1, set up a concentration cell of 0.001 M Zn2+ – 1.0 M Zn2+.

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2.4 Record the cell voltage.

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EXPERIMENT 4

PROJECTILE MOTION IINTRODUCTION

Launch Position

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AIM

The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The initial velocity of the ball is determined by shooting it horizontally and measuring the range and the height of the Launcher.

THEORY

To predict where a ball will land on the floor when it is shot off a table at an angle, it is necessary to first determine the initial speed (muzzle velocity) of the ball. This can be determined by launching the ball horizontally off the table and measuring the vertical and horizontal distances through which the ball travels. Then the initial velocity can be used to calculate where the ball will land when the ball is shot at an angle.

a) INITIAL HORIZONTAL VELOCITY:

For a ball launched horizontally off a table with an initial speed, vo, the horizontal distance travelled by the ball is given by x = vot, where t is the time the ball is in the air. Air friction is assumed to be negligible.

The vertical distance the ball drops in time t is given by

( ) 200 2

1sin gttvyy −+= θ

The initial velocity of the ball can be determined by measuring x and y. The time of flight of the ball can be found using:

gy

t2=

and then the initial velocity can be found using v0 = tx

.

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b) INITIAL VELOCITY AT AN ANGLE:

To predict the range, x, of a ball launched with an initial velocity at an angle, , above theθ horizontal, first predict the time of flight using the equation for the vertical motion:

( ) 200 2

1sin gttvyy −+= θ

where yo is the initial height of the ball and y is the position of the ball when it hits the floor. Then use x = (v0 cos ) θ t to find the range. If the ball is shot at an angle below the horizontal, then isθ negative.

Setup

1. Clamp the Mini Launcher near one end of a sturdy table as shown in Figure 1.1.

2. Adjust the angle of the Mini Launcher to zero degrees so the ball will be shot off horizontally.

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APPARATUS

Mini Launcher and steel ball, Plumb bob, Meter stick, Carbon paper, White paper.

PROCEDURE

PART A : Determining the initial Velocity of the Ball

1. Put the ball into the Mini Launcher and cock it to the long range position. Fire one shot to locate where the ball hits the floor. At this position, tape a piece of white paper to the floor. Place a piece of carbon paper (carbonside down) on top of this paper and tape it down. When the ball hits the floor, it will leave a mark on the white paper.

2. Fire about ten shots.

3. Measure the vertical distance from the bottom of the ball as it leaves the barrel (this position is marked on the side of the barrel) to the floor. Record this distance in Table 1.1 ).

4. Use a plumb bob to find the point on the floor that is directly beneath the release point on the barrel. Measure the horizontal distance along the floor from the release point to the leading edge of the paper. Record in Table 1.1.

5. Measure from the leading edge of the paper to each of the ten dots and record these distances in Table 1.1.

6. Find the average of the ten distances and record the value in Table 1.1.

7. Using the vertical distance and the average horizontal distance, calculate the time of flight and the initial velocity of the ball. Record in Table 1.1.

8. Calculate the Total Average Distance. Record in Table 1.1

PART B : Predicting the Range of the Ball Shot at an Angle

1. Adjust the Mini Launcher to launch at an angle between 20 and 60 degrees above the horizontal. Record this angle in Table 1.2.

2. Using the initial velocity and vertical distance found in the first part of this experiment, calculate the new time of flight and the new horizontal range for a projectile launched at the new angle. Record in Table 1.2.

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3. Draw a line across the middle of a white piece of paper and tape the paper on the floor so the line is at the predicted horizontal distance from the Mini Launcher. Cover the paper with carbon paper.

4. Shoot the ball ten times.

5. Measure the ten distances and take the average. Record in Table 1.2.

PART C : Predicting the Range of the Ball Shot at a Negative Angle

1. Adjust the Mini Launcher to launch at an angle between 10 and 40 degrees below the horizontal and record this angle in Table 1.3.

2. Using the initial velocity and vertical distance found in the first part of this experiment, calculate the new time of flight and the new horizontal range for a projectile launched at the new angle. Record in Table 1.3.

3. Draw a line across the middle of a white piece of paper and tape the paper on the floor so the line is at the predicted horizontal distance from the Mini Launcher. Cover the paper with carbon paper.

4. Shoot the ball ten times.

5. Measure the ten distances and take the average. Record in Table 1.3

ANALYSIS

PART B : Predicting the Range of the Ball Shot at an Angle

1. Calculate the Total Average Distance. Record in Table 1.2.

(Total Average Distance = Distance from Edge of Paper + Horizontal Distance to paper edge)

2. Calculate and record the percentage difference between the predicted value and the resulting average distance when shot at an angle.

3. Estimate the precision of the predicted range. How many of the final 10 shots landed within this range?

PART C : Predicting the Range of the Ball Shot at a Negative Angle

1. Calculate the Total Average Distance. Record in Table 1.3.

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(Total Average Distance = Distance from Edge of Paper + Horizontal Distance to paper edge)

2. Calculate and record the percentage difference between the predicted value and the resulting average distance when shot at an angle.

3. Estimate the precision of the predicted range. How many of the final 10 shots landed within this range?

EXPERIMENT 5

CENTRIPETAL FORCE

AIM

To verify the effects of varying the radius of the circles, the centripetal force and the mass of the

object on an object rotating in a circular motion.

THEORY

When an object of mass m, attached to a string of length r, is rotated in a horizontal circle, the

centripetal force on the mass is given by :

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ωmrr

mvF == (1)

where v is the tangential velocity and ω is the angular speed ( v = r ω ). To measure the

velocity, the time for one rotation (the period, T ) is measured. Then :

Tr

vπ2= (2)

and the centripetal force is given by :

2

24T

mrF

π= (3)

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APPARATUS

Centripetal Force Accessory comprises of centre post assembly and side post assembly, rotating

platform, “A” base, clampon pulley, hanging mass, string, stopwatch, rotational motor drive with

3step pulley and DC power supply.

Caution

1. Do not exceed the maximum power of motor, ( 15 VDC; 1.0 A )

2. Clear the area around rotating platform, to prevent damage or injury.

27

Fig 1 : Centripetal Force Apparatus

Fig 2 : Side Post Assembly


SETUP AND PROCEDURE

Part 1 : Varying Radius (constant force and mass)

1. The centripetal force and the mass of the hanging object will be held constant for this part

of the experiment. Weigh the object and record its mass in Table 1. Hang the object from

the side post and connect the string from the spring to the object. The string must pass

under the pulley on the center post. See Figure 1.

2. Attach a string to the hanging object and hang a known mass over the clampon pulley.

Record this mass in Table 1. This establishes the constant centripetal force.

3. Select a radius by aligning the line on the side post with any desired position on the

measuring tape. While pressing down on the side post to assure that it is vertical, tighten

the thumb screw on the side post to secure its position. Record this radius in Table 1. (The

recommended values of r are given in the table).

4. The object on the side bracket must hang vertically: On the center post, adjust the spring

bracket vertically until the string from which object hangs on the side post is aligned with

the vertical line on the side post.

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Fig 4 : Threading the Centripetal Force Accessory

Fig 3: Center Post Assembly


5. Align the indicator bracket on the center post with the orange indicator.

6. Remove the mass that is hanging over the pulley and remove the pulley.

7. Rotate the apparatus, increasing the speed until the orange indicator is centered in the

indicator bracket on the center post. This indicates that the string supporting the hanging

object is once again vertical and thus the hanging object is at the desired radius.

8. Maintaining this speed, use a stopwatch to time ten revolutions. Divide the time by ten and

record the period in Table 1.

9. Move the side post to a new radius and repeat the procedure. Do this for at least five radii.

Part II : Varying Force (constant radius and mass)

The radius of rotation and of the hanging object will be held constant for this part of the

experiment.

1. Weigh the object and record its mass in Table 2. Hang the object from the side post and

connect the string from the spring to the object. The string must pass under the pulley on

the center post.

2. Attach the clampon pulley to the end of the track platform. Attach a string to the hanging

object and hang a known mass over the clampon pulley. Record this mass in Table 2.

This determines the centripetal force.

3. Select a radius by aligning the line on the side post with any desired position on the

measuring tape, (r = 15.0 cm is recommended). While pressing down on the side post to

assure that it is vertical, tighten the thumb screw on the side post to secure its position.

Record this radius in Table 2.


bracket vertically until the string from which the object hangs on the side post is aligned

with the vertical line on the side post.




indicator bracket on the center post. This indicates that the string supporting the hanging

object is once again vertical and thus the hanging object is at the desired radius.

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9. To vary the centripetal force, clamp the pulley to the track again and hang a different mass

over the pulley. Keep the radius constant and repeat the procedure from step 4. Do this for

a total of five different forces. ( Use mass of M = 20, 40, 50, 60, 80, 100 (g) )

Part III : Varying Mass (constant radius and force)

The centripetal force and the radius of rotation will be held constant for this part of the experiment.

1. Weigh the object with the additional side masses in place. Record its mass in Table 3.

Hang the object from the side post and connect the string from the spring to the object.

The string must pass under the pulley on the center post.

2. Attach the clampon pulley to the end of the track nearer to the hanging object. Attach a

string to the hanging object and hang a known mass over the clampon pulley. Record this

mass in Table 3. This establishes the constant centripetal force.

3. Select a radius by aligning the line on the side post with any desired position

(r = 15.0 cm). While pressing down on the side post to assure that it is vertical, tighten the

thumb screw on the side post to secure its position. Record this radius in Table 3.


bracket vertically until the string from which the object hangs on the side post is aligned

with the vertical line on the side post.




indicator bracket on the center. The indicates that the string supporting the hanging object

is once again vertical and thus the hanging object is at desired radius.



9. Vary the mass of the object by removing the side masses. Keep the radius constant and

measure the new period. Weigh the object again and record the mass and period in Table

3.

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ANALYSIS

Part 1 : Varying Radius (constant force and mass)

1. The weight of the mass hanging over the pulley is equal to the centripetal force applied by

the spring. Calculate this force by multiplying the mass hung over the pulley by “g” and

record this force at the top of Table 1.

2. Calculate the square of the period for each trial and record this in Table 1.

3. Plot the radius versus the square of the period. This will give a straight line since :

224

Tm

Fr

=

π

4. Draw the bestfit line through the data points and measure the slope of the line.

5. Calculate the centripetal force from the slope and from Fc = mg.

6. Calculate the percentage difference between the two values found for the centripetal force.

Part II : Varying Force (constant radius and mass)


the spring. Calculate this force for each trial by multiplying the mass hung over the pulley

by “g” and record the results in Table 2.

2. Calculate the inverse of the square of the period for each trial and record this in Table 2.

3. Plot the centripetal force versus the inverse square of the period. This will give a straight

line since :

2

24T

mrF

π=

4. Draw the bestfit line trough the data points and measure the slope of the line.

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5. Calculate the mass of the object from the slope.

6. Calculate the percentage difference between the two values found for the mass of the

object.

Part III : Varying Mass (constant radius and force)


the spring. Calculate this force by multiplying the mass hung over the pulley by “g” and

record the result at the top of Table 3.

2. Calculate the centripetal force for each trial using :

2

24T

mrF

π=

and record this in Table 3.

3. Calculate the percentage difference between the calculated centripetal force for each trial

and Mg. record in Table 3.

Questions

1. When the radius is increased. Does the period of rotation increase or decrease?

2. When the radius and the mass of the rotating object are held constant, does increasing the

period increase or decrease the centripetal force?

3. As the mass of the object is increased, does the centripetal force increase or decrease?

EXPERIMENT 6

SIMPLE HARMONIC MOTION

AIM

At the end of this experiment, you should be able to:

• Verify Hooke’s Law and calculate the extension per gram of the added weight

• Determine the effective mass of a spring, M

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INTRODUCTION

A linear restoring force tends to return a body displaced from its position or point of equilibrium

back to its initial position. However due to inertia the body will move past its point of equilibrium.

The magnitude of the restoring force correspondingly increases, acting in a direction opposite to

the motion of the body. The body decelerates and eventually stops. The restoring force now

accelerates the body towards its equilibrium point. This behavior continues indefinitely (if there are

no frictional forces present) and the body is said to be in simple harmonic motion (SHM). The

restoring force for a springmass system oscillating in SHM is given by the equation:

kxdt

xdmF −== 2

2

(1)

where F is the restoring force, m is the mass undergoing SHM, x is the displacement from the

equilibrium position x = 0, k is the effective spring constant. The negative sign implies the

restoring force is always opposite in direction to the displacements.

In SHM, the maximum displacement from the equilibrium point (regardless whether it is to the left

or right) is known as the amplitude of displacement A whereas a complete oscillation is known as

a cycle. The time taken for a body to complete one cycle is known as the period of oscillation, T.

The number of cycles each second is known as the frequency, f. The unit for period is seconds

whereas the unit for frequency is cycles per second or the hertz (Hz). A general solution to

Equation (1) is:

)cos( φω += tAx (2)

where ω = fπ2 is the angular frequency and φ is the angular phase. Further analysis will show

that the period, T and angular frequency, ω is a function of mass, m and a constant of

proportionality, k i.e.:

km

T π2= (3)

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mk=2ω (4)

THEORY

A spring is vertically suspended and pulled below. The string will extend according to Hooke's

Law (Equation 1) where x is the extension of the spring and k is the spring constant. The restoring

force due to extension, x is:

kxF = (5)

The coefficient k can be calculated from the graph of weight, mg versus extension, x.

Since

mk=ω (6)

the period of oscillation T is as in Equation (3).

Note that Equations (6) and (3) neglect the mass of the spring, M. The period of the spring taking

into account the effective mass of the spring, M is:

kmM

T)(

2+= π (7)

or

kM

mk

T22

2 44 ππ +

= (8)

APPARATUS

spring

needle

plasticine

ruler (1 meter)

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scalepan and weights

stopwatch

retort stand

cork

SETUP AND PROCEDURE

Experiment A: Verification of Hooke's Law and calculation of the extension per gram of the

added weights.

1. Suspend a spring and ruler on a retort stand. Stick the needle

(indicator) on the free end of the spring with plasticine. Record the initial length of the

spring as indicated on the ruler.

2. Gradually add weights on the spring and record the length as

indicated on the ruler. Determine the extension of the spring.

3. Gradually reduce weights from the spring and record the length.

Determine the corresponding extension of the spring.

4. Tabulate the obtained data below.

Experiment B: Determination the effective mass of the spring, M.

1. Suspend the spring and add an initial amount of weights to it. Allow the spring to

stabilize.

2. Slightly displace the spring and allow the spring to oscillate.

3. Record the time for 20 oscillations.

4. Gradually add weights and repeat steps 1 – 3. Tabulate the data obtained as

shown below.

ANALYSIS

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1. Plot a graph of weight versus extension, x and calculate k which corresponds to the

gradient of the graph.

2. Plot the graph of T 2 versus mass, m. Calculate the value of M from your graph.

3. Compare with the actual value of M. What is the percentage difference between these

values ?

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