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SPH 2173 PHYSICS FOR ENGINEERS 1 AND PHYSICS FOR TIE

A1PRECISION MEASUREMENTS- Objectives:

To study some of the instruments and methods used in precision measurements , and to compute the

volume and density of various items.

Apparatus: Metre rule, vernier calipers ,micrometer screw gauge ,electronic balance and traveling

microscope .Such items as copper cylinder , steel ball and glass capillary tube are also supplied.

METHOD: The experiment comprises e measurement of the various objects supplied with the

appropriate instruments. Where feasible, at least two instruments should be used for each measurement

and the precision obtained in each case compared. In this way, the volume and density of atleast two

metal objects weighings should be done on the electronic balance.

In the second part of the experiment, some electrical circuits have been set up for you to measure the

current. Measure the current using an ammeter, a milliammeter and a microammeter, and estimate the

reading errors in each case.

N.B. in all cases an estimate of the precision obtained should be, i.e. note the reading errors on all

measurements. Where appropriate note the zero error.

Record the data in work sheet 1,working out any calculations asked for. Answer the questions posed on

the sheet.

WORKSHEET 1

N.B. You must include in the table the units of any measurements you take.

ITEMS MEASURING INSTRUMENTS

Met

er

rule

Verni

er

calip

ers

Micromete

r Screw

Gauge

Bala

nce

Amm

eter

Milli

Ammet

er

µA

scope

Travelling

Microscope

X Y Z

Zero error

Reading

error

Copper

cylinder:

mass

height

Diameter

(external)

Diameter

(internal)

Steel Ball:

Diameter

Copper

wire: length

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Diameter

glass rod:

diameter

length

Current

scope voltage

signal height

peak-peak height

peak height=

Analysis :

volume Density of the material

Copper cylinder: Internal volume

External volume

Steel bar

Glass rod

Calculation of voltage:

Instrument Value of Resistances

Calculated V= IR

From Ammeter

From Milli-Ammeter

From µA

scope voltage signal sensitivity= voltage = sensitivity x height

ERRORS

Now work out the errors in volumes and densities and voltages calculated above using the reading errors of

the appropriate instruments. Refer to the section on errors in this manual for instructions on how to calculate

errors.

volume Density of the material

Copper cylinder: Internal volume

External volume

Steel bar

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Glass rod

Instrument calculated V= IR

From Ammeter

From Milliammeter

From µA

from scope

QUESTIONS:Why is it appropriate to use the metre rule for measuring the length of the copper

wire but the micrometer screw gauge for he diameter?.What is the difference between accuracy and

precision? CONCLUSION:The volume of the copper cylinder was found to be --------------------------

---------------------------(units) ,and its density was found to be------------------------ ------------------- ------

------ (units)Write similar conclusions for the steel ball `and capillary tube , and give correct values

for the densities of copper and steel . The values may be found in the reference book Tables of

physical and chemical constants,15th Edition , G.W.C. Kaye.and Labye (Longman 1986 )

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A4:FRICTION

COEFFICIENT OF STATIC FRICTION

Apparatus

Wooden block A with a hook attached, a plane piece of wood B with a grooved wheel C at one end, scale-

pan S, light string, weights, boxes of weights, spring balance.

Method

Weigh the block A and the scale-pan S on the spring balance. Attach the scale-pan to the hook of A by light

string passing round the wheel C. Mark the position of A on the board B with pencil. Then gently add

increasing weights to S until A just begins to slide. Record the total weight in S. Now increase the reaction

of B by placing a known weight on A and by adding increasing weights to S until A just begins to slide.

Record the total weight in S. Now increase the reaction of B by placing a known weight on A and by adding

increasing weights to S again record the total weight in S when A begins to slip. Repeat for two more

increasing weights on A, returning the block A to its original place on B each time.

Measurements

Weight of scale-pan = …N

Weight of block A =… N

Normal reaction, R/N Weight in scale-pan on

slipping /N

Limiting frictional force,

F/N

Calculation

The limiting frictional force, F = weight in scale-pan when A slips + weight of scale-pan.

Normal reaction, R = weight of A + other weights on A.

Graph

Plot F v.R (Fig.8b)

The gradient a/b = μ = …

B C

S

F

R

F

R

b

a

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Conclusion

The coefficient of static friction between block and plane at the place concerned is …

Errors and order of accuracy

Draw the lines with the least and greatest slopes, which just agree with the plotted points. Find the error in μ

from the variation in slope.

1. COEFFICIENT OF DYNAMIC FRICTION

Apparatus

As before

Method

With the apparatus shown in Fig.8a, place a weight on S and give A a slight push towards C. Add increasing

weights to S, giving A a slight push each time. At some stage, A will be found to continue moving with a

steady, small velocity. Record the corresponding weight in the scale-pan S. Now increase the reaction of B

by adding weights to A and repeat. Repeat for two more weights on A, returning the block to its original

place in B each time.

Measurements

Weight of scale-pan = … N

Weight of block A = … N

Normal reaction, R/N Weight in scale-pan on

moving A/N

Frictional force, F’/N

Calculation

The frictional force, F’ = weight in scale-pan when A moves + weight of pan.

Normal reaction, R = weight of A + other weights on A

Graph

Plot F’ v.R (Fig. 8c)

The gradient, a/b = μ’= …

Fig. 8c

Conclusion

The coefficient of dynamic friction is …

Errors and order of accuracy: As before.

F

R

a

b

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HARMONIC MOTION-A7

Introduction:

If an object is strained and released (or if an impulse is delivered), it will oscillate periodically about

its equilibrium or rest position. Examples of such objects are a saw blade clamped at one end, a mass

attached to a spring, a mass attached to a rod (torsional oscillations), musical string instrument; drum head,

spider’s web, eardrum, and a car body (oscillates vertically on its springs).

If during the oscillation, the elastic restoring force has a magnitude, which is proportional to the

displacement from the equilibrium position and a direction such as to restore the object to that equilibrium

position, then the motion is simple harmonic.

In this exercise you are going to perform a set of experiments to illustrate simple harmonic motion

using a spiral spring.

Apparatus

Spiral spring to which a light pointer is attached by plasticine at its lower end, rigid stand and clamp, meter

rule, scale pan and weights, stop watch.

a) To find the spring constant

If a spring is stretched a distance x which is not too large then the Hooke’s law states that the spring exerts a

force F which is proportional to x:

F = -kx………(1)

Where k is the force constant of the spring.

Method

The spring, with scale pan attached, is firmly clamped and the meter scale placed vertically so that the

pointer moves slightly over it (Fig 1). Place weights on the scale pan and measure the stretch produced in

each case. The scale readings are also taken when unloading the spring and the mean stretch thus obtained.

Loads less than 1kg should be used as more may permanently deform the spring. Plot the magnitude of the

spring force (load) versus the stretch of the spring.

Fig.1

Question 1:

Is your graph describable by Hooke’s law? If so, determine the spring constant k.

Question 2:

Does your graph pass through the origin? If not, explain why.

Question 3:

From your graph what is the change in elastic potential energy of the spring when the load is increased from

0.5kg to 0.7kg?

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b) To determine the acceleration of gravity (g) and the effective mass if the

spring

Theory:

If a mass m is attached to a spring and the spring is extended by a further distance x a restoring force

kx is called into play. The spring on being released executes vertical oscillations the motion of the mass

being

Md2x/dt2 = -kx

i.e. d2x/dt2 + kx/M =0…. (2)

The motion is thus simple harmonic with periodic time T given by

T = 2π√ M/k…(3)

The above analysis assumes the spring to be weightless. In practice the spring has a mass and therefore a

correction has to be made to equation (3) to include the ‘effective’ mass of the spring.

Method:

A load is added to the pan, which is set in vertical vibration by giving it a small additional displacement. The

periodic time T is obtained by timing 20 oscillations. Repeat the experiment with different loads. Plot a

graph of T2 versus load and then find the values of g and m from it. Note that the mass of the scale-pan

should be included in the load in this experiment. Experimental errors must also be included.

Question 4:

Weigh the spring using a balance. What would you expect the effective mass of the spring to be using this

measured value? Compare it with the one obtained from the graph.

Question 5:

What is the percent discrepancy between your value of g and the expected value?

Damped Simple harmonic motion:

Theory:

For a real mechanical system the amplitude decreases with time and the motion is called damped simple

harmonic. The decrease in amplitude is due to friction and the energy of oscillations eventually dissipated as

thermal energy. The damping force is often proportional to the velocity of the mass but in the opposite

direction. Newton’s second law applied to the oscillator yields the equation of motion for the mass M:

F = -kx – bdx/dt = Md2x/dt2

So that, d2x/dt2 + b/M X dx/dt + kx/M = 0 …(5)

Where b is a positive constant, called the damping constant (Fig.2)

For a lightly damped harmonic oscillator the equation of motion is given by

X (t) = Ao e-bt/2M cos (ωt - Φ)…(6)

Where the periodic of oscillation is given by

T = 2π/W = 2π ……(7)

√ (k/m – (b/2M) 2)

Amplitude is A = Aoe-bt/2M…(8)

Method

Hang a medium size mass from the spring. Displace the mass from its equilibrium position by a

fairly large amount but do not exceed the linear portion of the spring. Release the mass and simultaneously

start the timer, then measure the amplitude and the time for after every 10 complete oscillations. Obtain 10

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or more measurements and be sure to keep the timer running; hence you will measure amplitude as a

function of time.

Using equation (8) plot a suitable graph connecting amplitude and time such that a straight line

would be expected.

Calculate the damping constant b from your graph.

Note

Remember to include the effective mass of the spring. If the scale pan was used include its mass in the load.

Question 6:

From equation (7) calculate T’ and its error.

Question 7:

In exp 5.1 it was assumed that damping was absent or at worst negligible. Obtain from the results of that

experiment the value for the period corresponding to the mass that was used in exp 5.3. Call it Texp

(experimental period). Now, calculate the theoretical periods T and T’ from equations (3) and (7)

respectively.

Compare the values of Texp, T and T’. Which theoretical period, T or T’, yields the smaller percent

discrepancy?

Discuss your results.

Question 8:

What is the percent discrepancy between T and T’. Is damping important with regard to the period?

Fluid

Fd V Fs

K

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H18: HEAT CAPACITY OF METAL BLOCK & SPECIFIC HEAT CAPACITY OF OIL BY

MIXTURES

i. HEAT CAPACITY OF A METAL BLOCK

ii. SPECIFIC HEAT CAPACITY OF OIL, BY MIXTURES

APPARATUS

Large mass of metal (about 0.2kg) A, beaker B, copper calorimeter C in insulating jacket D, copper stirrer E,

tripod, gauze, burner, chemical balance, weights, oil (e .g paraffin or castrolite), thread, stop-watch,

thermometer 0-100oC

E

i. HEAT CAPACITY OF METAL

METHOD

Fill the beaker B with some water, place the metal A inside it, and boil the water, meanwhile, weigh the

calorimeter and stirrer, fill it a bout one-half with tap water, and re-weigh. Take the temperature of the water

in the calorimeter. Take the temperature of the boiling water, and then quickly transfer metal A to the water

in the calorimeter C. Observe the water temperature every 10s until it reaches a maximum and then drops

several degrees below the maximum reached.

MEASUREMENTS

Mass of calorimeter + stirrer m1 (c1 =… Jkg-1K-1) =…kg

Mass of calorimeter + stirrer + water m1 + mass of A =…kg

Initial water temperature t1 =…0C

Final temperature observed =…0C

Final temperature, corrected for cooling t2 =…0C

Temperature of boiling water t =…0C

COOLING CORRECTION

This may be obtained by a graphical method, as explained 0n p. 49. An alternative method is as follows:

Suppose it took a time x for the water to reach its final temperature when the hot metal was dropped in; then,

approximately, the cooling correction is the temperature drop from the maximum temperature in a time x/2.

Since a metal is a good conductor, it gives up its heat quickly, and the cooling correction may therefore be

negligible.

CALCULATION

Heat lost by metal = Heat gained by water and calorimeter + stirrer. If C is the heat capacity of the metal and

m the mass of water of specific heat capacity

Cw(=4200Jkg-1K-1), then

CONCLUSION

The heat capacity of the metal was…JK-1

ERRORS

heat

A

C

D

E

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1. Heat lost by the hot metal on transferring it to the calorimeter;

2. Some hot water is carried over with the metal;

3. Observations of the temperature (e. g. 16.4+ 0.20c) and mass (e. g 194+ 194.6+ 0.1 x 10-3kg )

ORDER OF ACCURACY

ii. SPECIFIC HEAT CAPACITY OF OIL

METHOD

Add some water to the beaker, place the metal A inside it, and heat the water until it boils. Meanwhile weigh

the calorimeter, fill it about one-half with the oil, and re-weigh. Observe the oil temperature. Take the

temperature of the boiling water, and then quickly transfer A to the oil. Observe the time taken for the oil to

reach its maximum temperature, and then find the temperature drop c, in half this time. This is the cooling

correction

MEASUREMENTS

Mass of calorimeter m1+ stirer (c1 =…Jkg-1K-1) =…kg

Mass of calorimeter + oil m1 + stirrer +Mass of A =…kg

Initial oil temperature t1 =…0C

Final temperature, corrected for cooling t2 =…0C

Temperature of boiling water t =…0C

Heat capacity of metal (C) ~ from previous experiment =…JK-1

CALCULATION

Heat loss by metal = Heat gained by oil and calorimeter. If c is the oil’s specific heat capacity and m is the

mass of the oil, then with m and m1 in kg, calculate c from

H x (t-t1) = (mc + m1c1) (t2 – t1)

CONCLUSION

T he specific heat capacity of the oil was…Jkg-1K-1

ERRORS AND ORDER OF ACCURACY

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M2:MEASUREMENT OF SURFACE TENSION OF WATER BY

CAPILLARY TUBE

M

A

C

P B

Apparatus

Capillary tube A, traveling microscope M, beaker B, cork C with pin P, clamps and stand, thermometer, file

for cutting capillary tube.

Method

Do the experiment in a well-lit place for example near a window. Clean the capillary tube A with some

dilute caustic soda and wash out repeatedly with distilled water. Fill the beaker B with water and measure its

temperature. Now push the capillary tube A into the water so that the inside is wet then raise the capillary

tube so that the water inside reaches a level higher than the outside level of water in B, check that the level

falls back to a constant position after being drawn up the tube and fix the tube in a clamp. Push the pin P

through the cork C, place the cork in a clamp as shown and arrange the tip of the pin to just touch the water

surface in B well away from the tube. This can be done accurately by means of the image of P in the water.

Now focus the traveling microscope M on the meniscus, which is seen inverted in M. If there is any

difficulty in focusing M, hold a piece of paper on the glass at A and focus M on the paper first as a guide.

Read the traveling microscope. Mark the position of the meniscus A on the capillary tube with a pen or

sellotape. Now carefully remove the capillary tube from B, then remove B, and focus the microscope on the

tip of P; read the microscope vernier.

With the aid of a file, cut through the capillary tube at the position of the meniscus A. Measure two

diameters at right angles at A by means of the travelling microscope.

Measurements

Temperature of water =…oC

Meniscus reading on microscope =…mm

Pin reading on microscope =…mm

Diameter of capillary tube at A =…mm

Height of water column h =…mm= …m

Average radius of capillary tube r =…mm= …m

For water,

γ = rhρg =…Nm-1

2

Where h and l are in m, ρ is 1000kgm-3 and g = 9.8ms-2

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Conclusion

The surface tension of water at…oC was…Nm-1

Errors

The error in the capillary rise h is due to

i. Errors in the two vernier readings

ii. Error in setting the cross wires on the meniscus or pin

iii. Error in setting the pin at the water surface. Similar errors to (i) and (ii) occur in measuring the radius.

Order of accuracy

From the formula for γ in terms of measured quantities,

Max % error in γ = (δh /h + δr/r) +100%

Note

The mean radius r of the capillary tube can be found by measuring the length l and mass m of a mercury

thread drawn into it. The radius r in the surface tension formula however is the radius of the tube at the

meniscus and not the mean radius.

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SPH 2174 PHYSICS FOR ENGINEERS 2

REFRACTIVE INDEX- B9 LAWS OF REFRACTION Aim: 1. Determination of refractive index of glass and water by

plotting (graphical method) (glass)

apparent depth method (water)

A. PLOTTING (GRAPHICAL METHOD)

APPARATUS

ABCD is a rectangular glass block.P1, P2, P3 and P4 are pins on a drawing board and paper.

Method

1. Place a rectangular glass block on a paper on the drawing board.

2. Draw line P as shown in the figure.

3. Look in along the direction of P1 and P2 until the image of line P through the glass is in line with the pins.

4. Remove the pins and mark their positions on the paper.

5. Repeat the procedure for 5 more lines namely Q, R, S, T, and U. To get pins P3 and P4, P5 and P6, P7 and P8 P9 and P10 and P11

and P12. Make sure you mark the positions of the pins precisely.

6. Draw the outline of the glass block on the drawing paper.

7. Remove the glass block and pins from the paper.

8. Draw the normals at points E and F and join E&F.

9. Measure the angles i and R with a protractor, and calculate the refractive index. Repeat this for 5 more times and plot a graph

of sin i/sine r and get the refractive index of glass. Also calculate for each set of data sin i/sin r and get their average value.

Compare this with the one obtained from plotting.

i Sin i r Sin r Sin i/sin r

B. APPARENT DEPTH METHOD

Apparatus

Glass or Perspex block B, traveling microscope M, lycopodium powder L and beaker.

P

E

B

C D

A

F

P1

P2

r

i

i

r1

r2

r3

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ethod

Place the beaker B on a sheet of paper P and arrange the travelling microscope so that the microscope M and the scale s are vertical . Put a pin on

the bottom of the beaker. Focus the microscope M on the pin. Having achieved a sharp focus using the fine adjustment screw take the reading r3

(fig (c)). of the vertical scale of the microscope.

NOW almost fill the beaker B with water. Move the microscope down until the pin seen through the water is in sharp focus. Take the reading r2

fig (b)). of the vertical scale of the microscope.

Focus the microscope M on the upper surface of the water which is sprinkled using a little lycopodium powder L or chalk dust if necessary

Having achieved a sharp focus using the fine adjustment screw take the reading r1

(fig (a)). Of the vertical scale of the microscope.

Repeat the procedure above for 5 more different depths of water and fill the table below.

Measurements r

1 (mm) r

2 (mm) r

3 (mm) (r

1-r

2) (mm) (r

1-r

3) (mm)

1.

2.

3.

4.

5.

6.

Draw a graph of (r1-r3) (mm) versus (r1-r2) (mm) and find n for water graphically.

Conclusion:The refractive index of water is: Apparent method:…………+ ….%.The refractive index

of glass is: Plotting method:…………+ ….%.

B15…………..Vibrating string Aim:

Determine linear mass density of the wire, µ.

Determination of the frequency of the Local A.C. mains.

Determination of the velocity of the wave in Vibrating wire at the frequency of the Local A.C. mains

Apparatus Sonometer S with 24 s.w.g, wire X, ‘horseshoe’ magnet G, small masses mains transformer Y [240V-6V], weighing balance.

Method

-Determine linear mass density of the wire, µ.

-To find the mass per meter, µ, of the wire cut a known length X [at least 20cm] of the wire and weighs it carefully. If more convenient, µ ,can be found by measuring the diameter of the wire at

L

240V

Y R

M A S B

P X

(fig (c)).

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three different places in perpendicular directions to the length of the wire and obtaining the density of the material from physical tables. 1 2 3 mean

Length of wire X (m)

Mass, m, of X meters of wire, (kg)

Diameter of the wire (m)

Using appropriate formulae and method determine the, µ, of the wire. Measurement of the frequency ,f, of the Local A.C. mains Clean the wire X where it passes over the metal pulley P and at the far end where it is attached to sonometer S. Connect the wire, taking one lead from the pulley in series with the rheostat R and the 6V secondary of the mains transformer Y. Place the magnet G so that the wire passes between its poles and adjust the current [which may be checked with an ammeter] until the wire can be felt to vibrate slightly without becoming appreciably heated. Weigh the scale pan on the weighing balance and hang it on the wire. Adjust the positions of the bridges A and B until the wire between them resonates in its fundamental mode the magnet being at the center of AB. Measure the length L of the vibrating wire between A and B and record. Then Place a load of about 20g in the scale pan and get the combined mass M of the load and scale pan and repeat the above steps. Vary the load to about 120g in steps of 20g and each time measure the new resonating length.

Li near mass density of the wire,µ, =………………..g/m

Mass, M Tension, T LeLength of fundamental

loop,L

L2

Scale pan

Draw a graph of T against L2

Using the graph determination of the frequency of the Local A.C. mains Determination of the velocity of the wave in of vibrating wire at the frequency of the Local A.C. mains Now Hang a single mass of approximately 20g on the the wire Adjust the positions of the bridges A and B until the wire between them resonates in its fundamental mode ( 1 loop) the magnet being at the center of AB. Measure the length L of the vibrating wire between A and B and record.

Then move the bridges A and B to get the second, third, fourth, fifth, and sixth ….. loops. Each time measure the length L of the vibrating wire between A and B and record.

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Tension on the wire=………….N

linear mass density of the wire,µ, =………………..g/m

frequency of the wave=………….. Hz. No. of loops, N, Resonating length,L.

1

2

3

4

5

6

7

Draw a graph of L against N

Using the graph, determine the velocity of the wave in the vibrating string at Local A.C. mains.

C12- WHEATSTONE BRIDGE

Aim: to find the values of resistances

X1

, X2

and X3

To find out whether the formulas of 1. Resistances in series 2. And parallel are true.

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To find the resistivity of the material of the wire given

Theory

When resistances are connected as shown in Fig. 2 below, they constitute a wheatstone network. If P, Q and R are known resistances adjusted in such away that the galvanometer G reads zero, the

points B and D will be at the same potential and no current flows between them. The network is said to be balanced. Thus:If the current through the meter is Ig = 0 , I

1 =I

3 and I

2=I

4.Or I

2/I

1=I

4/I

3 also

PI1

/RI2

=QI3 =XI

4. Hence X = QR/P. If the above condition is satisfied then it is possible to use the network to determine the value of the unknown resistance X

Apparatus: Decade resistance box, wheat stone bridge, dry cell, three assorted resistors, galvanometer, resistivity wire, galvanometer and assorted wires.

Procedure/method: In Fig. below , P and Q are resistances of the portions AB and BC respectively, of a wire of uniform resistance. Commonly, this wire is 50 or

100 cm long. The point B on the wire is where the galvanometer G shows no deflection. P and Q will be proportional to the lengths AB and BC of the wire, respectively.

R is a standard resistance (decade resistance box). Set up the circuit as shown in Fig. 1 above. Find an approximate balance point with the protective resistor in the circuit (NB: this resistor limits

current flowing in the galvanometer). Now obtain the accurate balance point by shorting this protective resistor. Reverse the terminals of the accumulator E and repeat the measurement. Interchange R and X,

and repeat the procedure. How does the balance point change? Repeat the experiment for two other resistors X and tabulate your results with errors.Measure the resistances of the unknown resistor X and

compare the values with those from your experiment.

Use the chart below to determine the values of the resisances using the colour bands or codes.

Color 1st – significant figure 2nd – significant figure 3rd – multiplier 4th – tolerance

Black 0 0 100 + 0%

Brown 1 1 101 + 1%

Red 2 2 102 + 2%

Orange 3 3 103 -

yellow 4 4 104 + 5%

Green 5 5 105 + 0.5%

Blue 6 6 106 + 0.25%

violet 7 7 107 + 0.1%

Grey 8 8 108 + 0.5% (+10%)

white 9 9 109 -

Gold - - 10-1 + 5%

Silver - - 10-2 +10%

None - - - +20%

Part 2: Resistivity of the wire

Now use the bridge to measure the resistance of each of the wire given. Before connecting the battery to the

bridge, carefully check that all the connections are correct. Get the wire, attach it to the bridge, and set the

decade box resistance Rk to be as near to Rx as possible(you know Rx roughly from your DMM

measurements). Balance the bridge by moving the sliding contact along the wire while watching the

galvanometer. With the bridge balanced, measure L1 and L2, and compute

(11) .

Repeat this procedure as the table below shows.

From the results from the table , compute the average resistivity, and the uncertainty of the average (

). Compare your average value with the known value.

Ig

I1 I

3

I4 I

2

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Now use the resistance meter to determine the actual values of the resistances.

TABLE OF RESULTS :

LENGTHS DUE TO TERMINALS UNREVERSED TERMINALS REVERSED Actual resistance (meter)

P Q P Q

X1

X2

X3

X1 and X2 series

X1 and X3 series

X2 and X3 series

X1 , X2and X3 series

X1 and X2 parallel

X2and X3parallel

X1 and X3parallel

X1 , X2and X3parallel

Wire given length= ...………cm Diameter= …………. mm

AFTER INTERCHANGING R AND X:

LENGTHS DUE TO TERMINALS UNREVERSED TERMINALS REVERSED Actual resistance (meter)

P Q P Q

X1

X2

X3

X1 and X2 series

X1 and X3 series

X2 and X3 series

X1 , X2and X3 series

X1 and X2 parallel

X2and X3parallel

X1 and X3parallel

X1 , X2and X3parallel

Wire given length= ...………cm

Diameter= …………. mm

Questions: How would the resistance per unit length change if you used: A) a shorter wire B)a thicker wire, than

that used in Q. 2 above.What are the possible sources of error in the experiment?

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W4 THE RIPPLE TANK

AIMS: The aims of this experiment are:

1. To observe the characteristics and behavior of water waves.

2. To show the analogy between water waves and light waves.

APPARATUS Water ripple tank, Metal reflectors , Low voltage power unit (3.0 V D-C) ,Ammeter ,Variable resistor, Motor Vibrator, Lamp, Level.

INTRODUCTION The ripple tank is an apparatus for studying the phenomena of water waves. The wave generator is a vibrator set into motion by a 3V.D.C Motor. A variable

resistor in series with the motor varies its speed and therefore the frequency of vibrations. A lamp illuminates the wave pattern. The wave pattern is projected on

the table through the transparent bottom of tank. If one wishes to copy a wave pattern on paper the paper can be spread out on the table under the ripple tank.

When measuring wavelengths or other distances remember to measure these lengths as they are in the ripple tank. For calibration place an object of known length

on the bottom of the ripple tank and measure the length of its image.The ripple tank should be leveled using the spirit level. Use so much water that it stands

midways on the sloping walls. The wave generator with wooden plate and motor has to be raised or lowered so that the wave source just touches the water surface.

The wave pattern can be ‘stopped’ by viewing through stroboscope.

Single point source 1. Screw the bent metal rod onto the front of the place of the wave generator so that the rod points forwards. Switch on the power and let the motor run

slowly observe and draw a fig.1.

2. Place small pieces of paper on the water and see if they move. Are the pieces of paper displaced at the wave speed? If not explain your observations.

3. Switch off the power and remove the bent metal rod. Lower the plane generator to touch just touch the water surface.

4. Place the plane reflector at a small distance in front of the generator.

5. Observe the reflected pulse and draw a fig.2. Where is the center from which the reflected pulse seems to diverge? Compare your observations with

the plane mirror image of a light source.

6. Repeat step (3) using the two reflectors with a gap of 1-2cm between them observe and draw a fig.3 . Where is the source from which the transmitted

pulse seems to diverge? Compare your observation with Huygen’s principle.

7. Place the metal parabolic reflector (convex side) so that the point source is at its focus. Give a single push to the generator to produce a wave pulse.

Observe (and draw a fig.4 ) the reflected pulse and compare with the effect of a parabolic mirror when a light source is placed at its focus.

8. Repeat 7 metal parabolic reflector (concave side) observe and draw a fig.5

Two Synchronous point sources Attach the two bent metal rods to the plate of the wave generator. Start the vibrator. Observe and observe and draw a fig.4 the curves where the two waves

interfere so that the water is at rest. Vary the frequency of the waves by increasing the speed of the vibrator and observe observe and draw a fig.6 then explain the

effect on the interference pattern.

A Plane Wave 1. Use the plate of the wave generator itself as a source of waves. Produce waves with a wavelength about 2.5cm or to do this move the plate to and fro by

hand.

2. Place the long reflector diagonally in the tank and observe reflected waves. Compare your observation with the law of reflection for light observe and

draw a fig.7.

3. Replace the long reflector by the two shorter reflectors parallel to the wave fronts 5-6cm away from the wave generator and as far as possible from each

other. Generate waves by hand or with the motor (about 2cm)observe observe and draw a fig.8. Decrease the distance between the two reflectors until

about 1cm. Observe the wave fronts observe and draw a fig.9 then compare this with Huygen’s principle.

4. Place the very short reflector between the two reflectors so that two open spaces of 1cm or less are left between the reflectors. Observe (and draw a

fig.10) the interferences pattern and compare with the results of experiment W4.2 and the experiment of Young.

5. Now remove the reflectors and put the rectangular plane block in the ripple tank at about 5cm from the plane wave generator. The length of the block

should parallel to the wave fronts observe and observe and draw a fig.11.

6. Repeat 5 above with the block length about 450 to the wave front observe and draw a fig.12

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The Report The report should include the observations with carefully drawn neat figures and explanation where applicable as well as answers to every question.

PRECISION MEASUREMENTS- A1

Objectives:

To study some of the instruments and methods used in precision measurements , and to compute the volume and density of various items.

Apparatus:

Metre rule, vernier calipers ,micrometer screw gauge ,electronic balance and traveling microscope .Such items as copper cylinder , steel ball and glass

capillary tube are also supplied.

METHOD:

The experiment comprises e measurement of the various objects supplied with the appropriate instruments. Where feasible, at least two

instruments should be used for each measurement and the precision obtained in each case compared. In this way, the volume and density of atleast

two metal objects weighings should be done on the electronic balance.

In the second part of the experiment, some electrical circuits have been set up for you to measure the current. Measure the current using an ammeter, a

milliammeter and a microammeter, and estimate the reading errors in each case.

N.B. in all cases an estimate of the precision obtained should be, i.e. note the reading errors on all measurements. Where appropriate note the zero error.

Record the data in work sheet 1,working out any calculations asked for. Answer the questions posed on the sheet.

WORKSHEET 1

N.B. You must include in the table the units of any measurements you take.

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ITEMS

MEASURING INSTRUMENTS

Meter

rule

Vernier

calipers

Micrometer

Screw Gauge

Balance

Ammeter

Milli

Ammeter

Voltmeter

Travelling

Microscope

Zero error

Reading error

Copper cylinder:

height

Diameter (external)

Diameter (internal)

Steel Ball: Diameter

Copper wire: length

Diameter

glass rod:

diameter

length

Current

Analysis :

volume Density of the material

Copper cylinder:

Internal volume

External volume

Steel bar

Capillary tube

Internal volume

External volume

Calculation of voltage:

Instrument Value of

Resistances

Calculated RESISTANCE V= IR

From Ammeter

From Milli-Ammeter

From micro Ammeter

ERRORS

Now work out the errors in volumes and densities and voltages calculated above using the reading errors of the appropriate instruments. Refer to the section on

errors in this manual for instructions on how to calculate errors.

volume Density of the material

Copper cylinder:

Internal volume

External volume

Steel bar

Capillary tube

Internal volume

External volume

Instrument Calculated RESISTANCE V= IR

From Ammeter

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From Milliammeter

From micro Ammeter

QUESTIONS:

1. Why is it appropriate to use the metre rule for measuring the length of the copper wire but the micrometer screw gauge for he diameter?

2. .What is the difference between accuracy and precision?

CONCLUSION:

The volume of the copper cylinder was found to be ------------------

-----------------------------------(units) ,and its density was found to be------------------------ ------------------- ------------ (units)

Write similar conclusions for the steel ball `and capillary tube , and give correct values for the densities of copper and steel . The values may

be found in the reference book Tables of physical and chemical constants,15th Edition , G.W.C. Kaye.and Labye (Longman 1986 ) .