Ace Ahead .Physics Vol 1. Student. Practical Guide

1

Guidelines for STPM Physics Practical Examination

Introduction

This practical guide lists the aims, apparatus and procedures for selected experiments. The techniques, precautions, formulae and calculations which are relevant to the experiments are also included.

The section on techniques brings attention to more effi cient means of conducting the experiments. The section on precautions lists the steps to ensure a smaller error margin in the results obtained. The section on formulae and calculations helps students apply the results of the experiments and obtain the fi nal conclusion.

This practical guide does not provide experimental data or results. The actual data and results are subject to the specifi c conditions under which the experiments were conducted.

Guide to STPM Practicals

AA STPM Phys V1 Guideline 3rd.indd 1 3/7/2008 4:53:06 PM

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Calculations: T = 2π l—g

T 2 = 4π2

�——�g l

Hence, gradient = 4π2——g

g = 4π2

————gradient

From the graph, gradient = y2 – y1———x2 – x1

= b

∴ g = 4π2——b = k m s–2

Sources of errors/limitations: 1. Reaction times are inconsistent when measuring the time of oscillation. 2. Zero error on the stopwatch. 3. Pendulum is not oscillating in one plane. 4. Angle of oscillation is too large.

Steps taken to reduce the errors/overcome the limitations: 1. Reaction time can be reduced by making the time interval between the starting and stopping of

the stopwatch as large as possible. 2. Correct the zero error if it exists. 3. Restart the oscillation if it is not oscillating in one plane. 4. Make sure the angle between the pendulum and the vertical line through its equilibrium position

is not more than 10°.

Graph of T 2 against l

(x2, y2)

T 2(s2)

(x1, y1)

For a straight line graph, draw the best fit line by ensuring that the points scatter equally about the line.

Good choices of scales are 1:1, 1:2, 1:5, 1:10, etc.

Quantity/unit

Quantity/unit

(m)0 l


2

SAMPLE EXPERIMENT

Aim: To measure the acceleration due to gravity g using a simple pendulum.Apparatus: 1. A pendulum 2. Thread of length 160 cm 3. A stopwatch 4. A retort stand and a clamp 5. Cork padsProcedure: 1. Set up the apparatus as shown below.

2. Measure the length l of the pendulum. 3. Set the pendulum oscillating and measure the time for an appropriate number of oscillations. Repeat

the measurement to obtain the average time. Hence, calculate the corresponding period T. 4. Plot a graph of T 2 against l. 5. Using the graph, calculate the value of g.

Pendulum length,l (m)

Time for 20 oscillations, 20T Period of oscillation,

T (s)

(Period)2 T 2(s2)t1(s) t2(s) Average, t (s)

0.65 32.5 32.7 32.6 1.63 2.66

0.75 33.1 36.9 35.0 1.75 3.06

0.85

0.95

1.05

1.15

1.25

Raw data (measurements) are on the left hand side.

Processed data (calculated values) are on the right hand side.

Processed data

General rule:Processed data should be written in the same number of signifi cant fi gures as the raw data.

The quantity and unit of measurement for each column must be shown, e.g. l (m), t1(s), t2(s), t (s), T (s), T 2(s2)

The uncertainty in the measurement must be refl ected by the number of decimal places. The uncertainty in the reading of a metre rule is ±0.01 m. Hence, the reading is recorded to two decimal places.

The number of decimal places for all data must be consistent.

Uncertainty in the reading of stopwatch (with 0.2 s division) is ±0.1 s. Hence, the reading is recorded to one decimal place.

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Results:

PendulumRetort

stand

Cork

l

➤

Raw data

➤


3

Calculations: T = 2π l—g

T 2 = 4π2

�——�g l

Hence, gradient = 4π2——g

g = 4π2

————gradient

From the graph, gradient = y2 – y1———x2 – x1

= b

∴ g = 4π2——b = k m s–2

Sources of errors/limitations: 1. Reaction times are inconsistent when measuring the time of oscillation. 2. Zero error on the stopwatch. 3. Pendulum is not oscillating in one plane. 4. Angle of oscillation is too large.

Steps taken to reduce the errors/overcome the limitations: 1. Reaction time can be reduced by making the time interval between the starting and stopping of

the stopwatch as large as possible. 2. Correct the zero error if it exists. 3. Restart the oscillation if it is not oscillating in one plane. 4. Make sure the angle between the pendulum and the vertical line through its equilibrium position

is not more than 10°.

Graph of T 2 against l

(x2, y2)

T 2(s2)

(x1, y1)

For a straight line graph, draw the best fit line by ensuring that the points scatter equally about the line.

Good choices of scales are 1:1, 1:2, 1:5, 1:10, etc.

Quantity/unit

Quantity/unit

(m)0 l


2

SAMPLE EXPERIMENT

Aim: To measure the acceleration due to gravity g using a simple pendulum.Apparatus: 1. A pendulum 2. Thread of length 160 cm 3. A stopwatch 4. A retort stand and a clamp 5. Cork padsProcedure: 1. Set up the apparatus as shown below.

2. Measure the length l of the pendulum. 3. Set the pendulum oscillating and measure the time for an appropriate number of oscillations. Repeat

the measurement to obtain the average time. Hence, calculate the corresponding period T. 4. Plot a graph of T 2 against l. 5. Using the graph, calculate the value of g.

Pendulum length,l (m)

Time for 20 oscillations, 20T Period of oscillation,

T (s)

(Period)2 T 2(s2)t1(s) t2(s) Average, t (s)

0.65 32.5 32.7 32.6 1.63 2.66

0.75 33.1 36.9 35.0 1.75 3.06

0.85

0.95

1.05

1.15

1.25

Raw data (measurements) are on the left hand side.

Processed data (calculated values) are on the right hand side.

Processed data

General rule:Processed data should be written in the same number of signifi cant fi gures as the raw data.

The quantity and unit of measurement for each column must be shown, e.g. l (m), t1(s), t2(s), t (s), T (s), T 2(s2)

The uncertainty in the measurement must be refl ected by the number of decimal places. The uncertainty in the reading of a metre rule is ±0.01 m. Hence, the reading is recorded to two decimal places.

The number of decimal places for all data must be consistent.

Uncertainty in the reading of stopwatch (with 0.2 s division) is ±0.1 s. Hence, the reading is recorded to one decimal place.

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➤

➤

➤

➤ ➤ ➤ ➤ ➤ ➤

⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩ ⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

Results:

PendulumRetort

stand

Cork

l

➤

Raw data

➤


5

Chapter 2 Kinematics and Dynamics

Experiment BAim: To verify the principle of conservation of linear momentum for a collision of two bodies of

equal mass.Plan: 1. Set up the apparatus as shown below.

2. Determine the position of the centre of each bob, X01 and X02.

Technique:• Use another ruler to help determine the position of the centre of the bob more accurately.• Move one bob away while determining the centre of the other bob. Repeat the process and record

the position of the centre of the other bob.

3. Displace one of the bobs approximately 20 cm away. Record the position of the centre of the bob, X1. Then release the bob.

Technique:• Make sure the collision is head-on. If a head-on collision occurs, the fi rst bob will be at rest and

the other bob will swing away. Repeat this step if head-on collision does not occur.

4. Record the position of the centre of the second bob, X2.

Technique:• Use the screen marker to measure X2.

5. Repeat the above steps for displacements in the range between 10 cm and 20 cm.6. Record all the readings and tabulate X1, Z1 = (X1 – X01), X2 and Z2 = (X2 – X01).

Metal wire

Block

Metre rule

Screen as marker

Retortstand

Hookingplank

Bob

Hooks

Bob

Metre rule

Another rulerperpendicularto the metrerule

Position of the centre of bob


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Guidelines for STPM Practical Examination

Chapter 1 Physical Quantities and Units

Experiment AAim: To fi nd the density of 1. PVC 2. Steel 3. Cooking oilPlan: 1. (a) Measure the internal diameter, external diameter and length of a PVC tube using vernier

callipers. (b) Use a triple beam balance or an electronic balance to fi nd the mass of the tube.

Technique:• Measure the internal diameter, external diameter and length of the tube at different points.• Determine the average external diameter, internal diameter and length of the tube.

2. (a) Measure the length and the diameter of a steel wire. (b) Use a triple beam balance or an electronic balance to fi nd the mass of the steel wire.

Technique:• Measure the diameter of the wire at different points.• Determine the average diameter of the wire.

3. Measure the mass of 200 cm3 of cooking oil.

Technique:• Weigh an empty measuring cylinder.• Fill the measuring cylinder with 200 cm3 of cooking oil.• Weigh the fi lled measuring cylinder.

Precautions:• Check that the triple beam balance or electronic balance is zeroed.• (a) Make sure the cylinder is dry before measuring the mass of the cylinder. (b) After fi lling the cylinder with cooking oil, dry the outside of the cylinder before measuring

again.• Take note of the temperature of the cooking oil as its density is affected by temperature.

Formula:

mass, mDensity, ρ = ————— volume, V

Calculations:

1. Volume of PVC tube = π—4

(D2 – d 2)l

where D = external diameter d = internal diameter l = length

2. Volume of steel wire = π—4

D2l

where D = diameter l = length

3. Mass of cooking oil = M – M' where M = mass of cylinder and cooking oil M' = mass of empty cylinder


5

Chapter 2 Kinematics and Dynamics

Experiment BAim: To verify the principle of conservation of linear momentum for a collision of two bodies of

equal mass.Plan: 1. Set up the apparatus as shown below.

2. Determine the position of the centre of each bob, X01 and X02.

Technique:• Use another ruler to help determine the position of the centre of the bob more accurately.• Move one bob away while determining the centre of the other bob. Repeat the process and record

the position of the centre of the other bob.

3. Displace one of the bobs approximately 20 cm away. Record the position of the centre of the bob, X1. Then release the bob.

Technique:• Make sure the collision is head-on. If a head-on collision occurs, the fi rst bob will be at rest and

the other bob will swing away. Repeat this step if head-on collision does not occur.

4. Record the position of the centre of the second bob, X2.

Technique:• Use the screen marker to measure X2.

5. Repeat the above steps for displacements in the range between 10 cm and 20 cm.6. Record all the readings and tabulate X1, Z1 = (X1 – X01), X2 and Z2 = (X2 – X01).

Metal wire

Block

Metre rule

Screen as marker

Retortstand

Hookingplank

Bob

Hooks

Bob

Metre rule

Another rulerperpendicularto the metrerule

Position of the centre of bob


4

Guidelines for STPM Practical Examination

Chapter 1 Physical Quantities and Units

Experiment AAim: To fi nd the density of 1. PVC 2. Steel 3. Cooking oilPlan: 1. (a) Measure the internal diameter, external diameter and length of a PVC tube using vernier

callipers. (b) Use a triple beam balance or an electronic balance to fi nd the mass of the tube.

Technique:• Measure the internal diameter, external diameter and length of the tube at different points.• Determine the average external diameter, internal diameter and length of the tube.

2. (a) Measure the length and the diameter of a steel wire. (b) Use a triple beam balance or an electronic balance to fi nd the mass of the steel wire.

Technique:• Measure the diameter of the wire at different points.• Determine the average diameter of the wire.

3. Measure the mass of 200 cm3 of cooking oil.

Technique:• Weigh an empty measuring cylinder.• Fill the measuring cylinder with 200 cm3 of cooking oil.• Weigh the fi lled measuring cylinder.

Precautions:• Check that the triple beam balance or electronic balance is zeroed.• (a) Make sure the cylinder is dry before measuring the mass of the cylinder. (b) After fi lling the cylinder with cooking oil, dry the outside of the cylinder before measuring

again.• Take note of the temperature of the cooking oil as its density is affected by temperature.

Formula:

mass, mDensity, ρ = ————— volume, V

Calculations:

1. Volume of PVC tube = π—4

(D2 – d 2)l

where D = external diameter d = internal diameter l = length

2. Volume of steel wire = π—4

D2l

where D = diameter l = length

3. Mass of cooking oil = M – M' where M = mass of cylinder and cooking oil M' = mass of empty cylinder


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Technique:• Measure the value of h by placing a metre rule perpendicular to the ground.

3. Record the time t for the load to reach the ground.

Technique:• Take a few readings for t and fi nd the average time.

4. Use different values of m and record the corresponding values of t.5. Plot a graph of α against T. Hence, determine the moment of inertia of the wheel.

Precautions:• Make sure that the fl ywheel does not wobble as it turns. Also, ensure that the load is falling

straight down and not swinging sideways.• Let the thread cool down if it becomes too hot due to friction. Its length will increase due to

expansion, causing the value of h to change.

Calculations:

Considering the forces on the load, mg – T = ma T = m(g – a)

Considering the motion of the flywheel, TR – τ = Iα (I = miri

2)where τ = torque due to friction α = angular acceleration R τ ∴ α = —T – — I I

By plotting the graph of α against T,

Metrerule

h

R

T

mgh

T (N)

(rad s–2)

I

α

τ–

0

R Gradient = — I R I = ———— gradient


6

Precautions:• Make sure that the two pendulum bobs have the same mass. Otherwise, stick some plasticine so

that the bobs have the same mass.• The hooks that hold the string of the bobs must be separated by a distance which is equal to the distance

d(= X01 – X02) between the centres of the bobs when they are in contact.

Formula:Linear momentum = mvwhere m = mass v = velocity

Calculations:It can be shown that v ∝ Z.Based on the principle of conservation of linear momentum,

m1v1 = m2v2

where m1, m2 = masses of the bobs v1 = velocity of the fi rst bob before collisionand v2 = velocity of the second bob after collisionSince m1 = m2 and v ∝ Z, m1v1 = m2v2

v1 = v2

Z1 = Z2

Chapter 5 Rotation of a Rigid Body

Experiment CAim: To determine the moment of inertia of a fl ywheel.Plan: 1. Set up the apparatus as shown below.

2. Release the load from a height of h.

Same distance d

d

d

Axle

Flywheel

Thread

Load

mgh

T

Radius R


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Technique:• Measure the value of h by placing a metre rule perpendicular to the ground.

3. Record the time t for the load to reach the ground.

Technique:• Take a few readings for t and fi nd the average time.

4. Use different values of m and record the corresponding values of t.5. Plot a graph of α against T. Hence, determine the moment of inertia of the wheel.

Precautions:• Make sure that the fl ywheel does not wobble as it turns. Also, ensure that the load is falling

straight down and not swinging sideways.• Let the thread cool down if it becomes too hot due to friction. Its length will increase due to

expansion, causing the value of h to change.

Calculations:

Considering the forces on the load, mg – T = ma T = m(g – a)

Considering the motion of the flywheel, TR – τ = Iα (I = miri

2)where τ = torque due to friction α = angular acceleration R τ ∴ α = —T – — I I

By plotting the graph of α against T,

Metrerule

h

R

T

mgh

T (N)

(rad s–2)

I

α

τ–

0

R Gradient = — I R I = ———— gradient


6

Precautions:• Make sure that the two pendulum bobs have the same mass. Otherwise, stick some plasticine so

that the bobs have the same mass.• The hooks that hold the string of the bobs must be separated by a distance which is equal to the distance

d(= X01 – X02) between the centres of the bobs when they are in contact.

Formula:Linear momentum = mvwhere m = mass v = velocity

Calculations:It can be shown that v ∝ Z.Based on the principle of conservation of linear momentum,

m1v1 = m2v2

where m1, m2 = masses of the bobs v1 = velocity of the fi rst bob before collisionand v2 = velocity of the second bob after collisionSince m1 = m2 and v ∝ Z, m1v1 = m2v2

v1 = v2

Z1 = Z2

Chapter 5 Rotation of a Rigid Body

Experiment CAim: To determine the moment of inertia of a fl ywheel.Plan: 1. Set up the apparatus as shown below.

2. Release the load from a height of h.

Same distance d

d

d

Axle

Flywheel

Thread

Load

mgh

T

Radius R


9

Technique:• Record the angle θ only when the pendulum is stationary.

4. Add more wooden blocks on top of the fi rst. Record the new combined mass m. Repeat step 3.

5. Determine the mass m' for the corresponding length l2 from the graph l1 against m1.6. Plot a graph of m' against m.

Precautions:• Do not exceed the elastic limit of the spring when adding wooden blocks.• Displace the wooden block slowly so that the block does not oscillate.

Formula:T – mg sin θ = µmg cos θwhere µ = coefficient of static friction

Calculations: T – mg sin θ = µmg cos θ m'g – mg sin θ = µmg cos θ m' = m(µ cos θ + sin θ) where m' = mass corresponding to tension T

m'—–m = µ cos θ + sin θ

Gradient = µ cos θ + sin θ

µ = gradient – sin θ—–——————

cos θ

Chapter 8 Simple Harmonic Motion

Experiment EAim: To determine the acceleration due to gravity g using simple pendulum and to investigate the

effect of large amplitude oscillations.Plan: 1. Set up the apparatus as shown below.

2. Measure the length l of the pendulum.

mg

mg sin

Tension of spring T

m (kg)0

m' (kg)

Gradient = cos + sinµ

Pendulum

Protractor

Retort stand

Weight

Cork

l


8

Let t = time taken to reach the ground,

s = ut + 1—2

at2

Since u = 0, s = h, h = 1—2

at2

⇒ a = 2h—–t 2 , where a = acceleration of the load

Using a = Rα ⇒ α = a—R

= 2h—–Rt 2

Chapter 6 Statics

Experiment DAim: To determine the coeffi cient of static friction between two surfaces.Part 1: To determine the relationship between the mass of the load and the length of the spring.Plan: 1. Set up the apparatus as shown below.

2. Measure the length l1 of the spring. Record the mass m1 of the hanger and the slotted mass.

3. Increase the mass m1 and record the length l1 of the spring.4. Tabulate the values of m1 and l1.5. Plot a graph of l1 against m1.

Precautions:• Do not exceed the elastic limit of the spring.• Position the eyes at the same level as the pointer when taking the readings of l1.

Formula: F = kx (Hooke’s law)where F = weight of load k = force constant x = extension of spring

Part 2: To determine the coeffi cient of friction between two surfaces.Plan: 1. Set up the apparatus as shown below.

2. Record the mass of the wooden block. The plane is inclined at an angle of θ in such a way that the wooden block slides down with an acceleration.

3. Release the wooden block. Reduce the angle of inclination θ until the wooden block stays stationary upon release. Record the length l2 of the spring.

Retort stand

Metre rule

SpringPointer

Slottedmass

Masshanger

PendulumWeight

Protractor

Spring

Hook

Plane

Wooden block


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Technique:• Record the angle θ only when the pendulum is stationary.

4. Add more wooden blocks on top of the fi rst. Record the new combined mass m. Repeat step 3.

5. Determine the mass m' for the corresponding length l2 from the graph l1 against m1.6. Plot a graph of m' against m.

Precautions:• Do not exceed the elastic limit of the spring when adding wooden blocks.• Displace the wooden block slowly so that the block does not oscillate.

Formula:T – mg sin θ = µmg cos θwhere µ = coefficient of static friction

Calculations: T – mg sin θ = µmg cos θ m'g – mg sin θ = µmg cos θ m' = m(µ cos θ + sin θ) where m' = mass corresponding to tension T

m'—–m = µ cos θ + sin θ

Gradient = µ cos θ + sin θ

µ = gradient – sin θ—–——————

cos θ

Chapter 8 Simple Harmonic Motion

Experiment EAim: To determine the acceleration due to gravity g using simple pendulum and to investigate the

effect of large amplitude oscillations.Plan: 1. Set up the apparatus as shown below.

2. Measure the length l of the pendulum.

mg

mg sin

Tension of spring T

m (kg)0

m' (kg)

Gradient = cos + sinµ

Pendulum

Protractor

Retort stand

Weight

Cork

l


8

Let t = time taken to reach the ground,

s = ut + 1—2

at2

Since u = 0, s = h, h = 1—2

at2

⇒ a = 2h—–t 2 , where a = acceleration of the load

Using a = Rα ⇒ α = a—R

= 2h—–Rt 2

Chapter 6 Statics

Experiment DAim: To determine the coeffi cient of static friction between two surfaces.Part 1: To determine the relationship between the mass of the load and the length of the spring.Plan: 1. Set up the apparatus as shown below.

2. Measure the length l1 of the spring. Record the mass m1 of the hanger and the slotted mass.

3. Increase the mass m1 and record the length l1 of the spring.4. Tabulate the values of m1 and l1.5. Plot a graph of l1 against m1.

Precautions:• Do not exceed the elastic limit of the spring.• Position the eyes at the same level as the pointer when taking the readings of l1.

Formula: F = kx (Hooke’s law)where F = weight of load k = force constant x = extension of spring

Part 2: To determine the coeffi cient of friction between two surfaces.Plan: 1. Set up the apparatus as shown below.

2. Record the mass of the wooden block. The plane is inclined at an angle of θ in such a way that the wooden block slides down with an acceleration.

3. Release the wooden block. Reduce the angle of inclination θ until the wooden block stays stationary upon release. Record the length l2 of the spring.

Retort stand

Metre rule

SpringPointer

Slottedmass

Masshanger

PendulumWeight

Protractor

Spring

Hook

Plane

Wooden block


11

Chapter 9 Oscillations

Experiment FAim: To study the damped oscillation of a spring-mass system in air.Plan: 1. Set up the apparatus as shown below.

2. Record the mass m of the load and the reading y0 on the metre rule when the spring is in equilibrium.

Technique:• Record the reading y0 only when the load is completely still.

3. Displace the load with a small amplitude and determine the period of oscillation T.

Technique:• Measure the time for an appropriate number of oscillations. Calculate the average time and

determine the period of oscillation T.

4. Displace the load downwards by 6.0 cm from the equilibrium position and release it. Count the number of oscillations when the amplitude A of the oscillation drops to 5.0 cm.

Technique:• Locate a mark on the metre rule where the amplitude A is 5.0 cm. Once the indicator pin stops

at that mark, start counting the number of oscillations.

Precautions:• Secure the mass and spring properly so that the oscillation is only one-dimensional.• Do not exceed the elastic limit of the spring.

5. Record the reading y indicated by the pin after every 20 oscillations until the number of oscillations N = 200.

6. Tabulate N, y, A = |y0 – y| and ln A.7. Plot a graph of ln A against N and determine the gradient, k =

∆ln A—–—∆N .

Formula: Damping factor, b = 2mk——

T and time for the amplitude to reduce to half of the original value,

τ = 2m ln 2———–

b

Retort stand

Weight

Metre rule

Spring

Indicator pin

Nail

Cork

Load


10

Technique:• Measure the length of the pendulum by placing a metre rule next to it.

3. Displace the pendulum to one side and record the time for an appropriate number of oscillations. Repeat the measurements and obtain an average time, then determine the corresponding period T.

Technique:• Let the pendulum swing a few oscillations before starting the stopwatch.

4. Repeat the above steps for different values of l. Tabulate the readings for l and T.5. Plot a graph of T 2 against l. Hence, determine the value of g.6. Fix the length l at 120 cm and displace the bob by 70° from the vertical before release.7. Record the time for fi ve oscillations. Hence, calculate the period T.

8. Calculate the value of g using the formulae T' = 2π l—g (1 + 1—4

sin2 θ—2

) and T = 2π l—g .

Use the values of l and T from step 4.9. Compare the values of T' and T.

Precautions:• The displacement of the pendulum in step 3 must not be too large (�10°).• Make sure the pendulum is oscillating in one plane.• Correct the zero error of the stopwatch if it exists.

Formula:

T = 2π l—g

Calculations:

T = 2π l—g

T 2 = 4π2

�—–�g l

Hence, gradient = 4π2—–g

g = 4π2

—–——gradient

For large angle of displacement θ,

T = 2π l—g (1 + 1—4

sin2 θ—2

)

Metre rule

l

(m)0

T 2(s

2)

Gradient = 4 2

gπ

l


11

Chapter 9 Oscillations

Experiment FAim: To study the damped oscillation of a spring-mass system in air.Plan: 1. Set up the apparatus as shown below.

2. Record the mass m of the load and the reading y0 on the metre rule when the spring is in equilibrium.

Technique:• Record the reading y0 only when the load is completely still.

3. Displace the load with a small amplitude and determine the period of oscillation T.

Technique:• Measure the time for an appropriate number of oscillations. Calculate the average time and

determine the period of oscillation T.

4. Displace the load downwards by 6.0 cm from the equilibrium position and release it. Count the number of oscillations when the amplitude A of the oscillation drops to 5.0 cm.

Technique:• Locate a mark on the metre rule where the amplitude A is 5.0 cm. Once the indicator pin stops

at that mark, start counting the number of oscillations.

Precautions:• Secure the mass and spring properly so that the oscillation is only one-dimensional.• Do not exceed the elastic limit of the spring.

5. Record the reading y indicated by the pin after every 20 oscillations until the number of oscillations N = 200.

6. Tabulate N, y, A = |y0 – y| and ln A.7. Plot a graph of ln A against N and determine the gradient, k =

∆ln A—–—∆N .

Formula: Damping factor, b = 2mk——

T and time for the amplitude to reduce to half of the original value,

τ = 2m ln 2———–

b

Retort stand

Weight

Metre rule

Spring

Indicator pin

Nail

Cork

Load


10

Technique:• Measure the length of the pendulum by placing a metre rule next to it.

3. Displace the pendulum to one side and record the time for an appropriate number of oscillations. Repeat the measurements and obtain an average time, then determine the corresponding period T.

Technique:• Let the pendulum swing a few oscillations before starting the stopwatch.

4. Repeat the above steps for different values of l. Tabulate the readings for l and T.5. Plot a graph of T 2 against l. Hence, determine the value of g.6. Fix the length l at 120 cm and displace the bob by 70° from the vertical before release.7. Record the time for fi ve oscillations. Hence, calculate the period T.

8. Calculate the value of g using the formulae T' = 2π l—g (1 + 1—4

sin2 θ—2

) and T = 2π l—g .

Use the values of l and T from step 4.9. Compare the values of T' and T.

Precautions:• The displacement of the pendulum in step 3 must not be too large (�10°).• Make sure the pendulum is oscillating in one plane.• Correct the zero error of the stopwatch if it exists.

Formula:

T = 2π l—g

Calculations:

T = 2π l—g

T 2 = 4π2

�—–�g l

Hence, gradient = 4π2—–g

g = 4π2

—–——gradient

For large angle of displacement θ,

T = 2π l—g (1 + 1—4

sin2 θ—2

)

Metre rule

l

(m)0

T 2(s

2)

Gradient = 4 2

gπ

l


13

Chapter 11 Sound Waves

Experiment HAim: To determine the velocity of sound using a resonant tube.Plan: 1. Set up the apparatus as shown below. Start with a length l of air column of about 35.0 cm.

2. Slowly adjust the output of the audio generator from 0 Hz until the fi rst resonance is heard. Record the length l of the air column and the resonant frequency f when this occurs.

Technique:• Place the ear at the same level as the mouth of the cylinder. When resonance occurs, the volume

of sound from the air column is a maximum.

Precautions:• Place a metre rule next to the measuring cylinder to measure l.

• In order to be sure that the sound level is maximum, adjust the frequency of the generator above and below the frequency when resonance is fi rst heard. If the sound level is lower when the frequency is adjusted, the initial frequency is the resonant frequency.

3. Slowly decrease l until l = 10.0 cm by adding water into the measuring cylinder. Repeat step 2.

4. Tabulate the values of l, f and 1—

f . 5. Plot a graph of l against 1—

f .

Formula:

l + ε = λ—4where ε = end correction λ = wavelength of sound

Retort stand

1 cm

Measuringcylinder

Water

Audiogenerator

l

Metre rule

l


12

Chapter 10 Wave Motion

Experiment GAim: To study the stationary wave in a string and to determine the mass per unit length of the

string.Plan: 1. Set up the apparatus as shown below.

2. Connect the copper wire coil to the 2 V, 50 Hz power supply.3. Magnadur magnets are placed above and below the metal rod.4. Secure one end of the thread to the metal rod and the other end to the dish.

Technique:• Make sure the thread is properly secured and long enough (� 1.5 m).

5. Turn on the power supply. Adjust the length of the metal rod until it is vibrating at maximum amplitude. Clamp the metal rod when it is vibrating at maximum amplitude.

Technique:• Try different lengths of the metal rod before clamping it.

6. Place the wedge below the thread and next to the pulley. Adjust the position of the wedge until a stationary wave is produced.

Technique:• Adjust the wedge below the thread very slowly.

7. Add more masses to the dish and observe the stationary wave. 8. Record the distance l between successive nodes. Tabulate the values of l and W where

W = mg. 9. Plot a graph of W against l 2.10. Determine the gradient of the graph and the mass per unit length of the thread.

Precautions:• Make sure the thread is taut at all times.• Make sure the apparatus is secured properly to the table.

Formula:

f = 1—2l

T—m

where f = frequency of oscillation T = tension in the thread m = mass per unit length l = distance between two successive nodes

Metal rod

Magnadurmagnet

Copperwire coil

Woodenblock

G-clamp

Thread

Wedge

Pulley

Slotted mass

Plastic dish

Powersupply


13

Chapter 11 Sound Waves

Experiment HAim: To determine the velocity of sound using a resonant tube.Plan: 1. Set up the apparatus as shown below. Start with a length l of air column of about 35.0 cm.

2. Slowly adjust the output of the audio generator from 0 Hz until the fi rst resonance is heard. Record the length l of the air column and the resonant frequency f when this occurs.

Technique:• Place the ear at the same level as the mouth of the cylinder. When resonance occurs, the volume

of sound from the air column is a maximum.

Precautions:• Place a metre rule next to the measuring cylinder to measure l.

• In order to be sure that the sound level is maximum, adjust the frequency of the generator above and below the frequency when resonance is fi rst heard. If the sound level is lower when the frequency is adjusted, the initial frequency is the resonant frequency.

3. Slowly decrease l until l = 10.0 cm by adding water into the measuring cylinder. Repeat step 2.

4. Tabulate the values of l, f and 1—

f . 5. Plot a graph of l against 1—

f .

Formula:

l + ε = λ—4where ε = end correction λ = wavelength of sound

Retort stand

1 cm

Measuringcylinder

Water

Audiogenerator

l

Metre rule

l


12

Chapter 10 Wave Motion

Experiment GAim: To study the stationary wave in a string and to determine the mass per unit length of the

string.Plan: 1. Set up the apparatus as shown below.

2. Connect the copper wire coil to the 2 V, 50 Hz power supply.3. Magnadur magnets are placed above and below the metal rod.4. Secure one end of the thread to the metal rod and the other end to the dish.

Technique:• Make sure the thread is properly secured and long enough (� 1.5 m).

5. Turn on the power supply. Adjust the length of the metal rod until it is vibrating at maximum amplitude. Clamp the metal rod when it is vibrating at maximum amplitude.

Technique:• Try different lengths of the metal rod before clamping it.

6. Place the wedge below the thread and next to the pulley. Adjust the position of the wedge until a stationary wave is produced.

Technique:• Adjust the wedge below the thread very slowly.

7. Add more masses to the dish and observe the stationary wave. 8. Record the distance l between successive nodes. Tabulate the values of l and W where

W = mg. 9. Plot a graph of W against l 2.10. Determine the gradient of the graph and the mass per unit length of the thread.

Precautions:• Make sure the thread is taut at all times.• Make sure the apparatus is secured properly to the table.

Formula:

f = 1—2l

T—m

where f = frequency of oscillation T = tension in the thread m = mass per unit length l = distance between two successive nodes

Metal rod

Magnadurmagnet

Copperwire coil

Woodenblock

G-clamp

Thread

Wedge

Pulley

Slotted mass

Plastic dish

Powersupply


15

Formula:

Young’s modulus, E = 4gL3

——bt 3

. M—d

where L = length b = width t = thickness of metre rule M = mass of slotted masses d = defl ection at the end of the ruler

Calculations:

E = 4gL3

——bt 3

. M—d

d = 4gL3

——Ebt 3

M

Gradient = 4gL3

——Ebt 3

E = 4gL3

——bt 3

× 1—–——gradient

Chapter 14 Kinetic Theory of Gases

Experiment JAim: To verify Charles’ law using the air column trapped in a capillary tube.Plan: 1. Set up the apparatus as shown below.

2. Without turning the Bunsen burner on, leave the water to cool.3. Stir the water thoroughly until the temperature does not change, then record the length l of

the air column and the temperature θ.4. Turn on the burner and warm the water by 10 °C. Repeat step 3.

M0

d

Gradient = 4gL3

Ebt 3

Capillary tubeStirrer

Thermometer

Air column

Ruler

Beaker

Wire gauze

Tripod stand

Mixture ofice and water

Concentratedsulphuric

acid

Rubber band

Bunsenburner


14

Calculations:

l + ε = λ—4

Since λ = v—f

, where v = speed of sound in air and f = frequency of audio generator,

l + ε = v—–4f

l = v—4

1�—�f – ε

Gradient = v—4

v = 4 × gradient

Chapter 13 Deformation of Solids

Experiment IAim: To determine Young’s modulus by the cantilever method.Plan: 1. Set up the apparatus as shown below.

2. Place different values of slotted masses M and record the corresponding lengths d.

Technique:• Make sure the metre rule stops moving before taking the reading.

3. Tabulate the values of d and M.4. Plot a graph of d against M.

Precautions:• Always place the hook and slotted masses at the same mark on the metre rule.• Check if the elastic limit has been exceeded. If the extension during loading and unloading does

not change, the elastic limit is not exceeded.

v4

10

Gradient =

l

∫

Wooden blockMetre rule

Hook

G-clamp

d

L

Metre rule

Slottedmasses


15

Formula:

Young’s modulus, E = 4gL3

——bt 3

. M—d

where L = length b = width t = thickness of metre rule M = mass of slotted masses d = defl ection at the end of the ruler

Calculations:

E = 4gL3

——bt 3

. M—d

d = 4gL3

——Ebt 3

M

Gradient = 4gL3

——Ebt 3

E = 4gL3

——bt 3

× 1—–——gradient

Chapter 14 Kinetic Theory of Gases

Experiment JAim: To verify Charles’ law using the air column trapped in a capillary tube.Plan: 1. Set up the apparatus as shown below.

2. Without turning the Bunsen burner on, leave the water to cool.3. Stir the water thoroughly until the temperature does not change, then record the length l of

the air column and the temperature θ.4. Turn on the burner and warm the water by 10 °C. Repeat step 3.

M0

d

Gradient = 4gL3

Ebt 3

Capillary tubeStirrer

Thermometer

Air column

Ruler

Beaker

Wire gauze

Tripod stand

Mixture ofice and water

Concentratedsulphuric

acid

Rubber band

Bunsenburner


14

Calculations:

l + ε = λ—4

Since λ = v—f

, where v = speed of sound in air and f = frequency of audio generator,

l + ε = v—–4f

l = v—4

1�—�f – ε

Gradient = v—4

v = 4 × gradient

Chapter 13 Deformation of Solids

Experiment IAim: To determine Young’s modulus by the cantilever method.Plan: 1. Set up the apparatus as shown below.

2. Place different values of slotted masses M and record the corresponding lengths d.

Technique:• Make sure the metre rule stops moving before taking the reading.

3. Tabulate the values of d and M.4. Plot a graph of d against M.

Precautions:• Always place the hook and slotted masses at the same mark on the metre rule.• Check if the elastic limit has been exceeded. If the extension during loading and unloading does

not change, the elastic limit is not exceeded.

v4

10

Gradient =

l

∫

Wooden blockMetre rule

Hook

G-clamp

d

L

Metre rule

Slottedmasses


17

Technique:• Submerge the boiling tube as much as possible into the ice and water mixture.

3. Pour warm water into the tube until the water level in the tube is about 1 cm below the mixture of ice and water in the beaker as shown below.

4. Record the time t and the corresponding temperature θ around 30 °C. Record the time t and the corresponding temperature every 30 seconds until the thermometer shows a reading of about 3 °C.

Technique:• Continuously stir the ice-water mixture and the water in the beaker throughout the experiment.

5. Tabulate the values of t, θ and lg θ.6. Plot a graph of lg θ against t.

Precautions:• Allow the temperature of the ice-water mixture to stabilise before pouring hot water into the

boiling tube.• The thermometer must be completely submerged in the water. A white cardboard can be placed

behind the beaker so that the level of mercury can be seen more clearly.

Formula:

dQ——dt

= – kAdθ——dx

where k = thermal conductivity

dQ——dt

= rate of heat fl ow

A = cross-sectional area

dθ——dx

= temperature gradient

Calculations:The relationship between the temperature θ and the time t for the experiment is

lg θ0 – lg θ = k——Brx

t

where θ = temperature in °C at time t θ0 = 20 °C B = 4.84 × 106 J m–3 K–1

r = average radius of the boiling tube x = thickness of the wall of the boiling tube

Retortstand

Boilingtube

Stirrer

Thermometer

Cork stopper

Beaker

Warm waterIce-water mixture

1 cm


16

Technique:• Record the length l only when the temperature has stabilised.

5. Repeat step 4 in the range of 0 °C < θ < 100 °C.6. Tabulate the values of l and θ.7. Plot a graph of l against θ.

Precautions:• Make sure that the acid does not escape from the end of the capillary tube.• Before starting the experiment, make sure all ice has melted.• Keep the thermometer away from the flame.

Formula: V = V0(1 + αθ)where V = volume of trapped air V0 = initial volume of trapped air α = 3.66 × 10–3 °C–1 for all gases at low pressure θ = temperature of trapped air

Calculations:Since V = lA where l = length of trapped air column and A = cross-sectional area of capillary tube,then, V ∝ l V = V0(1 + αθ) l = l0(1 + αθ) where l0 = initial length of trapped air column ∴ l = (αl0)θ + l0

Gradient ≈ αl0

Gradient—–——l0

≈ α


≈ 3.66 × 10–3 °C–1

Chapter 16 Thermal Conduction

Experiment KAim: To determine the thermal conductivity of glass.Plan: 1. Measure the internal and external diameters of a boiling tube. Calculate the average radius r and the thickness x of the wall of the tube.

Technique:• Measure the diameters at different points on the tube using vernier callipers.

2. Fill a beaker with water and ice. A boiling tube is submerged into the ice and water mixture.

0

Gradient ≈

0

0

l

l

l


17

Technique:• Submerge the boiling tube as much as possible into the ice and water mixture.

3. Pour warm water into the tube until the water level in the tube is about 1 cm below the mixture of ice and water in the beaker as shown below.

4. Record the time t and the corresponding temperature θ around 30 °C. Record the time t and the corresponding temperature every 30 seconds until the thermometer shows a reading of about 3 °C.

Technique:• Continuously stir the ice-water mixture and the water in the beaker throughout the experiment.

5. Tabulate the values of t, θ and lg θ.6. Plot a graph of lg θ against t.

Precautions:• Allow the temperature of the ice-water mixture to stabilise before pouring hot water into the

boiling tube.• The thermometer must be completely submerged in the water. A white cardboard can be placed

behind the beaker so that the level of mercury can be seen more clearly.

Formula:

dQ——dt

= – kAdθ——dx

where k = thermal conductivity

dQ——dt

= rate of heat fl ow

A = cross-sectional area

dθ——dx

= temperature gradient

Calculations:The relationship between the temperature θ and the time t for the experiment is

lg θ0 – lg θ = k——Brx

t

where θ = temperature in °C at time t θ0 = 20 °C B = 4.84 × 106 J m–3 K–1

r = average radius of the boiling tube x = thickness of the wall of the boiling tube

Retortstand

Boilingtube

Stirrer

Thermometer

Cork stopper

Beaker

Warm waterIce-water mixture

1 cm


16

Technique:• Record the length l only when the temperature has stabilised.

5. Repeat step 4 in the range of 0 °C < θ < 100 °C.6. Tabulate the values of l and θ.7. Plot a graph of l against θ.

Precautions:• Make sure that the acid does not escape from the end of the capillary tube.• Before starting the experiment, make sure all ice has melted.• Keep the thermometer away from the flame.

Formula: V = V0(1 + αθ)where V = volume of trapped air V0 = initial volume of trapped air α = 3.66 × 10–3 °C–1 for all gases at low pressure θ = temperature of trapped air

Calculations:Since V = lA where l = length of trapped air column and A = cross-sectional area of capillary tube,then, V ∝ l V = V0(1 + αθ) l = l0(1 + αθ) where l0 = initial length of trapped air column ∴ l = (αl0)θ + l0

Gradient ≈ αl0


≈ α


≈ 3.66 × 10–3 °C–1

Chapter 16 Thermal Conduction

Experiment KAim: To determine the thermal conductivity of glass.Plan: 1. Measure the internal and external diameters of a boiling tube. Calculate the average radius r and the thickness x of the wall of the tube.

Technique:• Measure the diameters at different points on the tube using vernier callipers.

2. Fill a beaker with water and ice. A boiling tube is submerged into the ice and water mixture.

0

Gradient ≈

0

0

l

l

l


18

lg θ = k– —— Brx

t + lg θ0

k = – (gradient) × Brx

0

Gradient =

lg

kBrx

t

–


Ace Ahead .Physics Vol 1. Student. Practical Guide

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