9749/04/AJC/2017/Prelim

A student is interested in 'bungee jumping', where a person attached to an elastic cord falls from a height and travels downwards through a distance before moving upwards. Different cords are used for different people. A schematic diagram is shown in Fig. 4.1.

The student models 'bungee jumping' in the laboratory by using elastic cords of unstretched length 50.0 cm with different spring constants. An object is attached to each cord. The student investigates the relationship between the maximum distance h fallen by the object and the spring constant k of the elastic cord.

It is suggested that the relationship between h and k is

2

1k(h - L)2 = mgh

where L is the unstretched length of the cord, m is the mass of the object and g is the acceleration of free fall.

Design a laboratory experiment to test the relationship between h and k.

Explain how your results could be used to plot a graph with h

Lh 2)( on the y-axis and to

determine the value of g. You should draw a labelled diagram to show the arrangement of your apparatus.

In your account you should pay particular attention to

the procedure to be followed, the measurements to be taken, the control of variables, the analysis of the data, any precautions that would be taken to improve the accuracy and safety of the experiment.

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To test the relationship between h and k, and determine value of g.

1. Setup the experiment as shown in the diagram above. 2. Measure and record mass, m, of the given object using an electronic balance. 3. Hang the elastic cord from clamp of the retort stand. Measure and record the initial height h0

of mass m at its starting position using a metre rule. 4. Lower the attached mass m and allow it to come to rest. 5. Measure record the height h1 of mass m at its equilibrium position using a meter rule,

determine the spring constant k using Lhh

mg

)( 10

, where L is 50.0 cm.

6. Bring the mass m back to its initial height h0 and drop it from rest. 7. Measure and record the lowest height reached by the mass, h2 using a metre rule. 8. Determine the height fallen by the mass m, h using h = h2 – h0

9. Repeat the experiment using different elastic cords to obtain 6 sets of values for h and k.

Mass of object used is kept constant by using the same mass throughout the experiment.

k

mg

h

Lh 2)( 2

Plot a graph of h

Lh 2)(against

k

1 where the gradient is 2mg and y-intercept is zero.

Relationship is valid if the graph is a straight line passing through the origin.

Value of g can be determined from m

gradient

2.

h = h0 – h2

elasticcord

h0

h2

h1

mass, m,attached to elastic cord

brick

h0 – h1

lowest point

equilibriumpoint

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1. Take preliminary readings to locate approximate lowest height h2 / to prevent object hitting surface

2. Ensure that the position of the metre rule is not shifted during the experiment by clamping it to a retort stand.

3. Use set square to ensure that metre rule is vertical 4. Use a set square as a marker, repeat the experiment a few times to better locate the lowest

position of the mass h2 / ORUse of video camera with slow motion or frame by frame playback to determine lowest position of mass m / OR Place a motion sensor directly beneath the mass m to record its displacement from the sensor. Lowest position of the mass could be read off from the datalogger.

5. Ensure that cord obeys Hooke's law and has not exceeded proportional limit by checking the Lremains unchanged after the experiment.

6. Use sand tray to catch falling object to prevent mass / cord from hitting a person. 7. Use goggles / safety screen to prevent mass / cord from hitting a person 8. Use a heavy mass to stabilize the retort stand to prevent setup from toppling.

226

IJC 2017 9749/Prelim/17

A student investigates the power dissipated by a lamp connected to a model wind turbine as shown in Fig. 4.1.

The power P dissipated in the lamp depends on the angle between the axis of the turbine and the direction of the wind, as shown by the top view in Fig. 4.2.

It is suggested that

P = k cos

where k is a constant.

Design a laboratory experiment to test the relationship between P and and determine a value for k. You should draw a labelled diagram to show the arrangement of your apparatus. In your account you should pay particular attention to

(a) the identification and control of variables,

(b) the equipment you would use,

(c) the procedure to be followed,

(d) how the constant k is determined,

(e) any precautions that would be taken to improve the accuracy and safety of the

experiment.

[12]

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513

4

Diagram (1 × D1)

Diagram should show:

1. the method to produce the air flow (e.g. fan, hair dryer, etc)

2. the method to determine the power of the lamp connected to

turbine in closed circuit (e.g. ammeter and voltmeter)

Comments

In general, students need to be

specific in their statements. More

elaboration is given in the comments

below.

Many are penalized when they did not

show how the turbine is connected to

lamp in series. There should not be

any other electrical devices such as

e.m.f. or resistor as these would

affect the power of the lamp.

Procedure

(a) Set up the apparatus as shown above.

(b) Switch on the fan or hairdryer and close the switch of the

circuit with the lamp.

Procedure and Measurement marks (1 × P1, 2 × M1)

(c) Measure the angle between the direction of the wind from

the fan or hairdryer and the normal of the turbine using a

protractor. [M1]

(d) Measure the current I through the lamp and the potential

difference V across the lamp using an ammeter and

voltmeter respectively. [M1]

(e) Repeat step (c) & (d) to obtain additional 6 sets of current

and potential difference with different angles by rotating the

turbine. [P1]

Students should identify the variable,

the object and the instrument

needed.

The power of the lamp should be

measured directly rather than using

LDR.

Students need to be specific in

stating how the angle between the

wind and the normal of the turbine

can be varied.

Analysis marks (3 × A1)

(f) The power of the lamp is determined by P = IV [A1]

(g) Plot a graph of P against cos where k is the gradient of the

best fitted line. [A1]

(h) The relationship is valid if the plotted points follows a straight

line trend through the origin (y-intercept = 0) [A1]

Students should identify the symbol

used in the determination of power of

lamp.

The validity of the relationship is

often missing. For those who try to

answer this, they need to understand

that this relationship is unique where

the linearized trend is expected to

pass through the origin since the y-

nce with different angles by rotating the

[P1]wind andnd the

cacann bebe vvarriied

p iss ddeteterermiminened d byby P P == IIVV [A1]]

inst cos where k is theh grg addient of thehe

Sttududene ts sho

ususeded in the de

l

549

intercept of the linearized equation is

zero.

Control marks (2 × C1)

(i) Ensure that the speed of the wind/fan is the same (by

applying the power or voltage of the fan the same or by

monitoring it with an anemometer)

(j) Ensure that the distance between the fan/hairdryer and the

turbine is the same (by measuring it with a metre rule before

each reading).

(k) Ensure that the direction of the wind is the same (by using a

wind vane)

The control variables identified

should be focused on those that can

affect the input power provided by

the wind and the angle between the

wind and normal of the turbine.

Changes to the resistance of the lamp

does not affect the power of the lamp

since the current through lamp would

react inversely.

Safety (1 × S1): moving turbine and hot lamp

- Do not touch the turbine blades when it is moving

- Do not touch the hot lamp when it is operating for a period

of time.

It is important to highlight that the

lamp would be only dangerously hot to

touch when it is switched on for a

period of time. The brightness of the

lamp is usually not harmful to eyes.

Reliability (2 × R1)

To fix control variables

- As stated above

To measure independent variable accurately and precisely

- Measure the direction of the wind accurately using a wind

wave.

To measure dependent variable accurately and precisely

- Ensure that there is no other wind sources by doing the

experiment in an enclosed room.

- The speed of the wind should be large so that the power of

the lamp can be measurable.

- The turbine should have low friction so that there is minimal

loss of power during the transfer of power between the

turbine and the lamp.

- The readings should be taken only when the wind and/or

meter readings have stabilized.

Students need to focus on the key

ideas on how to

1. fix the control variables

2. measure independent variable

3. measure dependent variable

in given context.

550

T

T

a bT k

k a b

k a b

k a b

858

T

, keeping constant

constant

max

m T

T mg g

constant. max

, keeping constant

constant

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constant

m T

T mg g

constant.

T

a b k

T ( )

b a k

a b k

861

For

Examiner’s Use

v

v B

B

ov v e

B v

v B

v

1110

For

Examiner’s Use

B

–

v t B

1111

For

Examiner’s Use

1112

k

1900

r of the pulley via “circumference = 2 r

m

h

h

r

m

r offfffffff thhhehh pulley vviviviivia “ciiiirii cumffererencee = 2 r

1901

t

m

k

k

“k

S ”.

“ ”

The linear speed of the rim of the pulley is calculated using “t

hv ”.

is calculated using “r

v”.

h

t

v h

1902