A LevelPhysicsOCRTopic Questions3. Forces & Motion3.3 Dynamics

Dynamics (OCR A Level Physics)

Topic Questions

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1a2 marks

A toy rocket is made from a 1.5 litre plastic bottle with fins attached for stability.

The bottle initially contains 0.30 litres of water, leaving 1.2 litres of trapped air at a temperature of 17°C.

A pump is used to increase the pressure of the air within the plastic bottle to 2.4 × 105 Pa at the start of lift-off.

Fig. 1.1 shows the rocket at the start of lift-off.

1 litre = 10–3m3

q1a-paper-3-june-2019-ocr-a-level-physics

Fig. 1.1

a)
Calculate, in moles, the amount of trapped air in the bottle at the start of lift-off.

amount of air = ................................. mol   [2]

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1b3 marks
b)
The trapped air pushes the water downwards out of the hole, causing the rocket to rise.
The temperature of this air remains constant.

Calculate the final pressure of the trapped air just before all the water has been released.

final pressure = ...................................Pa  [3]

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1c5 marks
c)
Here is some data on the toy rocket.

mass of empty bottle and fins = 0.050 kg
area of cross-section of hole = 1.1 × 10–4 m2
initial pressure of trapped air = 2.4 × 105 Pa
atmospheric pressure = 1.0 × 105 Pa
density of water = 1.0 × 103 kgm–3

i)
Use the data above to show that the upwards force on the rocket at the start of lift-off is about 15 N.
[2]
ii)
Hence calculate the initial vertical acceleration of the rocket.

initial acceleration = ................................... ms–2  [3]

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1d3 marks
d)
Discuss whether adding more water initially would enable the rocket to reach a greater height.

[3]

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1a2 marks

A truck pulls a car up a slope at a constant speed.
The truck and the car are joined with a steel tow bar, as shown in the diagram.

q16-paper-1-nov-2020-ocr-a-level-physics

The diagram is not drawn to scale.

The slope is 10° to the horizontal ground.
The mass of the car is 1100 kg.
The car travels from A to B. The vertical distance between A and B is 120 m.

a)
There are four forces acting on the car travelling up the slope.

Complete the free-body diagram below for the car and label the missing forces.

q16a-paper-1-nov-2020-ocr-a-level-physics

[2]

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1b1 mark
b)
Show that the component of the weight of the car Ws acting down the slope is about 1900 N.

[1]

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1c1 mark
c)
The total frictional force acting on the car as it travels up the slope is 300 N.

Calculate the force provided by the tow bar on the car.



force = ...................................................... N [1]

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1d3 marks
d)
Calculate the work done by the force provided by the tow bar as the car travels from A to B.





work done = ............................................ J [3]

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1e3 marks
e)
The steel tow bar used to pull the car has length 0.50 m and diameter 1.2 × 10–2 m.
The Young modulus of steel is 2.0 × 1011 Pa.

Calculate the extension x of the tow bar as the car travels up the slope.





x = ......................................... m [3]

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2a3 marks

A student uses a motion-sensor connected to a laptop to investigate the motion of a hollow ball of mass 1.2 × 10–2 kg falling through air.

The ball is dropped from rest. It reaches terminal velocity before it reaches the ground.

The upthrust on the ball is negligible.

Fig. 17 shows the variation with time t of the velocity v of the ball as it falls towards the ground.

q17-paper-1-june-2019-ocr-a-level-physics

Fig. 17

a)
Draw a tangent to the curve at t = 0.25 s and determine the acceleration of the ball.

acceleration = ................................... ms–2    [3]

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2b1 mark
b)
Calculate the resultant force F acting on the ball at t = 0.25 s.

F = .......................................... N  [1]

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2c3 marks
c)
Use your answer in (b) to calculate the drag on the ball at time t = 0.25 s.

drag = ......................................... N  [3]

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2d4 marks
d)
The student now adds a small amount of sand inside the hollow ball.
As before, the ball is dropped from rest and it also reaches terminal velocity before it reaches the ground.

i)
Describe how the forces acting on the sand-filled ball at v = 0.50 ms–1 compare with the forces acting on the hollow ball at this speed.
[2]
ii)
Explain why the terminal velocity of the sand-filled ball will be greater than the terminal velocity of the hollow ball.
[2]

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3a4 marks

A swimming pool designer investigates the depth d below a water surface reached by a diver when diving from a height h above the water surface. The designer models the diver as a uniform wooden cylinder. The experimental arrangement is shown in Fig. 18.1.

q18-paper-1-june-2017-ocr-a-level-physics

Fig. 18.1

a)
The wooden cylinder has mass 5.0 × 10−3 kg, diameter 1.0 × 10−2 m and length 7.0 × 10−2 m.

i)
Calculate the density of the wood.




density = ....................................... kg m−3 [2]

ii)
Suggest why wood is an appropriate material to model the depth reached by a diver.

[2]

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3b2 marks
b)
The cylinder is released from rest from a trapdoor. The base of the cylinder is at a height h = 0.30 m above the water surface.
Calculate the speed of the cylinder just before the base hits the water. Ignore air resistance.




speed = ..................................... m s−1 [2]

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3c6 marks
c)
Fig. 18.2 shows the cylinder fully submerged under the water surface before it has come to rest. The cylinder is moving vertically down.

q18c

Fig. 18.2

i)
Add arrows to Fig. 18.2 to show the three forces acting on the wooden cylinder. Label the arrows.

[3]

ii)
Describe and explain how the resultant force on the wooden cylinder varies from the moment the cylinder is fully submerged until it reaches its deepest point.

[3]

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3d2 marks
d)
The graph of Fig. 18.3 shows the depth d reached for different initial drop height h.

q18d-paper-1-june-2017-ocr-a-level-physics

Fig. 18.3

The designer is required to double the height of a diving board for an existing swimming pool.
He suggests that the depth of the pool also needs to be doubled.
Use Fig. 18.3 to explain whether you agree with this suggestion.

[2]

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