Dynamics (OCR A Level Physics)

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.

Fig. 17

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

acceleration = ................................... ms^–2  

Calculate the resultant force F acting on the ball at t = 0.25 s.

F = .......................................... N 

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

drag = ......................................... N 

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]

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.

Fig. 18.1

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]

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

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

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]

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

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.