Conservation of energyAQA A-Level Physics: Subtopic test

1. 1
   A ball of mass 0.15 kg is released from rest at a height of 3.2 m above a hard floor. Ignore air resistance until the ball hits the floor. Take g = 9.81 N kg⁻¹.

   (a)

   What is the kinetic energy of the ball just before it hits the floor?

   [1 mark]

   • A0.48 J
   • B7.9 J
   • C4.7 J
   • D9.4 J

   (b)

   What is the speed of the ball just before it hits the floor?

   [1 mark]

   • A7.9 m s⁻¹
   • B63 m s⁻¹
   • C5.6 m s⁻¹
   • D4.7 m s⁻¹

   (c)

   The ball rebounds from the floor to a height of 2.4 m. Calculate the energy dissipated in the impact with the floor.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A pendulum bob of mass 0.50 kg is held at rest with the bob 0.20 m above the lowest point of its swing, then released. Assume that air resistance and friction at the pivot are negligible. Take g = 9.81 N kg⁻¹.

   (a)

   What is the kinetic energy of the bob at the lowest point of its swing?

   [1 mark]

   • A0.098 J
   • B0.98 J
   • C1.96 J
   • D4.9 J

   (b)

   What is the speed of the bob at the lowest point?

   [1 mark]

   • A1.4 m s⁻¹
   • B3.9 m s⁻¹
   • C0.98 m s⁻¹
   • D2.0 m s⁻¹

   (c)

   A second bob of mass 1.0 kg is released from the same height. Explain, using energy, why its speed at the lowest point is the same as that of the first bob.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A skier of mass 70 kg starts from rest at the top of a straight ski slope that is 600 m long and has a vertical drop of 150 m. At the bottom of the slope the skier is moving at 20 m s⁻¹. Take g = 9.81 N kg⁻¹.

   (a)

   Explain what happens to the gravitational potential energy lost by the skier.

   [3 marks]

   (b)

   Calculate the mean resistive force acting on the skier along the slope.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A roller-coaster carriage and passengers have a total mass of 450 kg. The carriage is released from rest at the top of the first hill, 40 m above the lowest point of the track. It travels 160 m along the track to the lowest point, where its speed is 24 m s⁻¹. Take g = 9.81 N kg⁻¹.

   (a)

   Calculate the mean resistive force acting on the carriage as it moves to the lowest point.

   [6 marks]

   (b)

   The designer plans to add a second hill whose top is 36 m above the lowest point. The track from the release point to the top of this hill is 250 m long. Assume the mean resistive force stays at 290 N. Evaluate whether the carriage released from rest at the top of the first hill can reach the top of the second hill, and determine the least release height needed.

   [6 marks]

   Total for question 4: 12 marks

End of questions