Collisions in two dimensionsEdexcel A-Level Physics: Subtopic test

1. 1
   A snooker cue ball of mass 0.17 kg, travelling at 2.0 m s⁻¹, strikes a stationary ball of identical mass. After the collision the cue ball moves at 1.2 m s⁻¹ at 53° to its original direction, and the other ball moves off at 1.6 m s⁻¹ on the other side of the original direction.

   (a)

   What is the total momentum of the two balls before the collision?

   [1 mark]

   • A0.34 kg m s⁻¹
   • B0.20 kg m s⁻¹
   • C0.27 kg m s⁻¹
   • D0.68 kg m s⁻¹

   (b)

   Which statement about the collision is correct?

   [1 mark]

   • AIt is inelastic, because the cue ball slows down.
   • BIt is inelastic, because momentum is not conserved in two dimensions.
   • CIt is elastic, because the total kinetic energy is the same before and after.
   • DIt is elastic, because momentum is conserved.

   (c)

   Calculate the angle between the direction of motion of the second ball and the original direction of the cue ball.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car of mass 1500 kg travelling east at 12 m s⁻¹ collides at a junction with a van of mass 1000 kg travelling north at 15 m s⁻¹. The vehicles lock together and move off as one body.

   (a)

   What is the eastward component of the momentum of the wreckage immediately after the collision?

   [1 mark]

   • A1.5 × 10⁴ kg m s⁻¹
   • B1.8 × 10⁴ kg m s⁻¹
   • C3.3 × 10⁴ kg m s⁻¹
   • D2.3 × 10⁴ kg m s⁻¹

   (b)

   Which statement about the collision is correct?

   [1 mark]

   • AIt is elastic, because the vehicles move off together.
   • BKinetic energy is conserved but momentum is not.
   • CMomentum and kinetic energy are both conserved.
   • DMomentum is conserved but some kinetic energy is transferred to other forms.

   (c)

   Calculate the speed of the wreckage immediately after the collision.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A neutron of mass 1.67 × 10⁻²⁷ kg and momentum 3.34 × 10⁻²¹ kg m s⁻¹ collides with a stationary proton, whose mass can be taken as 1.67 × 10⁻²⁷ kg. After the collision the neutron has momentum 2.74 × 10⁻²¹ kg m s⁻¹ at 35° to its original direction, and the proton has momentum 1.92 × 10⁻²¹ kg m s⁻¹ at 55° on the other side of the original direction.

   (a)

   Show that the kinetic energy of a non-relativistic particle of mass m and momentum p is p²/2m, and use it to calculate the initial kinetic energy of the neutron.

   [3 marks]

   (b)

   Show that the collision is elastic.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student films collisions between two small steel spheres on a smooth horizontal surface, using a high-speed camera and video analysis software to find their positions at regular time intervals. Sphere A has mass 0.060 kg and sphere B has mass 0.040 kg, with B initially at rest. In one trial A moves at 0.80 m s⁻¹ before the collision. After the collision A moves at 0.40 m s⁻¹ at 30° to its original direction, and B moves at 0.74 m s⁻¹ at 24° on the other side of the original direction.

   (a)

   Describe how the student could use video analysis to find out whether momentum is conserved in these collisions and whether they are elastic.

   [6 marks]

   (b)

   Use the data from the trial to show whether momentum is conserved in the collision and whether the collision is elastic.

   [6 marks]

   Total for question 4: 12 marks

End of questions