1. 1
   Two ice skaters of different masses stand still, facing each other, holding hands on a frictionless ice rink. They then push apart and glide away from each other in opposite directions across the ice.

   (a)

   Two ice skaters stand still, facing each other, holding hands on a frictionless ice rink. They push apart and glide away from each other in opposite directions. What is the total momentum of the two skaters immediately before they push apart?

   [1 mark]

   • AZero, since both skaters are at rest
   • BEqual to the sum of their masses
   • CEqual to the mass of the heavier skater only
   • DUndefined, since momentum only applies to moving objects

   (b)

   After pushing apart, the lighter skater moves away faster than the heavier skater. Which physical principle explains why the total momentum of the two skaters remains zero after they push apart, just as it was before?

   [1 mark]

   • ANewton's First Law
   • BThe law of conservation of energy
   • CConservation of momentum
   • DHooke's Law

   (c)

   The lighter skater has a mass of 45 kg and moves away at 3 m/s after pushing apart. Calculate the momentum of the lighter skater, and explain what this tells you about the momentum of the heavier skater immediately afterwards.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   On a freight railway line, a moving wagon rolls along a shunting yard and collides with a stationary wagon of equal mass, coupling onto it so that the two wagons move off together after the collision.

   (a)

   On a freight railway, a moving wagon collides with and couples onto a stationary wagon of equal mass, and the two wagons then move off together. What happens to the speed of the moving wagon compared with its speed just before the collision?

   [1 mark]

   • AIt stays exactly the same
   • BIt roughly halves, since the combined mass has doubled
   • CIt doubles
   • DIt becomes zero

   (b)

   If the moving wagon had instead collided with a stationary wagon of much greater mass, coupling onto it, how would the combined speed after the collision compare with the case where the two wagons had equal mass?

   [1 mark]

   • AThe combined speed would be greater, since more mass means more momentum
   • BThe combined speed cannot be determined without knowing the exact force involved
   • CThe combined speed would be unchanged, since momentum conservation applies equally
   • DThe combined speed would be smaller, since the same momentum is now shared between a greater total mass

   (c)

   The moving wagon has a mass of 8000 kg and is travelling at 5 m/s when it collides with and couples onto a stationary wagon of mass 8000 kg. Calculate the combined velocity of the two wagons immediately after the collision, showing how conservation of momentum is applied.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a school physics laboratory, students roll a trolley of mass 1.2 kg along a bench so that it collides with and sticks to a stationary trolley of mass 0.8 kg, and the combined trolleys then move off together.

   (a)

   Before the collision, the moving trolley travels at 2.5 m/s. Calculate the momentum of the moving trolley before the collision, and explain why momentum, rather than speed, is the quantity that is conserved when the two trolleys collide.

   [3 marks]

   (b)

   Calculate the combined velocity of the two trolleys immediately after the collision, and then calculate the force needed to bring the combined trolleys to rest in 0.5 seconds after they roll off the end of the bench, using the fact that force equals the rate of change of momentum.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A car manufacturer is designing a new family car and wants to improve its safety in the event of a front-end collision. The design team is considering adding crumple zones to the front of the car and airbags for the driver and front passenger, alongside seat belts and side impact bars.

   (a)

   Explain, using the force–momentum relationship (F = Δp/t), how crumple zones and airbags help to reduce injury to the people inside the car during a collision.

   [6 marks]

   (b)

   The design team also considers seat belts and side impact bars as additional safety features. Explain how seat belts use the force–momentum relationship to protect occupants during a frontal collision, and explain why side impact bars work differently, by making the car's structure more resistant to a sudden change in shape during a side collision rather than by extending the time of impact.

   [6 marks]

   Total for question 4: 12 marks

End of questions