1. 1
   At a rail freight yard, a stationary goods wagon is coupled to a moving locomotive, and the two move off together after coupling.

   (a)

   Which equation correctly defines momentum?

   [1 mark]

   • Ap = mv
   • Bp = m/v
   • Cp = v/m
   • Dp = m + v

   (b)

   In a closed system, what does the conservation of momentum state?

   [1 mark]

   • Atotal momentum before an event is greater than after
   • Btotal momentum before an event equals total momentum after the event
   • Ctotal momentum always increases over time
   • Dtotal momentum is always zero

   (c)

   The locomotive has mass 8000 kg and moves at 2 m/s before coupling to the stationary wagon. Calculate the locomotive's momentum before coupling.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   At a fairground, a bumper car of mass 300 kg moving at 4 m/s collides and sticks together with a stationary bumper car of mass 200 kg.

   (a)

   What is the total momentum of the system immediately before the collision?

   [1 mark]

   • A2000 kg m/s
   • B500 kg m/s
   • C1200 kg m/s
   • D0 kg m/s

   (b)

   According to the conservation of momentum, what is the total momentum of the bumper car system immediately after the collision, assuming no significant external forces?

   [1 mark]

   • Agreater than before the collision
   • Bexactly zero
   • Cless than before the collision
   • Dthe same as before the collision

   (c)

   Calculate the common velocity of the two bumper cars immediately after the collision, given they move off together with a combined mass of 500 kg and a total momentum of 1200 kg m/s.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A vehicle safety engineering team crash-tests a car fitted with a crumple zone and airbags, measuring how quickly the car's momentum changes to zero when it collides with a solid barrier.

   (a)

   Explain, using the equation $F = \frac{m\Delta v}{\Delta t}$, why increasing the time taken for a car's momentum to reach zero during a collision reduces the force experienced by the occupants.

   [3 marks]

   (b)

   Explain how crumple zones and airbags work together to increase the time taken for a car's occupants to stop during a collision, and explain the safety benefit this provides.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In 1966, engineers analyse the first Gemini spacecraft docking manoeuvre, where a manned capsule gently approaches and connects with an unmanned target vehicle in orbit, then engineers compare this with modern satellite docking systems that must carefully control momentum changes during contact.

   (a)

   Explain, using the principle of conservation of momentum, what must be true about the velocities of the spacecraft and target vehicle immediately after they dock and move together as a single combined object, given their masses and velocities before docking.

   [6 marks]

   (b)

   The spacecraft (mass 3800 kg) approaches the target vehicle (mass 3400 kg, initially stationary relative to the target's orbit) at a relative velocity of 0.2 m/s and docks with it. Calculate the combined velocity of the docked spacecraft and target immediately after docking, and evaluate why engineers would want the docking speed to be as low as reasonably possible rather than exactly zero.

   [6 marks]

   Total for question 4: 12 marks

End of questions