1. 1
   Two ice skaters, initially at rest and facing each other on frictionless ice, push off from one another. One skater has a mass of 50 kg and moves away at 3 m/s after pushing off.

   (a)

   Two ice skaters, initially at rest and facing each other, push off from one another. One skater has a mass of 50 kg and moves away at 3 m/s. What is this skater's momentum immediately after pushing off?

   [1 mark]

   • A150 kg m/s
   • B53 kg m/s
   • C16.7 kg m/s
   • D0.06 kg m/s

   (b)

   Before pushing off, the total momentum of the two skaters together was zero, since both were at rest. What must the total momentum of the two skaters be immediately after they push off from each other?

   [1 mark]

   • A150 kg m/s
   • BZero
   • C300 kg m/s
   • DIt cannot be determined

   (c)

   State the principle of conservation of momentum, and use it to calculate the velocity of the second skater, of mass 60 kg, immediately after pushing off.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A golf club strikes a stationary golf ball of mass 0.046 kg, exerting an average force of 4000 N on the ball for a contact time of 0.0005 s.

   (a)

   A golf club strikes a stationary golf ball, exerting an average force of 4000 N on the ball for a contact time of 0.0005 s. What impulse does the club give to the ball?

   [1 mark]

   • A8 000 000 kg m/s
   • B4000.0005 kg m/s
   • C2 kg m/s
   • D0.000000125 kg m/s

   (b)

   The impulse given to the golf ball is equal to which of the following?

   [1 mark]

   • AThe final speed of the golf ball
   • BThe change in momentum of the golf ball
   • CThe weight of the golf ball
   • DThe kinetic energy of the golf ball

   (c)

   Using your answer to the impulse calculation, calculate the speed of the golf ball immediately after being struck, and explain why a golf club with a softer, more flexible face would produce a smaller force on the ball for the same change in its momentum.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A goods train carriage of mass 8000 kg, moving at 3 m/s, collides with a stationary carriage of mass 4000 kg and the two couple together, moving off with a common velocity. Separately, a car of mass 1200 kg travelling at 20 m/s is brought to rest in a crash lasting 0.15 s.

   (a)

   Use the conservation of momentum to calculate this common velocity.

   [3 marks]

   (b)

   A car of mass 1200 kg, travelling at 20 m/s, is brought to rest in a collision lasting 0.15 s. Calculate the average force acting on the car during the collision, and explain, in terms of this equation, how a crumple zone in the front of the car reduces the force experienced by the occupants in a crash.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A space agency is designing rocket propulsion systems, while a separate car manufacturer is designing safety features such as crumple zones and airbags for a new car model.

   (a)

   Explain, using the principle of conservation of momentum, how a rocket in the vacuum of space is propelled forward by expelling exhaust gas backwards, including a sample calculation of the rocket's change in velocity if it expels 50 kg of gas at 800 m/s from an initial rocket (plus remaining fuel) mass of 2000 kg, initially at rest.

   [6 marks]

   (b)

   Explain, using the equation force = change in momentum / time and the idea of impulse, why crumple zones and airbags reduce the force experienced by the occupants of a car during a crash, compared with an otherwise identical car with a completely rigid body and no airbags.

   [6 marks]

   Total for question 4: 12 marks

End of questions