Momentum and Conservation of Momentum - UNSOLVED PRACTICE SET

Q7. Define momentum. Explain how it depends on both mass and velocity. Give one example from Indian sport where a high-momentum object is dangerous.

Q8. State the Law of Conservation of Momentum. State clearly the condition under which it holds true.

Q9. When a gun fires a bullet, the gun recoils. Using conservation of momentum, explain why the gun moves and why it moves much more slowly than the bullet.

Q10. What is impulse? Write its formula. Explain how increasing the time of contact reduces the force on an object, using a real-life example.

Q11. Two skaters of different masses push off each other from rest on an ice rink and slide apart. Who moves faster — the lighter or heavier skater? Justify using conservation of momentum.

Q12. In a carrom game, a striker hits a stationary coin and the striker comes to rest while the coin moves. Explain what happened to the striker's momentum using conservation of momentum.

Q13. Derive the Law of Conservation of Momentum using Newton's Third Law. Your derivation must cover:
(a) two objects A and B colliding with forces FAB and FBA,
(b) using Newton's Third Law to relate the forces,
(c) writing impulse (force × time = change in momentum) for each object,
(d) showing that total change in momentum = 0, and
(e) stating the Law of Conservation of Momentum as the conclusion.

Q14. In a railway yard, a locomotive of mass 6000 kg moving at 4 m/s collides with and couples to a stationary wagon of mass 9000 kg.
(a) Calculate the total initial momentum.
(b) Find the velocity of the coupled system after collision using conservation of momentum.
(c) Calculate KE before and after collision. Is kinetic energy conserved?
(d) What type of collision is this and what happened to the 'lost' KE?

Q15. Explain impulse and its real-life importance:
(a) Define impulse and write F × Δt = Δp.
(b) Why does a karate expert strike with maximum speed (short time)?
(c) Why does a cricketer draw his hands back when catching?
(d) Why do cars have crumple zones that increase collision time?
(e) Why does landing on a foam mattress hurt less than landing on concrete? In each case, explain using impulse = change in momentum.

Q16. A cricket ball of mass 0.16 kg is delivered at 25 m/s. A batsman hits it back at 35 m/s in the opposite direction.
(a) Calculate the initial and final momenta (take initial direction = positive).
(b) Calculate the change in momentum.
(c) If the ball was in contact with the bat for 0.025 s, calculate the average force using F = Δp/Δt.

Q17. A girl of mass 45 kg stands on a 12 kg skateboard. Both are at rest. She throws a 0.6 kg ball forward at 8 m/s.
(a) What is the total initial momentum?
(b) Using conservation of momentum, find the recoil velocity of the girl and skateboard.
(c) In which direction do the girl and skateboard move?
(d) What assumption did you make about external forces?

Q18. A 4 kg firecracker at rest explodes into three pieces. Piece A (1 kg) moves East at 20 m/s. Piece B (1.5 kg) moves North at 16 m/s.
(a) Calculate the momenta of A and B.
(b) The total initial momentum was zero. What is the total momentum of piece C (1.5 kg)?
(c) Find the velocity of piece C.
(d) In what general direction must piece C move? Justify using conservation of momentum.