Collisions – Elastic and Inelastic - UNSOLVED PRACTICE SET

Q7. Distinguish between elastic and inelastic collisions. Give one example of each.

Q8. State the laws governing all collisions. What additional condition applies to elastic collisions?

Q9. Two identical billiard balls collide elastically head-on. If one was moving at 2 m/s and the other was at rest, find their velocities after collision.

Q10. In your school, two students on skateboards push off from each other. If one student (40 kg) moves backward at 2 m/s, and the other (50 kg) moves forward at 1.6 m/s, what type of "collision" is this? Calculate the total kinetic energy before and after.

Q11. A 2 kg ball moving at 3 m/s collides with a stationary 4 kg ball. After collision, the 2 kg ball moves at 1 m/s in the same direction. Calculate the velocity of the 4 kg ball and determine if the collision is elastic.

Q12. Why does a ball bounce lower after each impact with the ground? Explain in terms of energy transformation.

Q13. Discuss collisions in one dimension. Derive expressions for the final velocities of two bodies after:

(i) An elastic collision

(ii) A perfectly inelastic collision

For the elastic case, show that kinetic energy is conserved. For the inelastic case, calculate the loss in kinetic energy.

Q14. Two bodies of masses m₁ = 2 kg and m₂ = 3 kg moving in the same direction with velocities u₁ = 5 m/s and u₂ = 2 m/s respectively collide elastically.

(a) Calculate their velocities after collision.

(b) Verify that momentum is conserved.

(c) Verify that kinetic energy is conserved.

(d) Calculate the impulse delivered to each body.

(e) What would be their common velocity if the collision were perfectly inelastic?

Q15. A neutron (mass m) collides head-on elastically with a stationary nucleus (mass M).

(a) Derive the expression for the velocity of the neutron after collision.

(b) Show that if M = m, the neutron comes to rest.

(c) Show that if M >> m, the neutron's velocity is approximately reversed.

(d) Explain why heavy water (D₂O) is used as a moderator in nuclear reactors based on this result.

Q16. A 10 g bullet is fired into a 2 kg wooden block suspended by a 1 m long string. The block (with bullet embedded) swings up to a height of 10 cm.

(a) Calculate the velocity of the block+bullet immediately after collision.

(b) Calculate the initial velocity of the bullet.

(c) Calculate the kinetic energy before and after the collision.

(d) Calculate the percentage loss in kinetic energy.

(e) What type of collision is this? Explain.

Q17. Two pendulum bobs A (mass 1 kg) and B (mass 2 kg) are suspended side by side. Bob A is pulled aside until its string makes 60° with the vertical and released. It collides elastically with stationary Bob B.

(a) Calculate the velocity of Bob A just before collision.

(b) Calculate the velocities of both bobs after elastic collision.

(c) Calculate the maximum height reached by each bob after collision.

(d) Verify that kinetic energy is conserved in the collision.

(e) Describe what would happen if the collision were perfectly inelastic.

Q18. In a school physics lab, two gliders on an air track collide. Glider A (mass 0.4 kg) moves at 0.5 m/s towards Glider B (mass 0.2 kg) moving at 0.3 m/s in the opposite direction. After collision, Glider A moves at 0.1 m/s in its original direction.

(a) Calculate the velocity of Glider B after collision.

(b) Determine if the collision is elastic or inelastic.

(c) Calculate the coefficient of restitution.

(d) If the collision were elastic, what would be the velocities of both gliders?

(e) Calculate the impulse on each glider during the collision..