Kinetic Energy - UNSOLVED PRACTICE SET

Q7. Define kinetic energy. Derive the expression for kinetic energy of a body moving with velocity v.

Q8. A 1500 kg car moves at 36 km/h. Calculate its kinetic energy. If the speed is doubled, what is the new kinetic energy?

Q9. The kinetic energy of a body is increased from 100 J to 400 J. Calculate the ratio of initial and final momenta.

Q10. In your school, a 200 g cricket ball is bowled at 30 m/s. Calculate its kinetic energy. If the batsman hits it back at 25 m/s, what is the change in kinetic energy?

Q11. A body of mass m is lifted to height h and then dropped. Using energy conservation, find its kinetic energy just before hitting the ground.

Q12. Two bodies A and B have kinetic energies in the ratio 1:4. If they have the same mass, compare their velocities and momenta.

Q13. Define kinetic energy and derive its expression from Newton's second law. Discuss the relationship between kinetic energy and momentum. Show that for a given momentum, kinetic energy is minimum when mass is maximum.

Q14. An electron (mass 9.11 × 10⁻³¹ kg) and a proton (mass 1.67 × 10⁻²⁷ kg) are accelerated through the same potential difference.

(a) Which particle has greater kinetic energy? Explain.

(b) Calculate the ratio of their kinetic energies.

(c) Which particle moves faster?

(d) Calculate the ratio of their speeds.

(e) What does this tell you about the relationship between mass and velocity at the same energy?

Q15. A 10 g bullet is fired from a 5 kg rifle with a speed of 400 m/s.

(a) Calculate the kinetic energy of the bullet.

(b) Calculate the recoil velocity and kinetic energy of the rifle.

(c) Compare the kinetic energies of the bullet and the rifle.

(d) Explain why the bullet has much more kinetic energy despite having much less mass.

(e) Calculate the total kinetic energy of the system and comment on its source.

Q16. A 1000 kg car accelerates from rest to 72 km/h in 10 seconds on a level road.

(a) Calculate the change in kinetic energy of the car.

(b) Calculate the average power delivered by the engine.

(c) If the engine efficiency is 25%, calculate the energy consumed from the fuel.

(d) Calculate the work done against friction if the actual distance covered is 150 m and the engine force is 3000 N.

(e) What happens to the kinetic energy when the brakes are applied?

Q17. In a particle accelerator, a proton is accelerated from rest to a speed of 2 × 10⁷ m/s.

(a) Calculate the kinetic energy of the proton in joules.

(b) Convert this energy to electron volts (eV). (1 eV = 1.6 × 10⁻¹⁹ J)

(c) If the proton is accelerated through a potential difference V, calculate V.

(d) At what fraction of the speed of light is the proton moving? (c = 3 × 10⁸ m/s)

(e) At higher speeds, why does the classical formula for kinetic energy become inaccurate?

Q18. A 2 kg block slides down a frictionless curved track from a height of 3 m.

(a) Calculate the kinetic energy at the bottom using energy conservation.

(b) Calculate the speed at the bottom.

(c) The block then compresses a spring (k = 500 N/m). Calculate the maximum compression.

(d) If the track had friction (μ = 0.1) and length 5 m, calculate the speed at the bottom.

(e) Compare the spring compression in both cases.