Newton's Second Law - UNSOLVED PRACTICE SET

Q7. State Newton's second law of motion in terms of momentum. Show how F = ma is a special case of F = dp/dt.

Q8. Define impulse. How is it related to force and time? Write its SI unit.

Q9. A ball of mass 0.5 kg is moving with a velocity of 10 m/s. It is brought to rest by a player in 0.2 seconds. Calculate the average force exerted by the player.

Q10. In a carrom board game, the striker hits the coin and the coin moves. Explain how F = dp/dt applies to this situation. Why does the coin move faster than the striker after the collision?

Q11. A force acts on a body for 5 seconds and its momentum changes by 25 kg m/s. If the same change in momentum is to be achieved in 2.5 seconds, what force is required?

Q12. Why does a fielder in cricket pull his hands backward while catching a fast-moving ball? Explain using the concept of impulse.

Q13. State and explain Newton's second law of motion in its general form F = dp/dt. Show that for a body of constant mass, this reduces to F = ma. Discuss why the general form is more powerful and applicable to situations where mass changes (like rockets).

Q14. A body of mass 5 kg is acted upon by a force that varies with time as shown below (describe verbally): F = 0 for 0 ≤ t < 2 s; F increases linearly from 0 to 10 N for 2 ≤ t < 4 s; F = 10 N for 4 ≤ t < 6 s; F decreases linearly to 0 for 6 ≤ t < 8 s.

(a) Sketch the force-time graph.

(b) Calculate the impulse delivered to the body.

(c) If the body starts from rest, calculate its velocity at t = 8 s.

(d) Calculate the momentum of the body at t = 5 s.

Q15. Analyse the statement: "A large force acting for a short time can produce the same change in momentum as a small force acting for a long time." Discuss this with reference to:

(i) A karate expert breaking a tile

(ii) A car's crumple zone in a collision

(iii) A rocket ejecting fuel continuously

Show how F = dp/dt explains each situation.

Q16. A 1500 kg car accelerates from rest to 72 km/h in 10 seconds.

(a) Calculate the change in momentum of the car.

(b) Calculate the average force acting on the car.

(c) If the engine provides a constant force and the car experiences a resistive force of 500 N, what is the force exerted by the engine?

(d) Calculate the distance travelled by the car during this acceleration.

Q17. A machine gun fires bullets at a rate of 600 per minute. Each bullet has a mass of 25 g and leaves the gun at 400 m/s.

(a) Calculate the momentum of each bullet.

(b) Calculate the rate of change of momentum (force) exerted on the bullets.

(c) By Newton's third law, what is the recoil force on the gun?

(d) If the gun has a mass of 20 kg and is free to move, calculate its initial recoil acceleration.

Q18. In a physics experiment, a student applies a variable force to a 2 kg block on a frictionless surface. The force varies as F = 3t² + 4t, where F is in newtons and t is in seconds.

(a) Calculate the acceleration of the block at t = 2 s.

(b) Calculate the impulse delivered to the block between t = 0 and t = 3 s.

(c) If the block starts from rest, calculate its velocity at t = 3 s.

(d) Calculate the momentum of the block at t = 3 s.