Question

AP PHYSICS I - UNIT 4- tomentum and Impulse Problem Set 12-2 Due 11/21 2. A man standing on very slick ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kg, and the mass of the bullet is 10 g. The bullet leaves the muzzle at a speed of 500 m/s. a. Explain why the man will move backwards after he fires the gun. b. Calculate the speed at which the man recoils. C. Which is greater, the impulse on the bullet or the impulse on the gun? d. Which is greater the acceleration of the bullet, or the acceleration of the gun? e. Which is greater, the force of the bullet on the gun, or the force of the gun on the bullet?

Answer 1

a) According to the law of conservation of linear momentum, the momentum must be conserved.

The momentum of each object in the system is 0 initially. After firing, the gun moves forward and thus has some momentum. Since the total momentum of the system should remain 0, the man and the gun must have a backward momentum that is equal and opposite to the momentum of the gun. This causes recoil after firing.

b) Momentum of bullet=mv= (10*10^-3)(500)=5kgm/s

Momentum of the man=p=-5kgm/s

Therefore, speed of man = p/M=5/70

= 0.0714 m/s

c) By the impulse-momentum theorem, the impulse has to equal the change in momentum.

We know magnitude of the momentum of the bullet and man+gun is the same. Therefore, the impulse is the same

d) The acceleration of the bullet is greater than the acceleration of the gun since the forces are the same but the mass of the bullet is lesser than the gun.

As we know acceleration is force/mass

e) By Newton's third law, the force of the bullet on the gun is equal to the force of the gun on the bullet as they constitute an action-reaction pair.