A horizontal flat plate of mass 1.5 kg is suspended in mid-air by a stream of identical bullets fired vertically upwards from below. Each bullet has a mass of 10 g and strikes the plate with a speed of 150 m s ⁻¹ . If the bullets rebound elastically downwards with the same speed, the number of bullets that must be fired per second to keep the plate stationary is : (Take g = 10 m s ⁻² )

Step-by-step solution

For the plate to remain stationary, the upward force exerted by the bullets must balance the weight of the plate. Weight of the plate, W = Mg = 1.5 10 = 15 N . Since the collision is elastic, the bullet rebounds with the same speed. The change in momentum of a single bullet is: p = m v - (-m v) = 2 m v Let n be the number of bullets fired per second. The total upward force exerted on the plate is the rate of change of momentum of the bullets: F = n (2 m v) Equating the force to the weight of the plate: n (2 m v) =