Question
Thu July 05, 2012 By:

A gun is mounted on a vehicle which is at rest on a frictionless road.The mass of vehicle + gun is 1600 kg.the gun fires 20 bullets per second with a velocity of 400 m/s . Mass of each bullet is 20 gm.find the acceleration of the vehicle.

Expert Reply
Thu July 05, 2012
Total mass: M = 1600 kg
Velocity of bullets: v = 400 m/s
mass of each bullet: m = 0.020 kg
number of bullets fired per second: n = 20
Thus total momentum carried by bullets each second: P = nmv = 160 kgm/s
By law of conservation of momentum, the momentum tranferred to the vehicle each second will be P
This is the rate of momentum change of the vehicle and hence is equal to the amount of force exerted on the vehicle according to second law of motion.
Thus acceleration of vehicle, a = P/M = 160/1600 (considering the mass diference by the bullet s in the mass of vehicle is negligiable)
a = 0.1 m/s2
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