Professional Application Military rifles have a mechanism for reducing the recoil forces of the gun on the person firing it. An internal part recoils over a relatively large distance and is stopped by damping mechanisms in the gun. The larger distance reduces the average force needed to stop the internal part. (a) Calculate the recoil velocity of a 1.00-kg plunger that directly interacts with a 0.0200-kg bullet fired at 600 m/s from the gun. (b) If this part is stopped over a distance of 20.0 cm, what average force is exerted upon it by the gun? (c) Compare this to the force exerted on the gun if the bullet is accelerated to its velocity in 10.0 ms (milliseconds).
Step-by-step solution In this problem mechanism of a military rifles is explain,considering the given data calculate the recoil velocity of plunger and according to the given condition calculate the average force exerted upon it and finally compare this to the force exerted on the gun if the bullet is accelerated to its velocity. Step 1 of 5 (a) The expression of conservation of momentum is, Here is mass of plunger, is mass of bullet, is initial velocity of plunger, is initial velocity of bullet, is final velocity of plunger and is final velocity of bullet Substitute, 1.00 kg for , 0.0200 kg for , 0 m/s for , 0 m/s for and 600 m/s for in the above expression. Hence the recoil velocity of plunger is . Step 2 of 5 (b) The expression for final velocity of plunger from kinematics is, Rearrange the expression for acceleration a. Substitute, 0 m/s for , for and for in the above expression, s (2) Step 3 of 5 So, the expression to find the force acting on the plunger is, Substitute for and for in the expression of force, The force acting on the plunger is .