(6%) Problem 6: Military rifles have a mechanism for reducing the recoil forces

Question

(6%) Problem 6: 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. 33% Part (a) Calculate the recoil velocity in the horizontal direction, in meters per second, of a 0.85-kg plunger that directly interacts with a 0.0205-kg bullet fired at 605 m/s from the g un. Take the firing direction to be the positive direction. 33% Part (b) If this part is stopped over a distance of 21 cm, what average force, in newtons, is exerted upon it by the gun? gp= |506 sin0 tan() | ( 789HOME cos0 cotan0asin acos0 atan0 acotan sinhO cosh0 tanh cotanh0 END Degrees Radians BACKSPACEEL CLEAR Submit Hint Feedback I give up! Hints: 000 deduction per hint. Hints remaining: 1 Feedback: deduction per feedback. 33% Part (c) To see how effective this is at reducing the force on the gun, find the ratio of the force that the plunger exerts on the gun to the force that the bullet would exert on the gun without this mechanism, if the bullet is accelerated to its final velocity in 11.5 ms

Explanation / Answer

a. m = 0.85 kg

M = 0.0205 kg

v = 605 m/s

recoil velocity = u

then from conservation of moemtnum

mu = Mv

u = 14.5911 m/s

b. d = 0.21 m

force = F

F = m(a)

also

2*a*d = u^2

hence a = 506.9 m/s/s

hence F = ma = 430.86945 N

c, t = 11.5*10^-3 s

force directly form the bullet, Fb = rate of change of momentum = 0.0205*605/11.5*10^-3

Fb = 1078.4782 N

Fb/F = 2.503 times

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