A bullet of mass m is fired into a block of mass M that is at rest. The block, w

Question

A bullet of mass m is fired into a block of mass Mthat is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is k

(a) Find an expression for the bullet's speed

vbullet.

Express your answer in terms of the variables m, M, k, d, and appropriate constants.

(b) What is the speed of a 9.0

g bullet that, when fired into a 11 kg stationary wood block, causes the block to slide 4.8 cm across a wood table? Assume that k=0.20.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

mass of bullet = m

initial speed = u

block of mass = M ( at rest)

final speed = v

distance slid on the floor = d

coefficient of fricion = k

a. from conservation of meomentum

mu = (M + m)v

v = mu/(M + m)

also, frictional acceleration = k*g

hence

2*kg*d = v^2 = m^2*u^2/(M + m)

u = sqroot((2*kg*d*(M + m)))/m

b. m = 0.009 kg

M = 11 kg

d = 0.048 m

k = 0.2

u = sqroot(2*0.2*9.81*(11 + 0.009))/0.009

u = 730.29 m/s

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