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 M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is mu_k. Find an expression for the bullet's speed u_bullet. Express your answer in terms of the variables m, M,mu_k, d, and appropriate constants. What is the speed of a 11 g bullet that, when fired into a 11 kg stationary wood block, causes the block to slide 5.0 cm across a wood table? Assume that mu_k = 0.20. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A:

Initial momentum = Final momentum
p = mV = (m + M)v

Combined KE = p²/(2(m+M)) = (m+M)²v²/(2(m+M)) = ½(m+M)v²
This gets converted to work = friction force * distance:
work = µ(m+M)g * d = ½(m+M)v²
v² = 2µgd
v = (2µgd)

rearrange the first momentum eqn:
V = (m+M)v/m = ((m+M)/m)(2µgd) = Bullet speed, Vbullet.

Part B:

Putting all these values in the above expression -

V = [(0.011+11.0)/0.011](2x0.20x9.81x0.05) = 443.39 m/s.

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