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

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 is mu_k Find an expression for the bullet's speed Express your answer in terms of the variables m, M, mu_k, d and appropriate constant What is the speed of a 8.0 g bullet that when fired into a 10 kg wood block. causes the block to slide 5.2 cm across a wood table? Assume that mu_k = 0.20 Express your answer to two significant and include the appropriate units

Explanation / Answer

a) Conserve momentum at impact:
m*Vb + 0 = (m+M)v
v = Vb*m/(m+M)

Post-impact KE becomes friction work:
½(m+M)v² = µk*(m+M)*g*d mass (m+M) cancels; substitute for v
½*[Vb*m/(m+M)]² = µk*g*d
Vb*m/(m+M) = (2*µk*g*d)
Vb = (1 + M/m)·(2*µk*g*d)

b) Conserve momentum at impact:
m*Vb + 0 = (m+M)v
v = Vb*m/(m+M)

Post-impact KE becomes friction work:
½(m+M)v² = µk*(m+M)*g*d mass (m+M) cancels; substitute for v
½*[Vb*m/(m+M)]² = µk*g*d
Vb*m/(m+M) = (2*µk*g*d)
Vb = (1 + M/m)·(2*µk*g*d) = (1 + 10/0.008)·(2*0.2*9.81*0.052) = 565 m/s

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