Dr. Francisco Von II
Jan 20, 2025
Find an expression for the bullet’s speed.?
A bullet of mass ( m ) is fired into a block of mass ( M ) that is initially at rest. After the collision, the block, with the embedded bullet, slides a distance ( d ) across a horizontal surface. The coefficient of kinetic friction between the block and the surface is denoted as ( \mu_k ). Find an expression for the speed of the bullet, ( V_{\text{bullet}} ), using the variables ( d ), ( \mu_k ), ( m ), and ( M ).
3 Answers
(K + U)initial – NC = (K + U)final, NC being non-conservative forces. μ is kinetic friction
initially, K = mv^2/2 and U = 0, NC = (m + M)gμ
finally, K = 0 and U = 0
mv^2/2 + 0 – (m + M)gμ = 0 + 0
mv^2 = 2(m + M)gμ
v^2 = (2(m + M)gμ) / m
v = √[(2(m + M)gμ) / m]
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