Physic Labs

Problem 1

A bullet of mass mm travels horizontally at speed v0v_0 through a stationary wooden block of mass MM. After exiting, the bullet has speed v0/2v_0/2. The block then slides on a rough horizontal surface with kinetic friction coefficient μ\mu. Find the block's speed immediately after the interaction and its stopping distance. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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Ff=μMg,af=μgF_f=\mu Mg,\qquad a_f=\mu g
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Kinetic friction has magnitude μMg\mu Mg, giving the block deceleration μg\mu g. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.