Chapter 6, Problem 81AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# Measuring the speed of a bullet. A bullet of mass m is fired horizontally into a wooden block of mass M lying on a table. The bullet remains in the block after the collision. The coefficient of friction between the block and table is μ, and the block slides a distance d before stopping. Find the initial speed v0 of the bullet in terms of M, m, μ, g, and d.

To determine
The initial speed of the bullet in terms of M,m,μ,g and d.

Explanation

The kinetic frictional force when the block and the embedded bullet slides a distance is,

fk=Î¼kn=Î¼k(M+m)g

• Î¼k is the coefficient of kinetic friction
• M is the mass of the block
• m is the mass of the bullet
• g is the acceleration due to gravity

The net work done on the block and the embedded bullet during the time is,

Wnet=(fkcos180Â°)d=KEfâˆ’KEi=0âˆ’12(M+m)V2

• V is the velocity of the combined mass
• d is the distance moved by the combined mass

So, the velocity of the combined mass is,

V=âˆ’2f1dâˆ’(M+m)

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