Agent Arlene devised the following method of measuring the muzzle velocity of a

Question

Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (the figure below). She fires a bullet into a 4.293-kgwooden block resting on a smooth surface, and attached to a spring of spring constant k = 162.8N/m . The bullet, whose mass is 7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be9.460cm .

What is the speed v of the bullet?

Agent Arlene devised the following method of measuring the muzzle velocity of a rifle (the figure below). She fires a bullet into a 4.293-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 162.8N/m . The bullet, whose mass is 7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be9.460cm.

Explanation / Answer

Start with PE = KE for the spring

.5kx^2 = .5mv^2

(162.8)(.0946)^2 = (4.293 + .00787)(v^2)

v = .582 m/s

Then by conservation of momentum

mv = (M +m)v

.00787 v = (4.293 + .00787)(.582)

v = 318.1 m/s

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