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 4.183-kgwooden block resting on a smooth surface, and attached to a spring of spring constant k = 161.9N/m . The bullet, whose mass is7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460cm .

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 4.183-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 161.9N/m . The bullet, whose mass is7.870 g, remains embedded in the wooden block. She measures the maximum distance that the block compresses the spring to be 9.460cm. What is the speed v of the bullet?

Explanation / Answer

velocity of bullet + block after it embeds.. = (m / (M+m) ) * v = 0.007870 / ( 4.183 + 0.007870) * v
= 0.0018778917 * v m/sec

so. 0.5 * 161.9 * 0.0946^2 = 0.5 * ( 4.183 + 0.007870) * (0.0018778917)^2 * v^2

so.. v = 313.1063843 m/sec

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