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 4.046-kg wooden block resting on a smooth surface, and attached to a spring of spring constant k = 161.3 N/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 9.460 cm .

What is the speed v of the bullet?

Express your answer to four significant figures and include the appropriate units.

Explanation / Answer

energy conservation

loss in KE of (M+m) block = gain in spring energy

=> 1/2*(4.046+7.870)*V^2 = 1/2*161.3*(0.09460)^2

=> V = 0.347 m/s

now momentum conservation

(4.046+7.870)*0.347 = 0.07870*V

=> V = 52.53 m/s

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