A block of mass M = 6.00 kg, at rest on a horizontal frictionless table, is atta

Question

A block of mass M = 6.00 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 5130 N/m. A bullet of mass m = 9.70 g and velocity ModifyingAbove v With right-arrow of magnitude 550 m/s strikes and is embedded in the block (the figure). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion.

Explanation / Answer

a) from law of conservation of momentum

v = [m / m + M] * v1

= [0.0097 / 6 + 0.0097] * 550

speed of the block = 0.89 m/s

b) 1/2 k x2 = 1/2 (M + m) v2

x = sqrt [(m + M / K) ] * v

= sqrt [(0.0097 + 6 / 5130)] * 0.89

amplitude = 0.030 m = 3.0 cm

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