A block of mass M that is attached to a spring is resting on a frictionless hori

Question

A block of mass M that is attached to a spring is resting on a frictionless horizontal table. Assume the spring is massless and its spring constant is k. A bullet of mass m is fired into the block from the left with a speed vo and comes to rest in the block. (Assume that this happens instantaneously). The motion of the block-bullet system results in simple harmonic of the block.

What is the speed of the block-bullet system immediately after the bullet comes to rest in the block.

Find the amplitude of the resulting simple harmonic motion.

How long does it take the block to first return to the position x = 0?

What is the magnitude of the velocity of the block when it first returns to the equilibrium position?

What is the magnitude of the acceleration of the block when it first returns to the equilibrium position?

Explanation / Answer

1) Pf = Pi

(M+m)*V = m*vo

V = m*vo/(M+m)

2) KE = PE

0.5*(M+m)*V^2 = 0.5*K*A^2

m^2*vo^2/(M+m) = k*A^2

A = m*vo*sqrt(1/k*(M+m))

3) t = T/4 = sqrt((M+m)/k) / 4

4) V = m*vo/(M+m)

5) a = 0

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