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An m = 4.57 kg box slides into a spring of spring constant 332 N/m, compressing...

An m = 4.57 kg box slides into a spring of spring constant 332 N/m, compressing it 26.8cm. What is the incoming speed of the block? How long is the box in contact with the spring before it bounces off in the opposite direction?

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Answer #1

A.

Using energy conservation

dKE = dPE

0.5*m*v^2 - 0 = 0.5*k*dx^2

v = sqrt (k*dx^2/m)

v = dx*sqrt (k/m)

v = 0.268*sqrt (332/4.57)

v = 2.28 m/sec

B.

T = 2*pi/w

w = sqrt (k/m)

t = T/2

t = pi*sqrt (m/k)

t = pi*sqrt (4.57/332) = 0.368 sec

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