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?
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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