A vertical ideal spring is mounted on the floor and has a spring constant of 134

Question

A vertical ideal spring is mounted on the floor and has a spring constant of 134 N/m. A 0.80-kg block is placed on the spring in two different ways. (a) In one case, the block is placed on the spring and not released until it rests stationary on the spring in its equilibrium position. Determine the amount (magnitude only) by which the spring is compressed. (b) In a second situation, the block is released from rest immediately after being placed on the spring and falls downward until it comes to a momentary halt. Determine the amount (magnitude only) by which the spring is now compressed.

Explanation / Answer

A) Apply, F = k*y

m*g = k*y

==> y = m*g/k

= 0.8*9.8/134

= 0.0585 m or 5.85 cm

B) Apply energy conservation

0.5*k*y^2 = m*g*y

k*y^2 = 2*m*g*y

y = 2*m*g/k

= 2*0.8*9.8/134

= 0.117 m or 11.7 m

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