spring

You are holding a 5.0kg block just above the spring.The vertical spring has k=490 N/m.

a)How far does the spring compress if you let go of the block SUDEENLY
b)How far does the spring compress if you slowly lower the block to the point where you can remove your hand without disturbing it.
c)why are the two answers different?


Ans:
a)
if the block is let go SUDEENLY,
maximum compression
= 2mg/k
= 2 x 5kg x 10m/s^2 / 490N/m
= 0.204m

b)
if the blcok is lower to the point a equilibrium,
compression
= mg/k
= 5kg x 10m/s^2 / 490N/m
= 0.102m

c)
In case a), the potential energy of the block is converted to the energy stored in the spring.
Let x be the maximum compression, then mgx = 1/2 kx^2.
Therefore, x = 2mg/k

In case b), when the hand is remove without disturbing the block and spring, the weight of the block is balanced by the force exerted by the spring,
Let x be the compression at equilibrium, then mg = kx.
x = mg/k