A #3.0# #kg# bag of potatoes is sitting on top of a spring with a spring constant #k=600# #Nm^-1#. (a) What is the compression of the spring at the equilibrium point?
The sack is lifted by #0.5# #m# above the spring and dropped on it. (b) What is the maximum compression of the spring?
The sack is lifted by
1 Answer
a) The compression of the spring at equilibrium is
b) The maximum compression of the spring is
Explanation:
a) The weight force of the bag of potatoes is given by:
The Hooke's law expression for the spring is
b) We need to calculate the kinetic energy of the falling bag just before it hits the spring, then convert that kinetic energy into spring potential energy:
But we don't yet know the velocity of the bag:
Therefore
Then:
This converts to spring potential energy:
Rearrange to make