URGENT physics Help Please Please - Block on Spring without Friction?

Question

Block on Spring without Friction

A spring is stretched a distance of Dx = 40 cm beyond its relaxed length. Attached to the end of the spring is an block of mass m = 8 kg, which rests on a horizontal frictionless surface. A force of magnitude 40 N is required to hold the block at this position. The force is then removed.
a) When the spring again returns to its unstretched length, what is the speed of the attached object?

v0 = m/s

HELP: Apply the work energy theorem: KEfinal - KEinitial = Wspring.
HELP: What is the work done by the spring? How do we find it from the information given?
b) When the spring has returned only halfway (20 cm), what is the speed of the attached object?

v1/2 = m/s

Answer 1

The spring equations are:

F(D) = -Cs x D
Es = (1/2) x Cs x D^2

where
F(D) is the force exerted by the spring at displacement D
Cs is the spring constant
Es is the potential energy of the spring at displacement D

So with the data given, you can compute the spring constant with the force equation and the potential energy from the energy equation.

When the spring is at its unstretched length, all that potential energy has been converted to kinetic energy. Kinetic energy is given by:

Ek = (1/2) x M x V^2

You know, Ek and M so you can compute V^2 and then V.

Work = Energy so you can answer the remaining questions.