Work on Spring?

Question

A mass of 0.129 kg hangs from a vertical spring in the lab room. You pull down on the mass and throw it vertically downward. The speed of the mass just after leaving your hand is 3.40 m/s.
a) While the mass moves downward a distance of 0.10 m, how much work was done on the mass by the Earth? Include the appropriate sign.
At the instant in part (a) when the mass has moved downward a distance of 0.10 m, the speed of the mass has decreased to 1.84 m/s. How much work was done on the mass by the spring? Include the appropriate sign.

Answer 1

For a, work = F*d
the force of gravity is m*g
w=.129*10*.10
0.129 Joules

that was using g=10

b) The work done by the spring moving an additional .10 m is equal to the delta energy stored in the spring which is the work done by the spring
I have to make an assumption
your hand did work, but we don't where you let go, just that the speed was 3.4 m/s, which translates to a kinetic energy of .5*m*v^2
The assumption is that you threw the mass instantaneously

This allows us to set up the following energy equation
PE-spring energy=delta kinetic energy
or
spring energy=PE-delta kinetic
=m*g*0.1-0.5*m*(1.84^2-3.4^2)
0.656 Joules using g=10

j