Work and Potential/Kinetic Energy (spring problem)

[stevebrstlct]

Homework Statement

A)
A ball with a mass of .360kg is dropped from a height of 1.20 meters above the top of a fixed vertical spring, whose force constant is 350 N/m. What is the speed of the ball when the spring has been compressed 5.0cm?
(Ignore the mass of the spring; also, notice that this problem contains both forms of potential energy (gravitational and spring pot'l En.)

B)
What is the maximum distance the spring is compressed by the ball?

Homework Equations

Work=F$$\cdot$$D
PE:
U=1/2K(x_f-x_i)²
$$\Delta$$U=mg$$\cdot$$$$\Delta$$Y
K_i+U_i=K_f+U_f

m=.360 Kg
H=1.2m
$$\Delta$$X=5.0 cm
K=350 Nm

The Attempt at a Solution

We did a problem similar to this on a frictionless horizontal plane. We used the conservation of energy to solve it. In the picture we drew we found where the Pot. and Kin. energies were zero which left the equation with only one unknown left. In that problem there was constant velocity but in the problem I just posted we have an acceleration of mg down which leaves me confused on what the right way to solve this is. I also know for part B the velocity will be 0.

 

[LowlyPion]

Welcome to PF.

Figure your changes in potential energy.

m*g*h = .36*9.8*(1.2 + .5)

Now how much potential energy is in the spring?

1/2*k*x²

Whatever is left over then must be kinetic energy right?

 

[stevebrstlct]

Wow that makes much more sense now, thanks a lot!