- #1

uchicago2012

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## Homework Statement

In the figure the block starts from rest at A, slides down the ramp, compresses the spring 0.75 meters, and goes back. The spring constant is 520 N/m, the block's mass is 12 kg, and the ramp is inclined at 30°. The horizontal part of the sliding is frictionless. If point A is 2 meters above the floor, (a) what is the block's speed at the bottom of the ramp? (b) How much work does friction do while the block descends the ramp? (c) After rebounding, the block starts back up the ramp. What is its speed at the bottom, heading up? (d) How far does it move back up the ramp? (Give a vertical distance.)

See Figure 1

## Homework Equations

W

_{nonconservative forces}= Change in KE + Change in PE

## The Attempt at a Solution

for a.

in the equation W

_{non}= KE

_{2 }- KE

_{1}+ PE

_{2}- PE

_{1}

where the initial is at the top of the ramp and the final is the point at which the spring is at its maximum compression

is PE

_{2}= 1/2kx

^{2}? I think that should be the only component of PE

_{2}, I just wasn't sure. It gave a reasonable answer once I solved for everything, it just made me a bit nervous to have the only final potential energy of the box be that of the spring.

for c.

now W

_{non}= 0 so

U

_{i}+ K

_{i}= U

_{f}+ K

_{f}

where the initial is the point at which the spring is at its maximum compression and the final is the point at which the box begins heading up the ramp.

I was confused as to what U

_{f}should be. It's mgy, but I'm not sure what to use for y. The box is beginning to head up the ramp but I'm unclear on whether it actually has an elevation at that point.