# A Box, A Slope, and a Spring

## Homework Statement

A 16.0kg box slides 4.0m down the frictionless ramp shown in the figure, then collides with a spring whose spring constant is 240N/m.

Figure Attached

It is a two part question, I got neither and don't understand why.

a)What is the maximum compression of the spring?
b)At what compression of the spring does the box have its maximum speed?

## Homework Equations

See next section.

## The Attempt at a Solution

For part a I did this two ways. First was to find the velocity at the spring and solve for delta s. This is what I did.
1/2mv^2 = 1/2ks^2 Solving for s using an initial velocity of 6.26 m/s I got a compressed lenght of 1.6m.

I then did it using U_g = U_sp or mgh = 1/2ks^2 which got me the same answer of 1.6m, still wrong. The correct answer is 1.98m.

The second part I thought was obvious and didn't need a forumla. I figured s soon as the mass hits the spring it is going to slow down. Because of this the max V would be the exact instant before the mass hits the spring, so I said 0cm. This turned out to the wrong as well, the correct answer being 32.7cm. This is the one I am most curious about. How isn't that zero?

#### Attachments

• knight_Figure_10_69.jpg
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