# A Box, A Slope, and a Spring

erok81

## 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
10.7 KB · Views: 513

## Answers and Replies

Homework Helper
Gold Member
Consider the total vertical distance that the mass travels. It is not just 4sin(30) meters. Once the mass hits the spring, the spring compresses by amount s. So the mass also travels a little more verically by the sin(30) component of s. 