# Application with conservative and nonconservative forces

## Homework Statement

A 3.0-kg block sliding on a horizontal surface is accelerated by a compressed spring. At first, the block slides without friction. But after leaving the spring, the block travels over a new portion of the surface, with a coefficient of friction 0.20, for a distance of 8.0 m before coming to rest (see Figure 8.12). The force constant of the spring is 120 N/m.

(a) What was the maximum kinetic energy of the block?
(b) How far was the spring compressed before being released?

Here is a link to the picture (Figure 8.12)
http://img148.imageshack.us/img148/3631/figure812pp1.jpg [Broken]

## The Attempt at a Solution

I do not really understand how to start with this problem. I probably have to break it up into two cases, the distance where forces are conservative (the spring) and the distance where forces are not conservative (the friction). I do not know how to set up the problem because a distance isn't given for where the block is when the spring is compressed. Therefore, I am not sure how I can describe potential energy and apply the formulas for energy conservation.

Any hints to get me started would be greatly appreciated, then I will work some of it out and continue to relay back and forth in this post.

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nrqed
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## Homework Statement

A 3.0-kg block sliding on a horizontal surface is accelerated by a compressed spring. At first, the block slides without friction. But after leaving the spring, the block travels over a new portion of the surface, with a coefficient of friction 0.20, for a distance of 8.0 m before coming to rest (see Figure 8.12). The force constant of the spring is 120 N/m.

(a) What was the maximum kinetic energy of the block?
(b) How far was the spring compressed before being released?

Here is a link to the picture (Figure 8.12)
http://img148.imageshack.us/img148/3631/figure812pp1.jpg [Broken]

## The Attempt at a Solution

I do not really understand how to start with this problem. I probably have to break it up into two cases, the distance where forces are conservative (the spring) and the distance where forces are not conservative (the friction). I do not know how to set up the problem because a distance isn't given for where the block is when the spring is compressed. Therefore, I am not sure how I can describe potential energy and apply the formulas for energy conservation.

Any hints to get me started would be greatly appreciated, then I will work some of it out and continue to relay back and forth in this post.
You could do it in two steps (from initial until it touches the spring and then from the moment it touches the spring until it's fully compressed) or in one step, it does not matter.

You can solve for the distance of compression. All you need to do is to use the fact that at maximum compression the speed is zero. So all the kinetic energy the block has when it reaches the spring (after the friction part) is cnverted into potential energy stored in the spring when the spring is fully compressed)

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I thought the block is starting at the point where the spring is fully compressed.. then being let go and being shot to the right (in the picture).. all the way through the no-friction surface.. and then the friction surface (for 8 m)...

It seems like you're saying that the block is coming in from the right of the photo (through the friction surface)... then hitting the spring.

Does it matter which way you look at it?