# Horizontal spring problem with friction?

## Homework Statement

A 4-kg object sliding at speed 5 m/s along a smooth horizontal surface encounters a rough surface, 1.5 meters wide. The coefficient of kinetic friction over the rough surface is 0.20. After leaving the rough surface, the object continues over smooth surface until it strikes the ends of a horizontally-aligned spring, whose spring constant is 200 N/m, and whose opposite end is attached to a wall. What will be the maximum compression of the spring, in meters?

## The Attempt at a Solution

I know this must be a conservation of energy problem.

0.5 mv2 + 0.5 kx2 = 0.5 mv02 + 0.5 kx02

But since friction is involved, I'm not sure how to incorporate it.

## Answers and Replies

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*edit* Welcome TO PF!!!!! remember to post any additional questions, we help with homework not do it, that way it helps you get a grasp on things :)

Almost, this isnt a conservation of energy problem. This is the law of mechanical energy with Non-Conservative Forces.

Your formula should be something like:

$$\sum{E_{before}} = \sum{E_{after}} + W_{NC}$$

so the total energy before is equal to the total energy after plus the work done by non conservative forces, in this case. Friction. remember its work not force. $$W_{NC} = F_fdcos\theta$$

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*edit* Welcome TO PF!!!!! remember to post any additional questions, we help with homework not do it, that way it helps you get a grasp on things :)

Almost, this isnt a conservation of energy problem. This is the law of mechanical energy with Non-Conservative Forces.

Your formula should be something like:

$$\sum{E_{before}} = \sum{E_{after}} + W_{NC}$$

so the total energy before is equal to the total energy after plus the work done by non conservative forces, in this case. Friction. remember its work not force. $$W_{NC} = F_fdcos\theta$$
Thank you for the help! I was able to work it out!