# Block on Spring with Friction Problem

#### weebedink

1. The problem statement, all variables and given/known data
A block of mass m is moving at a speed of v0 at a distance L away from a spring of on a table with coefficient of friction μk. How much does the block compress the spring? Determine the average power generated due to friction during the compression of the spring.

I'm not sure if there is a problem with the question or is it just my methods, but is there a spring constant K needed to solve this problem? Also how would I solve for the average power?

2. Relevant equations
W+Wfriction=ΔKE+ΔUspring

Wfriction=Ffrictionx=μkmgx

3. The attempt at a solution
I split the problem into three sections. When the spring is compressed, right after the block reaches the end of the spring, and when the block is a distance L away from the spring. From these positions I got two equations and combined them into this:

kx2-2μkmgx=m(v0+2μkgL)

Now if the k was given, I would just solve for x and that would be the compression of the spring. Am I missing something? or do I need a k to keep on going?

For the average power dissipated by friction, I would use the Wfrictionkmgx and then maybe integrate with respect to time or divide by time. Am I right in my assumption?

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#### Delphi51

Homework Helper
Welcome to PF!
Yes, you sure do need k. The block will compress the spring more if k is smaller. The answer depends on k.

There must be a typo in your equation - the v should be squared, shouldn't it?
Otherwise, it makes perfect sense.

#### ehild

Homework Helper
Now if the k was given, I would just solve for x and that would be the compression of the spring. Am I missing something? or do I need a k to keep on going?

For the average power dissipated by friction, I would use the Wfrictionkmgx and then [STRIKE]maybe integrate with respect to time or[/STRIKE] divide by time. Am I right in my assumption?
You need the spring constant.
The average power is work done divided by time. The friction is a constant force, so its work along a distance x is W=μkmgx.
Find the time needed to stop the object.

The instantaneous power is P=Fv. You can get a rough estimate of the average power by using the half of the speed the object reaches the spring with.

ehild

#### weebedink

There must be a typo in your equation - the v should be squared, shouldn't it?
Yeah my bad haha it is.

The average power is work done divided by time. The friction is a constant force, so its work along a distance x is W=μkmgx.
Find the time needed to stop the object.
Yeah I was able to solve using forces and kinematics.

Thank you so much for all of the help!

Homework Helper
You are welcome.

ehild

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