Block on Spring with Friction Problem

[weebedink]

Homework Statement

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 μ_k. 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?

Homework Equations

W+W_friction=ΔKE+ΔU_spring

W_friction=F_frictionx=μ_kmgx

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:

kx²-2μ_kmgx=m(v₀+2μ_kgL)

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 W_friction=μ_kmgx and then maybe integrate with respect to time or divide by time. Am I right in my assumption?

 

[Delphi51]

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]

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 W_friction=μ_kmgx 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=μ_kmgx.
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!

 

[ehild]

You are welcome.ehild