# Kinetic Friction Coefficient

## Homework Statement

A block is projected up an inclined plane that makes an angle
θ to the horizontal. It returns
to its initial position with half its initial speed. What is the coefficient of kinetic friction
between the block and the plane in terms of the angle of the incline?

Not sure?

## The Attempt at a Solution

I know that generally, the co-efficient is tanθ, and I know how to derive that, but I am unsure what to do here

arildno
Homework Helper
Gold Member
Dearly Missed
Try to set up the equation for the mechanical energy of the system.
Remember to include the work of friction.
You have essentially TWO unknows in this problem, the height the block attains, and the coefficient of friction.:

Use the energy equation twice, one for comparing initial mechanical energy relative to position of maximal height (where you know the velocity is 0), and the second when the block has returned.
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And no, the kinetic friction coefficient (mu) is NOT generally equal to tan(theta).

The coefficient for maximal STATIC friction, though, can be estimated by the SLIP ANGLE "theta" by that formula.

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What do you mean the work energy theorem? Are you referring to Wnet=change in Kinectic energy, and if so, then the change from the start at the bottom to the end when its at the bottom again? How do I involve friction into this?

arildno
Homework Helper
Gold Member
Dearly Missed
Yes, I mean the work-energy theorem.
The frictional force will yield a net work, even though the block returns to its initial position.

Chestermiller
Mentor
In terms of θ, what is the normal force acting on the block? In terms of θ and μ (coefficient of kinetic friction), what is the frictional force acting on the block? If the block moves up the plane a distance L (where it stops), how much work does the frictional force do on the block? If the block has an initial velocity v0 and it stops after a distance L, what is its change in kinetic energy? What is its change in potential energy. How is the distance L related to v0, μ, and θ? How much frictional work has been done after the block has gone up the plane and come back down to its original position? What is the change in potential energy. If its final velocity is half its initial velocity up the plane, what is its change in kinetic energy? What coefficient of kinetic friction required to make all this happen?

"how much work does the frictional force do on the block?"
How do you find this?

haruspex
Homework Helper
Gold Member
2020 Award
"how much work does the frictional force do on the block?"
How do you find this?
If the block travels a total distance s, and throughout that travel its movement has been opposed by a frictional force F, how much work has been done against friction?

arildno
Homework Helper
Gold Member
Dearly Missed
Well, the frictional force is a CONSTANT! Then the work is easy to set up.
Set up the work energy theorem for the two nstances:
1.Start versus at maximal height
2. Maximal height versus return position.

(The work from friction will NOT cancel if you set up this properly!)

you have been told WHAT to do, several times over in this thread.
Now, DO it, rather than anything else.

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Chestermiller
Mentor
"how much work does the frictional force do on the block?"
How do you find this?

Let's see you answer my first two questions first before you address this question. If you can't answer them, then you will not be answer this question.