# Finding the coefficient of friction on a ramp

## Homework Statement

You do 2.2 kJ of work pushing a trunk at a constant speed 3.1 m along a ramp inclined upward at 22 degrees. What is the frictional coefficient between the trunk and the ramp?

## Homework Equations

W = F*d
Ff = μmg * cos(θ)
Fg = mg * sin(θ)

## The Attempt at a Solution

To find the force exerted on the trunk up the ramp, I divide 2200 J by 3.1 m to get 710 N.

Since the trunk is moving at a constant speed, the forces pulling the trunk down the ramp must equal the forces pushing it up the ramp.

So,

710 = Fg + Ff

710 = mg*sin(22) + μmg*cos(22)

710 = mg( sin(22) + μcos(22) )

...Aaaaand this is where I get stuck. I feel like there is some obvious way to either solve for or get rid of the mass that I'm just not seeing. My book gives 0.6 as the answer.

Any help would be greatly appreciated.

Hey you told it moves up with constant speed 3.1m/s
then why are you dividing work with speed to get the force

Simon Bridge
Homework Helper
Viru.universe said:
Hey you told it moves up with constant speed 3.1m/s
then why are you dividing work with speed to get the force
possibly:
1. that would not give force - work/speed has dimensions of force per unit time.
2. the time the work was done in was not given
3. the "3.1" figure is "3.1m" - not "3.1m/s". Spot the difference.

Mastevvs said:
I feel like there is some obvious way to either solve for or get rid of the mass that I'm just not seeing.
Welcome to PF;
Indeed: there is information provided in the problem that has not been used in the attempt at a solution. eg. it says that the movement was at constant speed - what does this tell you about the forces?

The way to handle this sort of problem is, usually, though conservation of energy.
Start by describing the energy changes that happen and recall how this is related to the work.
But in this case you have done enough groundwork already to get away without it.

Last edited:
ehild
Homework Helper
710 = mg( sin(22) + μcos(22) )

...Aaaaand this is where I get stuck. I feel like there is some obvious way to either solve for or get rid of the mass that I'm just not seeing. My book gives 0.6 as the answer.

Any help would be greatly appreciated.

Your work is correct and the problem can not be solved without the mass given.

ehild