# Finding coefficient of kinetic friction

## Homework Statement

A 100 N force directed 37° below the horizontal is applied to a 30 kg object on a horizontal surface. If the magnitude of the acceleration of the object is 1.3 m/s2, what is the coefficient of kinetic friction (μk) between the object and the surface?

F = ma

## The Attempt at a Solution

I drew the body diagram and tried calculating the net force in the x direction.
This is what I got:

F = Fpx (the 100 N force) - Ffr
Fpx is 100cos37 and Ffr is μmg, so
ma = 79.86 - 294μ

I plugged in 1.3 for a and got 0.24 for the answer.
The correct answer is 0.12.
Not sure where I went wrong, any help would be appreciated. Thanks!

## Answers and Replies

Simon Bridge
Homework Helper
Ffr is μmg
... this is not correct.
Did you remember to sum the forces in the y direction?

It said friction force equals u*normal force.. isn't normal force mg?

Simon Bridge
Homework Helper
It said friction force equals u*normal force.. isn't normal force mg?
No.

You have a free body diagram - add up the forces in the y direction.

ok.
In the diagram I drew I just have the 100N force, normal force, friction force and mg. Is that correct?
So the forces in the y direction would be just "100sin37 + Fn - mg" ?
But can I still set it equal to m*a with a being 1.3?

Simon Bridge
Homework Helper
100sin37 + Fn - mg
What direction does the magnitude 100sin37 force act in?
What do these forces add up to? (hint: does the object move in the y direction?)
Solve for Fn.

So it's 100sin37 - Fn - mg = 0 ?
When I solve for Fn I get 233.81. I solved for the forces in the x direction (ma = 100cos37 - Ffr) and I got Ffr to be 40.86.
So do I just divide that by Fn to get the coefficient?
It's still wrong, I'm confused

haruspex
Homework Helper
Gold Member
2020 Award
So it's 100sin37 - Fn - mg = 0 ?
No, that's still wrong. The normal force has to balance the sum of the other vertical forces.

OHHHH I got one of the signs wrong... Just making sure, so it's Fn = 100sin37 + mg? Because then I get 0.115 which should be right

Simon Bridge
Homework Helper
Well done.

Use your free body diagram to get the signs right.
You should draw the diagonal forces as diagonal arrows - then divide into components on the diagram.
Thus the 100N force would be diagonally downwards and you cannot get the component directions wrong.

Note: The forces all add head-to-tail to make a resultant force pointing horizontally.
If you fiddle with the order of the addition, you should get an easy triangle.