Finding coefficient of kinetic friction

In summary, 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, μk is the coefficient of kinetic friction between the object and the surface.
  • #1
chococho
20
0

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?

Homework Equations



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!
 
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  • #2
chococho said:
Ffr is μmg
... this is not correct.
Did you remember to sum the forces in the y direction?
 
  • #3
It said friction force equals u*normal force.. isn't normal force mg?
 
  • #4
chococho said:
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.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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
 
  • #8
chococho said:
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.
 
  • #9
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
 
  • #10
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.
 

1. What is coefficient of kinetic friction?

The coefficient of kinetic friction is a value that represents the amount of friction between two surfaces in contact when one of the surfaces is in motion. It is denoted by the symbol "μ" and is a unitless quantity.

2. How is coefficient of kinetic friction calculated?

The coefficient of kinetic friction is calculated by dividing the force of kinetic friction by the normal force between the two surfaces. This can be represented by the formula μ = Fk/N, where μ is the coefficient of kinetic friction, Fk is the force of kinetic friction, and N is the normal force.

3. What factors affect the coefficient of kinetic friction?

The coefficient of kinetic friction can be affected by several factors, including the nature of the surfaces in contact, the roughness of the surfaces, the speed of motion, and the presence of any lubricants or contaminants.

4. How does the coefficient of kinetic friction differ from the coefficient of static friction?

The coefficient of kinetic friction represents the amount of friction between two surfaces when one is in motion, while the coefficient of static friction represents the amount of friction between two surfaces when there is no motion. The coefficient of static friction is typically higher than the coefficient of kinetic friction for the same two surfaces.

5. Why is knowing the coefficient of kinetic friction important?

Knowing the coefficient of kinetic friction is important for understanding and predicting the behavior of objects in motion. It is especially relevant in engineering and design, as it can help determine the amount of force needed to move an object or the amount of energy that will be lost due to friction.

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