2D Friction-Finding the Force of Friction without Mu

In summary, the problem involves finding the force of friction without knowing the coefficient of friction. After drawing a free-body diagram and using the equations FW=mg and [Sigma]Fy=0, the force of friction can be solved for by setting up equations in the y and x directions. The unknowns can then be solved for and the force of friction can be found.
  • #1
2D Friction--Finding the Force of Friction without Mu

Homework Statement

A 1500kg car is parked on a 4-degree incline. The acceleration of gravity is 9.8 m/s2. Find the force of friction keeping the car from sliding down the incline.

Homework Equations

[Sigma]Fy=0, so Top=Bottom
"Friction is Fun:" fs=musFN
Since the degree of incline is 4 degrees, the angle with the "left" part of the x-axis on the free-body diagram and FW is 86 degrees.

The Attempt at a Solution

After drawing a free-body diagram, I calculated Fw=(1500)(9.8)=14700N
Next, I used Top=Bottom to calculate FN=14700sin(86)=14664.19154N
Third, fs=musFN. This is where I got stuck. How can I solve for the force of friction without mu?
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  • #2

In your free body diagram, you should have oriented your axis so the y points normal to the plane and x points along the plane.

In the +y direction, you have a normal force N and a component of the weight force W.
In the +x direction you have a friction force f and the other component of the weight force.

In each direction, write out all the forces in a row (some of them will be negative), put "+" signs between them and an "= ma" at the end. What is the acceleration?
Remember to write W just as W (you can put W=mg later if you need to) and friction just as f (you can put f=μsN later if you need to.)

This will give you two equations, and you have two unknowns. The unknowns are f and N.
But I think you'll find that the equation with f in it has no other unknowns so you can solve it right off.

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