Static Friction of box on a ramp

AI Thread Summary
A 100kg box on a ramp begins to slide at a 15-degree incline, prompting the need to calculate the coefficient of static friction. The relevant equations involve the forces acting on the box, including gravitational components and the normal force. Participants emphasize using trigonometric functions to determine the gravitational force parallel to the ramp and the maximum static friction force. The discussion highlights the relationship between static friction and the normal force, which is affected by the ramp's angle. The solution requires setting up an equation to solve for the coefficient of friction based on these forces.
elbonymcbride
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Homework Statement


A 100kg box is placed on a ramp. As part of the ramp is raised, the box begins to move downward just as the angle of inclination reaches 15 degrees. What is the coefficient of static friction between the box and the ramp?


Homework Equations


Fn = mg-Fsin15


The Attempt at a Solution


Fcos15 = Mk(mg-Fsin15)
F(cos15+sin15) = Mkmg
F=Mkmg/cos15+Mksin15
= 0.2(100kg)(9.8)\cos15+0.2sin15
I continued to solve this problem, however the answer that I got was not one of my answer choices. I believe that I used the wrong equation; but even with the right equation, I never know where to start. Can anybody help me?
 
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Hint: At the point where the box just barely begins to slide, the force acting down the ramp (the component of gravity) is just overcoming the static friction.

What's the component of gravity down the ramp?
What's the maximum value of static friction?

These both depend on the angle. Set up an equation and [STRIKE]solve for the angle[/STRIKE]. Edit: You are given the angle; I meant set up an equation and solve for the coefficient of friction.
 
Last edited:
would the maximum value of static friction be zero?
How would I find the component of gravity with the information given?
 
elbonymcbride said:
would the maximum value of static friction be zero?
No. Hint: How does friction force relate to the normal force? How does the normal force depend on the angle?
How would I find the component of gravity with the information given?
You are given the angle of the ramp. Use a bit of trig to find the component parallel to the ramp.
 

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