Please help! Problem on friction.

[andrealim]

A body of mass 2kg lies on a rough plane which is inclined at 30^o to the horizontal. A horizontal force of 20N is applied to the body in an attempt to push it up the plane, the body is found to be on the point of moving up the plane. Find μ, the coefficient of friction, between the body and the plane.

The answer is 0.279. Any help is greatly appreciated!

[FizziksGuy]

When I work through this I get a different answer... you can find a web tutorial on ramps as well as a video tutorial on ramps on the main APlusPhysics website or through the links above for more information. To dive into your specifics, however:

First, draw a diagram of the situation.

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The, draw the free body diagram and then the pseudo-free body diagram. When I do this, along the x-axis I see an applied force going up the ramp, and the force of friction as well as the horizontal component of the object's weight down the ramp (mgsinΘ). Along the y-axis you have the normal force up, and the vertical component of the object's weight down the y-axis (mg*cosΘ).

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Then, you can use Newton's 2nd Law in the x- direction to solve for the frictional force. Note that if the body is JUST at the point of moving up the plane, the acceleration of the object is just barely at zero, so the net force in the x-direction must be zero.

Next, we'll use Newton's 2nd Law in the y- direction to solve for the normal force.

Finally, we can solve for the coefficient of friction.

So, a slightly different answer compared to the one you provided. Note that I estimated g as 10 m/s² as opposed to 9.8 m/s² on the surface of Earth. Hope this helps!