A 5.0 kg crate is on an incline that makes 30 degrees with the horizontal. If th

Question

A 5.0 kg crate is on an incline that makes 30 degrees with the horizontal. If the coefficient of static friction is 0.5, the maximum force (as shown in the image) that can be applied parallel to the plane of the incline without moving the crate is how many Newtons?

Please show all work, substitutions, and name the principles used.

A 5.0 kg crate is on an incline that makes 30 degrees with the horizontal. If the coefficient of static friction is 0.5, the maximum force (as shown in the image) that can be applied parallel to the plane of the incline without moving the crate is how many Newtons?

Explanation / Answer

The maximum force would have to total friction and the component of the weight down the plane.

Friction = uFn and Fn = mgcos(angle) on an incline, so

F = mgsin(angle) + umgcos(angle)

F = (5)(9.8)(sin 30) + (.5)(5)(9.8)(cos 30)

F = 45.7 N

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