A force of 132N is a push applied horizontally on a mass of 20kg up a incline at

Question

A force of 132N is a push applied horizontally on a mass of 20kg up a incline at angle 30 degrees and a coefficient of kenetic friction of 0.20. Calculate the value this force must have to keep the mass moving up the plane at a constant speed. (B) Is there an agle for the plane at which no horizontal force can keep the mass moving at a constant speed?

Explanation / Answer

A) One key-phrase to watch for here is "constant speed." This indicates that there is no acceleration, and thus no effective force in the x-direction. More simply, this means that the frictional force is equal to the applied force, that's why it's not accelerating. ?Fx = 0 = mgsinø - Ff --> Ff = mgsinø First off, lets establish our given. Force applied: 132N at 30°, effectively 132cosø in the x-direction. (This is evident after drawing a free-body diagram and realizing that the force applied is horizontal to the block inclined 30° on the plane.) So.. Force applied = 132cos30 =114.3 N Gravitational force down-slope that the block experiences: mgsinø = 20(9.8)sin30 = 98 N - this is also the force required to move the block up the plane at a constant speed. B) I might be misunderstanding your question, but I'll answer it in two ways. 1) The only way it would be impossible to move the block up the planes slope is if the force applied was perpendicular to the normal force. This would mean that the slope would have to be = 90° (If it's greater than 90° you'd actually be moving the block down the slope rather than just holding it against a wall). 2) The second way I'll answer this is by establishing the maximum angle the plane can have so that the applied force of 132 N will continue to move the block up the slope. I'll use the gravitational value the block experiences down the slope, and solve for ø. mgsinø = 132 --> ø = arcsin(132/[(20)(9.8)]) = 42.3° is the maximum ø possible that will keep the block moving up slope at a constant speed. I hope this is what you needed, or at least points you into the right direction.

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