a box with mass 20kg rests on a frictionless ramp with a 15degree slope. a mover pulls up on a rope attached to the box to pull it up the incline. if the rope makes a 40 degree angle with the horizontal, what's the smallest force that the mover will have to exert to move the box up the ramp?

Question

a box with mass 20kg rests on a frictionless ramp with a 15degree slope.  a mover pulls up on a rope attached to the box to pull it up the incline.  if the rope makes a 40 degree angle with the horizontal, what's the smallest force that the mover will have to exert to move the box up the ramp?

bobpursley · Accepted Answer

Ok, the rope makes a 25 degree pull from the direction of the ramp. That means it has a component in the direction of the ramp (F*cos25)

Weight of the box is directed down the ramp, mgSin15
So F*cos25=mgSin15 to put it in equilibrium, and F has to be slightly larger to move it up the ramp. Solve for F

Angjabgkj · Answer

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