A 21.0-kg box rests on a frictionless ramp with a 15.1° slope. The mover pulls on a rope attached to the box to pull it up the incline. If the rope makes an angle of 43.6° with the horizontal, what is the smallest force F the mover will have to exert to move the box up the ramp?

Answer 1

I would like to have one of these frictionless ramps.

The force in the direction of the ramp is Fcos43.6
The weight portion trying to slide the box down the ramp is 21Sin15.1

Net pulling force up the ramp
Fcos43.6-21sin15.1
set that to zero, andsolve for F