14. Bob drags a box with a mass m=45kg up a ramp. The ramp makes an angle of 25◦ with the horizontal direction. Bob pulls the the box upwards at a constant velocity 5m/s by applying a force F~ whose direction makes angle of 30◦ with the ramp. The coefficient of kinetic friction between the ramp and the box µk = 0.2. Determine the magnitude of the force F~ .
Answer is F=275.7N
Let us consider that the angle made by the ramp with horizontal is
and the angle made by the force with ramp is
Following figure depicts the situation and the forces acting on the box. Frictional force will be acting opposite the direction of motion that means, downwards along with mgsin().
So, the Normal force acting on the rough surface is given by,
Where F is the force that is applied by the Bob.
Since the box is moving with uniform speed, the component of forces acting parallel to the direction of motion must be equal.
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