A box of mass must be moved up a straight ramp of length that rises a vertical height…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A box of mass m must be moved up a straight ramp of length L that rises a vertical height h above the floor. The ramp surface exerts a constant kinetic friction force of magnitude f on the box, independent of speed. A worker plans to push the box up the ramp with a constant horizontal force F so that the box reaches the top with speed vf.
Assume the box starts from rest at the bottom of the ramp and remains in contact with the ramp surface at all times. Ignore air resistance.
(a) Express the work done on the box by each of the following forces in terms of the given symbols and fundamental constants, as appropriate.
(i) Gravity
(ii) Kinetic friction
(iii) The worker’s applied force
(b) Derive an expression for the magnitude F of the horizontal force the worker must exert so that the box arrives at the top of the ramp with speed vf. Your final answer may contain m,L,h,f,vf, and physical constants.