A box is pushed a distance d along a ramp at a constant speed by a horizontal fo

Question

A box is pushed a distance d along a ramp at a constant speed by a horizontal force, Fa. The mass of the box is m. The ramp is inclined at an angle of ? above the horizontal.
1. If the ramp if frictionless, how much work is done by the horizontal force as the box moves a distance d up the ramp? Your answer should only contain the parameters m, d, ?, and the physical constant g.
??

2. If the coefficient of kinetic friction between the box and the ramp is ?k, how much work is done by the horizontal force as the box moves a distance d up the ramp? Your answer should only contain the parameters m, d, ?, ?k, and the physical constant g.
?

Explanation / Answer

1) so the block gained an amount of energy going up the ramp by gaining height:

E=mgh = mg d sin

this energy change comes from the work, so W =mg d sin

b) now we have to gain the energy from part a and provide the energy used by friction

W friction= -Nd

N-mgcos=0 so N=mgcos

thus W friction = - mgd cos

so W from the force = mg d sin + mgd cos

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