Your cat \"Ms.\" (mass 7.00 {\ m kg}) is trying to make it to the top of a frict

Question

Your cat "Ms." (mass 7.00 { m kg}) is trying to make it to the top of a frictionless ramp 2.00 { m m} long and inclined upward at 30.0 ^circ above the horizontal. Since the poor cat can't get any traction on the ramp, you push her up the entire length of the ramp by exerting a constant 100 { m N} force parallel to the ramp.

If Ms. takes a running start so that she is moving at 2.40 { m m/s} at the bottom of the ramp, what is her speed when she reaches the top of the incline? Use the work-energy theorem.

Explanation / Answer

The mass of the cat m = 7.0kg

the length of the ramp l = 2.0m

the applied force F = 100N

then the work done

W = F*l

      =( F - mgsin)*l

       = [100 - (7)(9.8)sin30](2.0)

        = 131.4 J

from work energy theorem

     W = 1/2mv^2 - 1/2mv0^2

     131.4 J = (0.5)(7)[ v^2 - v0^2]

     v^2 - v0^2 = 37.54

      v^2 = (2.4)^2 + 37.54

      therefore the speed

       v = 6.58 m/s

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