A mass m = 16.0 kg is pulled along a horizontal floor, with a coefficient of kinetic friction μk = 0.14, for a distance d = 8.3 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle θ = 38.0° with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 38.0° (thus on the incline it is parallel to the surface) and has a tension T = 56.0 N.
2. The attempt at a solution
1) What is the work done by tension before the block gets to the incline?
T*cos(rad(theta))*d = 366.267398276404 J
2) What is the work done by friction as the block slides on the flat horizontal surface?
-muk*m*g*d = -182.38752 J
3) What is the speed of the block right before it begins to travel up the incline?
sqrt(2*(366.267+(-182.38))/m) = 4.79435866409679 m/s
4) How far up the incline does the block travel before coming to rest?
I have tried everything I can think of, but I keep getting it wrong...
5) What is the work done by gravity as it comes to rest?
This question depends on 4 if I'm not mistaken, so haven't been able to do it yet...