A crate of mass 12.5 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 12.5 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 21.0° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.20 m.
(a) How much work is done by gravity?
1 J
(b) How much mechanical energy is lost due to friction?
2 J
(c) How much work is done by the 100 N force?
3 J
(d) What is the change in kinetic energy of the crate?
4 J
(e) What is the speed of the crate after being pulled 5.20 m?
5 m/s

Explanation / Answer

1) work of gravity is -mgh.
-(12.5 kg)(9.80m/s^2)(5.20sin21.0) = -228.280 J

2) change in kinetic energy (here you will also find speed of the crate too):
Ff= uk*Fn = 0.400*12.5kg*9.80cos21.0 = 45.74 N

Distance moved 's' = 5.20 m

work done against friction Wf =fs= 45.74 x 5.20

                                               = 237.84 J

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