A crate of mass 11.5 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 11.5 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 18.5° 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?

(b) How much mechanical energy is lost due to friction?

(c) How much work is done by the 100 N force?

(d) What is the change in kinetic energy of the crate?

(e) What is the speed of the crate after being pulled 5.20 m?

Explanation / Answer

a) gravitational force = mgsin(18.5) = 35.8 N

work done by gravity = 35.8 * (-5.2) = -186.16 J

b)

friction force = u*mgcos(18.5) = 42.8 N

mechanical energy lost due to friction force = 42.8*5.2 = 222.56 J

c)

work done by 100 N force = 100*5.2 = 520 J

d) using conservation of energy

change in kinetic energy of the crate = 520 - 186.16 - 222.56 = 111.28 J

c)

.5 m(v^2 - u ^2 ) = 111.28

speed of the create after being pulled 5.2 m = v = 4.65 m/s

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