A crate of mass 9.0 kg is pulled up a rough incline with an initial speed of 1.4

Question

A crate of mass 9.0 kg is pulled up a rough incline with an initial speed of 1.48 m/s. The pulling force is 92 N parallel to the incline, which makes an angle of 19.2 degree with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.94 m. (a) How much work is done by the gravitational force on the crate? -150 (b) Determine the increase in internal energy of the crate-incline system owing to friction. -164.4 (c) How much work is done by the 92-N force on the crate? -313.4 (d) What is the change in kinetic energy of the crate? 313.4 (e) What is the speed of the crate after being pulled 4.94 m?

Explanation / Answer

According to the given problem,

After resolving the forces,

a) work done by gravity = mglsin = 9*9.8*4.94 *0.3288 J = 143.3J

b) Internal energy increased due to friction

= WORK BONE BY FRICTION = -mglcos = -0.4*9*9.8*4.94*0.944 = -164.6 J

c) Work done by the 92- N force IS F*l = 92*4.94 = 454.48 J

d) Using work-kinetic energy principal

change in kineti energy = total work done = 433.18 J

e) Using the definition of kinetic energy,

1/2m(v2 - 1.482) = 433.18

v = 9.92 m/s

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