A crate of mass 10.2 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 10.2 kg is pulled up a rough incline with an initial speed of 1.42 m/s. The pulling force is 104 N parallel to the incline, which makes an angle of 19.4° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.06 m (a) How much work is done by the gravitational force on the crate? (b) Determine the increase in internal energy of the crate-incline system owing to friction. c) How much work is done by the 104-N force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5.06 m? m/s

Explanation / Answer

(A) W = F.d = F d cos(theta)

Wg = m g L cos(90 + 19.4)

= 10.2 x 9.8 x 5.06 x sin19.4

= - 168 J

(B) f = uk N = uk m g cos19.4

Wf = - f.L = - 0.4 x 10.2 x 9.8 x cos19.4 x 5.06

Wf = - 190.83 J  

increase in internal energy = 190.83 J  

(C) W = 104 x 5.06 = 526.24 J

(D) change in KE = total work done

= 167.4 J  

(e) 167.4 = 10.2 (v^2 - 1.42^2) / 2

v = 5.85 m/s

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