(i) W = FS = – mg sin q × h = – 14·7 J is the W.D. by gravitational force in moving the body up the inclined plane.
W′ = FS = + mg sin θ × h = 14·7 J is the W.D. by gravitational force in moving the body down the inclined plane.
∴ Total W.D. round the trip, W1 = W + W′ = 0.
(ii) Force needed to move the body up the inclined plane,
F = mg sin θ + fk
= mg sin θ + µk R
= mg sin θ + µk mg cos θ
∴ W.D. by force over the upward journey is
W2 = F × l = mg (sin θ + µk cos θ) l
= 18·5 J
(iii) W.D. by frictional force over the round trip,
W3 = – fk (l + l) = – 2fk l
= – 2µk mg cos θ l = – 7·6 J
(iv) K.E. of the body at the end of round trip
= W.D. by net force in moving the body down the inclined plane
= (mg sin θ – µk mg cos θ) l
= 10·9 J
⇒ K.E. of body = net W.D. on the body.