A 7.4-kg box is being lifted by means of a light rope that is threaded through a

Question

A 7.4-kg box is being lifted by means of a light rope that is threaded through a single, light, frictionless pulley that is attached to the ceiling.

(a) If the box is being lifted at a constant speed of 2.0 m/s, what is the power delivered by the person pulling on the rope?

145.04 Incorrect: Your answer is incorrect. kW

(b) If the box is lifted, at constant acceleration, from rest on the floor to a height of 1.8 m above the floor in 0.42 s, what average power is delivered by the person pulling on the rope?

I have got this wrong 0.310 Incorrect: Your answer is incorrect. kW

Explanation / Answer

A) F = mg = 7.4 x 9.81 = 72.59 N

P = F v = 72.59 x 2 = 145.19 W = 0.145 kW

B) h = 1.8 m, t = 0.42 s

h = (1/2) a x t2

a = 2h / t2 = 3.6 / 0.1764 = 20.41 m/s2

final velocity, v = sqrt(2 x a x h) = sqrt(2 x 20.41 x 1.8) = 8.57 m/s

kinetic energy of the box after lift = 1/2 mv2 = 0.5 x 7.4 x 8.572 = 271.84 J

potential energy gained by the box = m x g x h = 7.4 x 9.81 x 1.8 = 130.67 J

total energy of box after lift = 271.84 + 130.67 = 402.51 J

thus, the average power delvered by man is 402.51/0.42 = Energy delivered/time taken

= 958.36 W = 0.958 kW

Please rate my answer if you find it helpful, good luck..

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