A safe with a weight of 3.40 kN is lifted with a constant speed by means of a pu

Question

A safe with a weight of 3.40 kN is lifted with a constant speed by means of a pulley system attached to the roof of a building. The safe is lifted from street level to an open window that is 25.5 m above the street. Three men pull on the rope connected to the safe. Each man delivers 138 W of power, and the pulley system has an efficiency of 75.0%. That is, 25.0% of the mechanical energy is dissipated due to friction within the pulley. How much time does it take to lift the safe from the street level to the window? You may neglect the mass of the pulley.

Explanation / Answer

let
F = 3.4 kN = 3400 N

Workdone in lifting the weight, W = F*d

= 3400*25.5

= 86700 J

let t is the time taken

efficiency*Power of three person*time taken = Workdone

0.75*3*138*t = 86700

==> t = 86700/(0.75*3*138)

= 279 s

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