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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A 3.50-kN piano is lilted by three workers at constant speed to an apartment 25.0 m above the street using a pulley system fastened to the roof of the building. Each worker is able to deliver 165 W of power, and the pulley system is 75% efficient (so that 25% of the mechanical energy is lost due to friction in the pulley). Neglecting the mass of the pulley, find the time required to lift the piano from the street to the apartment.

To determine
The time required to lift the piano form the street to the apartment.

Explanation

Given Info:

The weight of the piano is 3.50kN .

The height of the apartment is 25.0m .

The power that each of the worker can deliver is 165W .

25% Of the mechanical energy is getting lost due to the friction in the pulley.

Since, the piano is lifting up to the apartment with a constant speed; the change in kinetic energy of the system is zero.

Thus, according to energy conservation, the work done by non-conservative force is,

Wnc=ΔPEg=mg(Δh)       (I)

  • Δh is the height to which the piano is lifting
  • m is the weight of piano
  • g is acceleration due to gravity

Since, the pulley system is only 75.0% efficient, the rate at which the three workmen do work on the piano is,

Pnet=0.75(3Poneworker)       (II)

Thus,

Formula to calculate the time required to lift the piano is,

Δt=WncPnet       (III)

On substituting equation (I) and (II) in (III),

Δt=mg(Δh)0

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