A 3.20-kN piano is lifted by three workers at a constant speed to an apartment 20.8 m above the street using a pulley system fastened to the roof of the building. Each worker is able to deliver 179 W of power, and the pulley system is 75.0% efficient (so that 25.0% 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.

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skyluke89 skyluke89 · Answer 1 · 2019-10-21T12:01:55+02:00

Answer:

165.3 s

Explanation:

The amount of work required to lift the piano is equal to its gain in gravitational potential energy, so:

[tex]W=(mg)\Delta h = (3200 N)(20.8)=66560 J[/tex]

where

mg = 3200 N is the weight of the piano

[tex]\Delta h = 20.8[/tex] is the change in height

We know that the pulley is 75.0% efficient, so the actual work that must be done by the workers is:

[tex]W = 0.75 W_i\\W_i = \frac{W}{0.75}=\frac{66560}{0.75}=88747 J[/tex]

The three workers have a combined power of

[tex]P=3 \cdot 179 W = 537 W[/tex]

And power is defined as

[tex]P=\frac{W_i}{t}[/tex]

So rearranging the equation, we can find the time required, t:

[tex]t=\frac{W_i}{P}=\frac{88474}{537}=165.3 s[/tex]