Lifting a 2.80*10^2 kg Piano: How Long Does it Take?

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To lift a 2.80*10^2 kg piano to a height of 12.0 m, the work done is calculated using the formula Work = F * distance, resulting in 32,928 joules. The crane's power output is 4.00*10^2 W, allowing the time to lift the piano to be determined by the equation Time = Work / Power. This calculation yields a time of approximately 82.3 seconds. The potential energy gained by the piano during the lift is also confirmed using the formula PE = mgh. The discussion effectively illustrates the relationship between work, power, and time in the context of lifting heavy objects.
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A 2.80*10^2 kg piano is being lifted at a steady speed from ground level straight up to an apartment 12.0 m above the ground. The crane that is doing the lifting produces a steady power of 4.00*10^2 W. How much time does it take to lift the piano?

i know that i have to use the equation Time= Work/Power. Power is given. How would I find work? i know that work=F*distance. Would work= 280*9.8*12.0=32928?
 
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the answer i got 82.3 s. Is that correct?
 
Just make an energy argument.

How much potential energy does the piano gain by being hoisted up 12 meters? It's just PE = mgh, right?

The crane produces a specific amount of power. Power is work (or energy) per unit time.

Hoisting the piano requires x joules, and the crane can deliver P joules per second. The time it'll take is just x / P.

- Warren
 

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