Help please, power (piano pulled up by workers through pulley)

[xregina12]

A 3.50 kN piano is lifted by 3 workers at constant speed to an apartment 25 m above ground. Each worker is able to deliver 165 W of power and the pulley is 75% efficient (25% lost due to friction on pulley). Neglecting mass of pulley, what is the time required to lift the piano from the street to the apartment.
I know that F=T-mg=ma=0
T=3500N
Work=3*165=495W=F/t
But I'm not really sure how to sort this problem out and incorporate the 75% efficiency of the pulley and the height above ground. Please help me.

 

[Redbelly98]

Work=3*165=495W=F/t

Not quite. You are equating work (units: Joules) with power (units: Watts) here, but they are not the same. And neither of those would equal force/time.

At any rate, 495W is the power exerted by the 3 people. So how much of that power gets transmitted to the piano? (hint: it is not 100% of the power)

 

[thomate1]

Based on the given information, we can calculate the work done by the workers to lift the piano as follows:

Work = Force * Distance
Work = 3500N * 25m
Work = 87500J

Since the pulley is 75% efficient, we can calculate the actual work done by the workers as follows:

Actual Work = Work / Efficiency
Actual Work = 87500J / 0.75
Actual Work = 116667J

Now, we can use the equation for power to calculate the time required to lift the piano:

Power = Work / Time
Time = Work / Power
Time = 116667J / (3 * 165W)
Time = 116667J / 495W
Time = 235.4 seconds

Therefore, it will take approximately 235.4 seconds (or 3.92 minutes) for the workers to lift the piano from the street to the apartment.