A 3.60 102-kg piano is being lifted at a steady speed from ground level straight up to an apartment 18.0 m above the ground. The crane that is doing the lifting produces a steady power of 4.00 102 W. How much time does it take to lift the piano?
Use an energy method. Power x time = Potential energy change
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1.10
To find the time it takes to lift the piano, we can use the formula for power:
Power = Work / Time
In this case, the power of the crane is given as 4.00 * 10^2 W. We need to calculate the work done to lift the piano and use this information to find the time.
The work done to lift an object is given by the equation:
Work = Force * Distance
In this case, the force needed to lift the piano is equal to its weight. The weight of an object is given by the equation:
Weight = Mass * Gravity
The mass of the piano is given as 102 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Using these values, we can calculate the weight of the piano.
Weight = 102 kg * 9.8 m/s^2
Now we can substitute this value into the equation for work to find the total work done to lift the piano.
Work = Weight * Distance
The distance the piano is being lifted is given as 18.0 m. Substituting the weight and distance values, we get:
Work = (102 kg * 9.8 m/s^2) * 18.0 m
Now we can substitute the work value into the equation for power to find the time it takes to lift the piano.
Power = Work / Time
Rearranging this equation to solve for time:
Time = Work / Power
Substituting the work value and the power value given, we get:
Time = [(102 kg * 9.8 m/s^2) * 18.0 m] / (4.00 * 10^2 W)
Now we can calculate the time it takes to lift the piano using this equation.