Power = Work done / Time taken
Rearranging the formula to solve for time taken, we get:
Time taken = Work done / Power
First, we need to calculate the work done in lifting the piano. Work done is equal to the force applied multiplied by the displacement in the direction of the force. In this case, the force applied is the weight of the piano, which is:
Weight = mass * acceleration due to gravity
Weight = 100 kg * 9.8 m/s²
Weight = 980 N
The displacement is the height to which the piano is lifted, which is 16.0 m. Therefore, the work done is:
Work done = Force * Displacement
Work done = 980 N * 16.0 m
Work done = 15680 J
Now, we can substitute the power of the motor (1700 W) and the work done (15680 J) into the formula for time taken:
Time taken = Work done / Power
Time taken = 15680 J / 1700 W
Time taken ≈ 9.22 s
Therefore, it will take approximately 9.22 seconds for the 1700 W motor to lift the 100 kg piano to the sixth-story window 16.0 m above the street.
