A piano whose mass is 106 kg is being lifted at a steady speed from ground level straight up to an apartment 12.4m above the ground. The crane that is doing the lifting produces a steady power of 565W. How much time does it take to lift the piano?
Although a piano requires considerable art to play it well; its weight is really not 'artistic'.
Power=weight*height/time
time=weight*height/power.
time will be in seconds.
To solve this problem, we need to find the time it takes to lift the piano using the given power and the distance it is lifted. We can use the equation:
Power (P) = Work (W) / Time (t)
First, let's calculate the work done in lifting the piano.
Work is defined as the force applied over a certain distance. In this case, the force applied is equal to the weight of the piano, as it is being lifted at a steady speed. The weight of an object can be calculated using the equation:
Weight (W) = mass (m) * acceleration due to gravity (g)
Where mass (m) is 106 kg and acceleration due to gravity (g) is approximately 9.8 m/s^2.
Weight (W) = 106 kg * 9.8 m/s^2 = 1038.8 N
Now, let's calculate the work done:
Work (W) = Weight (W) * distance (d)
The distance the piano is lifted is given as 12.4 m.
Work (W) = 1038.8 N * 12.4 m = 12860.32 J
Now we can substitute the values into the power equation:
Power (P) = Work (W) / Time (t)
565 W = 12860.32 J / Time (t)
To solve for time (t), rearrange the equation:
Time (t) = Work (W) / Power (P)
Time (t) = 12860.32 J / 565 W
Time (t) ≈ 22.75 seconds
Therefore, it takes approximately 22.75 seconds to lift the piano.