How long will it take a 1830 W motor to lift a 285 kg piano to a sixth-story window 16.0 m above?
To determine how long it will take for the motor to lift the piano to the sixth-story window, we need to use the concept of work and power.
First, let's calculate the amount of work required to lift the piano. Work (W) is given by the formula:
W = m * g * h
Where:
W = work done (in joules),
m = mass of the piano (in kg),
g = acceleration due to gravity (approximately 9.8 m/s^2),
h = height (in meters).
In this case, the mass of the piano is 285 kg, and the height is 16.0 m. So, the work required is:
W = 285 kg * 9.8 m/s^2 * 16.0 m
Next, we need to calculate the time it will take to perform this work. Power (P) is given by the formula:
P = W / t
Where:
P = power (in watts),
W = work done (in joules),
t = time taken (in seconds).
In this case, the power is 1830 W, and we want to find the time taken. Rearranging the formula, we get:
t = W / P
Now, let's substitute the values into the formula:
t = (285 kg * 9.8 m/s^2 * 16.0 m) / 1830 W
Simplifying the expression further, we can cancel out units:
t = (285 * 9.8 * 16) / 1830 s
Evaluating the expression, we get:
t ≈ 2.906 seconds
Therefore, it will take approximately 2.906 seconds for the motor to lift the 285 kg piano to a sixth-story window 16.0 m above.