Final answer:
To find out how long it will take a 1900 W motor to lift a 350 kg piano to a sixth-story window 16.5 m high, we use the formula t = (m × g × h) / P, incorporating the mass of the piano, gravitational acceleration, the height of the window, and the power of the motor.
Step-by-step explanation:
To calculate the time it will take for a 1900 W motor to lift a 350 kg piano to a sixth-story window 16.5 m above, we must consider the concept of power, work, and gravitational potential energy (GPE).
The work done by the motor to lift the piano is equal to the change in the piano's GPE, which is calculated by the formula Work (W) = mass (m) × gravitational acceleration (g) × height (h). For the piano, this would be W = 350 kg × 9.8 m/s² × 16.5 m. The power of the motor (P) is defined as the work done per unit time, so we can say P = W/t, where t is the time in seconds. Rearranging this formula to solve for time, we get t = W/P.
If we plug in the values, the time (t) can be found as follows:
t = (350 kg × 9.8 m/s² × 16.5 m) / 1900 W.
After completing the calculations, we will have the time it takes to lift the piano to the sixth-story window using the 1900 W motor.