How long will it take a 1080 W motor to lift a 330kg piano to a sixth-story window 16.0m above?
P*t = M*g*H
Solve for t
P is the power in Watts.
You can guess the rest.
48.88 seconds
To calculate the time it will take for a motor to lift a piano to a sixth-story window, we need to use the concept of work and power.
First, let's calculate the work required to lift the piano. The work done is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force is the weight of the piano, which can be calculated using the formula:
Weight = mass * gravity
The mass of the piano is given as 330 kg, and gravity is approximately 9.8 m/s^2. Therefore, the weight of the piano is:
Weight = 330 kg * 9.8 m/s^2 = 3234 N
Next, we need to calculate the time required to lift the piano. The power output of the motor is given as 1080 W, which is equal to the rate at which work is done. Mathematically, power is defined as:
Power = work / time
Rearranging the formula, we can solve for time:
Time = work / power
Substituting the values:
Time = (3234 N * 16.0 m) / 1080 W
Simplifying the calculation, we get:
Time ≈ 0.487 seconds
Therefore, it will take approximately 0.487 seconds for a 1080 W motor to lift a 330 kg piano to a sixth-story window 16.0 m above.