How long will it take a 1280 W motor to lift a 345 kg piano to a sixth-story window 19.0 m above?
Power * Time = M g H = work required
Solve for Time
y= mx + b
To determine how long it will take for the motor to lift the piano to the sixth-story window, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the motor is equal to the change in potential energy of the piano.
The formula for calculating work (W) is:
W = F * d * cos(theta)
Where:
W is the work done,
F is the force applied,
d is the distance moved,
theta is the angle between the force and the displacement.
In this case, the force applied by the motor is equal to the weight of the piano, which can be calculated using the formula:
F = m * g
Where:
F is the force applied,
m is the mass of the piano,
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, we can calculate the work done by the motor using the formula:
W = F * d * cos(theta)
Since the force applied and the displacement are in the same direction (vertical direction), the angle between them is 0 degrees, so the cos(0) term simplifies to 1, and the formula becomes:
W = F * d
Now, let's substitute the values we have:
W = (m * g) * d
W = (345 kg) * (9.8 m/s^2) * (19.0 m)
We know that power is the rate at which work is done, and it can be calculated using the formula:
Power = Work / time
Rearranging the formula, we have:
Work = Power * time
Substituting the known values, we get:
(m * g * d) = (Power * time)
Now we can solve for time:
time = (m * g * d) / Power
Substituting the given values:
time = (345 kg * 9.8 m/s^2 * 19.0 m) / 1280 W
Now, we can calculate the time it will take for the motor to lift the piano to the sixth-story window.