How long will it take a 1080 W motor to lift a 330kg piano to a sixth-story window 16.0m above?

To calculate the time it will take for the motor to lift the piano to a sixth-story window, we can use the work-energy principle. The work done by the motor is equal to the change in potential energy of the piano.

The work done (W) is given by the equation:
W = mgh

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 the piano is lifted (in meters)

To find the time, we can divide the work done by the power of the motor.

Power (P) is given by the equation:
P = W / t

Where:
P = Power (in watts)
t = Time taken (in seconds)

Given:
Power of the motor (P) = 1080 W
Mass of the piano (m) = 330 kg
Height the piano is lifted (h) = 16.0 m
Acceleration due to gravity (g) = 9.8 m/s^2

Let's calculate the time taken:

Work done (W) = mgh
W = (330 kg)(9.8 m/s^2)(16.0 m)
W = 513,120 joules

Time taken (t) = W / P
t = 513,120 joules / 1080 W
t ≈ 475.56 seconds

Therefore, it will take approximately 475.56 seconds (or about 7.93 minutes) for the 1080 W motor to lift the 330 kg piano to a sixth-story window 16.0 m above.

To calculate the time it will take for the 1080 W motor to lift the 330 kg piano to a sixth-story window that is 16.0 m above, we can use the concept of work and power.

1. First, we need to calculate the work done to lift the piano. Work (W) is given by the formula:

W = force x distance

In this case, the force (F) required to lift the piano is its weight. Weight is calculated by multiplying the mass (m) by the acceleration due to gravity (g). The formula for weight is:

Weight = mass x acceleration due to gravity

F = m x g

Given that the mass of the piano is 330 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:

F = 330 kg x 9.8 m/s^2

2. Now that we have the force required, we can calculate the work done to lift the piano. The distance (d) is given as 16.0 m:

W = F x d

3. The calculated work will give us the energy needed to lift the piano. Since power (P) is defined as the rate at which work is done, we can use the formula:

P = W / t

Rearranging the formula, we get:

t = W / P

Here, W is the previously calculated work, and P is the power of the motor (1080 W).

4. Substitute the values into the equation:

t = (F x d) / P

5. Calculate the time:

t = (F x d) / P

Now you can plug in the values to find the time it will take for the motor to lift the piano.