Question

what is the useful mechanical power output for a 60.0-kg woman who runs up a 3.00 m high flight of stairs in 3.50s, starting from rest but having a final speed of 2.00 m/s?

Answer 1

The power output for the 60.0-kg woman running up the flight of stairs is 538.29 W.

Step-by-step explanation:

To calculate the useful mechanical power output for the 60.0-kg woman running up a 3.00 m high flight of stairs, we can use the formula:

Power = Work / Time

First, we need to calculate the work done by the woman:

Work = Potential Energy + Kinetic Energy

Since the woman starts from rest, her initial kinetic energy is zero.

The potential energy can be calculated using the formula:

Potential Energy = mass * gravity * height

Substituting the known values, we get:

Potential Energy = (60.0 kg) * (9.8 m/s^2) * (3.00 m)

= 1764 J

Next, we need to calculate the final kinetic energy:

Kinetic Energy = (1/2) * mass * velocity^2

Substituting the known values, we get:

Kinetic Energy = (1/2) * (60.0 kg) * (2.00 m/s)^2

= 120 J

Adding the potential energy and kinetic energy together gives us the total work done:

Work = 1764 J + 120 J

= 1884 J

Finally, we can calculate the power output using the formula:

Power = 1884 J / 3.50 s

= 538.29 W