An escalator is 30.0 meters long and slants at 30.0° relative to the horizontal. If it moves at 1.00 m/s, at what rate does it do work in lifting a 50.0-kg woman from the bottom to the top of the escalator?

Question

Quizplus · Accepted Answer

To find the rate at which work is done, we need to find the power, which is given by the formula:

power = force x velocity

In this case, the force is the weight of the woman (mg), which we need to calculate first:

weight = mg = (50.0 kg)(9.81 m/s^2) = 490.5 N

Next, we need to find the component of the weight that is parallel to the direction of motion of the escalator. This is given by:

force parallel = weight sin θ = (490.5 N) sin 30° = 245.25 N

Finally, we can plug in the values for force and velocity to find the power:

power = force x velocity = (245.25 N)(1.00 m/s) = 245 W

Therefore, the answer is C: 245 W.

An Escalator Is 30