Answer to Question #168074 in Mechanics | Relativity for Roaa Mohamed

Question

Moving walkways are often found in airports. One moving walkway carries passengers up an incline of 30°, A single passenger of mass 72 kg stands on the walkway. The speed of the walkway is 0.51ms−1. Show that the rate at which the walkway does work on the passenger is about 200W.

Answer 1

The weight of the passenger is

$W = mg$

where $m = 72kg$ is they mass, and $g = 9.8N/kg$ is the gravitational acceleration. The component of the weight that acts along the walkway is:

$W_a = W\sin \theta$

where $\theta = 30\degree$.

By definition, the power is:

$P = Wv$

where $v = 0.51m/s$ is the speed of motion. Thus, obtain:

$P = mgv\sin\theta\\ P = 72\cdot 9.8\cdot 0.51\cdot \sin 30\degree \approx 180W$

Answer. 180 W.