Answer:
[tex]\dot E = 15602.842\,W[/tex]
Explanation:
By an adequate application of the Principle of Energy Conservation, the escalator need energy to elevate from to the bottom to the top. Hence:
[tex]E = m_{total}\cdot g \cdot y[/tex]
An expression for power needed is found by deriving the equation with respect to time:
[tex]\dot E = m_{total}\cdot g \cdot v_{y}[/tex]
The minimum power is found by substituting known inputs:
[tex]\dot E = (50)\cdot (75\,kg) \cdot (9.807\,\frac{m}{s^{2}} )\cdot (0.6\,\frac{m}{s} )\cdot \sin 45^{\textdegree}[/tex]
[tex]\dot E = 15602.842\,W[/tex]
