Answer to Question #158234 in Physics for tara

Question

A cable exerts a constant upward tension of magnitude 2.5 x 10⁴ N on a fully loaded elevator with a mass of 1.8 x 10³ kg as it rises to a vertical distance of 25.5 m.

(a) Find the work done by the tension force on the elevator.

(b) Find the work done by the force of gravity on the elevator.

(c) Find the power of motor if it takes 12 seconds in moving the elevator car.

Answer 1

(a) The work done by the tension force on the elevator:

$$W_a=Th=2.5\cdot10^4\cdot25.5=637500\text{ J}.$$

(b) The work done by the force of gravity on the elevator:

$$W_b=mgh=1.8\cdot10^3\cdot9.8\cdot25.5=449820\text{ J}.$$

(c) The power of motor if it takes 12 seconds in moving the elevator car:

$$P=\frac{W_a}{t}=53.125\text{ kW}.$$