Question

A 975-kg elevator accelerates upward at 0.754 m/s2, pulled by a cable of negligible mass. Find the tension force in the cable.

Answer 1

To solve this problem we will apply the concepts of equilibrium and Newton's second law.

According to the description given, it is under constant ascending acceleration, and the balance of the forces corresponding to the tension of the rope and the weight of the elevator must be equal to said acceleration. So

$\sum F = ma$

$T-mg = ma$

Here,

T = Tension

m = Mass

g = Gravitational Acceleration

a = Acceleration (upward)

Rearranging to find T,

$T = m(g+a)$

$T = (975)(9.8+0.754)$

$T= 10290.15N$

Therefore the tension force in the cable is 10290.15N