Question

an 1150kg elevator moving down speeds up at a rate of 3.5m/s. what is the tension in the supporting cables?

Answer 1

The tension force in the supporting cables is 7245N

Step-by-step explanation:

There are two forces acting on the elevator: the force of gravity pointing down (+) with magnitude (elevator mass) x (gravitational acceleration), and the tension force of the cable pointing up (-) with an unknown magnitude F. The net force is the sum of these forces:

`F_(net) = F_g - F = m\cdot g - F\\`

We are given the resulting acceleration along with the mass, i.e., we know the net force, allowing us to solve for F:

`1150kg\cdot 3.5(m)/(s^2)= 1150kg \cdot 9.8(m)/(s^2)-F\\\implies F = 1150kg\cdot(9.8-3.5)(m)/(s^2)= 7245N`

The tension force F in the supporting cables is 7245N