Question

A box of mass m hangs by a string from the ceiling of an elevator that is accelerating upward.1) Is the tension T in the string greater then the weight (mg) of the box.2) explain briefly?

Answer 1

(a). Yes, the tension acting in the string is greater than the weight of the box.

(b). Let a be the acceleration of the elevator in the upward direction.

As the mass m is also moving in the upward direction with the elevator,

The given system is represented as,

Thus, the tension and weight is balanced by the applied force.

The tension in terms of the weight of the box is,

`\begin{gathered} T-mg=ma \\ T=ma+mg \end{gathered}`

Thus, the tension acting in the string is more than the weight of the box.