What condition causes maximum tension in an elevator cable?

When an elevator accelerates upward, the tension in the cable reaches its maximum value. This is because the elevator must not only support the weight of the elevator itself and any passengers but also generate additional force to accelerate upwards.

To understand this, consider the forces acting on the elevator. The weight, which is the force due to gravity, acts downwards, while the tension in the cable acts upwards. When the elevator accelerates upwards, according to Newton's second law, you must add the force required for this upward acceleration to the force needed to balance the weight of the elevator.

Mathematically, the net force acting on the elevator can be expressed as:

( T - mg = ma )

Here, ( T ) is the tension in the cable, ( mg ) is the weight of the elevator (where ( m ) is the mass and ( g ) is the acceleration due to gravity), and ( a ) is the upward acceleration of the elevator. Rearranging gives:

( T = mg + ma = m(g + a) )

This shows that the tension ( T ) increases with the elevator's upward acceleration, leading to maximum tension when the elevator is accelerating upwards.

In contrast, moving