 # In a lift, When will the apparent weight become twice the actual weight?

While going up & speeding up (acceleration a is positive) the apparent weight become twice the actual weight.

### How does the weight increase in the lift?

In this case, the elevator and the person are beginning from rest on a lower floor. The elevator or the lift accelerates upward. The inertia of the person would favour staying stationary, so the elevator floor and scale must push up on the person to accelerate him upward along with the elevator. The scale, therefore, has to push upward with extra force on the person to stimulate the person’s mass upward. This happens in a greater contact force between the scale and the person.

Therefore the Normal Force is larger, so the reading on the scale is a number that is greater than the true weight. According to Newton’s 2nd Law F=ma acting on the person.

The overall acceleration of the person is upward (with the elevator). So the parameter ‘ma’ is positive (upward).

The only external forces acting on the person are the force of gravity acting down is -W=-mg and the supporting normal force.

When the lift is moving up with acceleration g, then we have

R = m (g+a) = m (g+g) = 2mg

Hence while going up & speeding up (acceleration a is positive) the apparent weight become twice the actual weight. (6) (3)