Elevator problems

Intermediate

Apparent weight changes with the elevator's acceleration.

Key relationN = m(g+a)

Apparent weight is the normal force on you: N = m(g + a) for upward acceleration a, m(g − a) for downward. In free fall N = 0 (weightlessness).

Worked example

70 kg in a lift accelerating up at 2 m/s²: N = 70·11.8 = 826 N.

Common mistake

Your mass doesn't change; your apparent weight does.

In more detail

In an accelerating lift, your apparent weight changes. Accelerating up increases the normal force, while accelerating down reduces it.

Scales in lifts show a different weight during acceleration.
Lift engineers design acceleration limits for passenger comfort.
People in a lift feel heavier when it accelerates upward, which is why lift systems are designed with the right acceleration limits.

Why do I feel heavier in a lift going up?

Because the floor pushes harder to accelerate you upward, so the normal force is greater than your weight.

What if the cable breaks?

The lift falls freely, and you feel weightless because the normal force drops to zero.

Do I weigh less if the lift accelerates downward?

Yes, your apparent weight is the normal force, which drops when the lift accelerates downwards.