Apparent Weight in a Lift

What apparent weight is

Your "weight" as felt by you — or as read by a weighing scale — is not always $mg$. It is the normal force the surface exerts on you. This is called apparent weight.

In a stationary lift or one moving at constant velocity, the normal force equals $mg$. But in an accelerating lift, the normal force changes.

Case 1: Lift accelerating upward ($a$ upward)

Taking upward as positive, Newton's Second Law:

$N - mg = ma$

$N = m(g + a)$

$\boxed{W_{app} = m(g+a)}$

Apparent weight increases. You feel heavier. The scale reads more than your actual weight.

Case 2: Lift accelerating downward ($a$ downward)

$mg - N = ma$

$N = m(g - a)$

$\boxed{W_{app} = m(g-a)}$

Apparent weight decreases. You feel lighter. The scale reads less.

Case 3: Free fall ($a = g$ downward)

$W_{app} = m(g - g) = 0$

Weightlessness. The scale reads zero. You float inside the lift.

This is not because gravity has disappeared — gravity still acts. It is because both you and the lift are falling at the same rate. There is no contact force between you and the floor.

This is exactly the condition of astronauts in orbit — they are in continuous free fall around the Earth.

Case 4: Lift moving at constant velocity (up or down)

$a = 0 \implies W_{app} = mg$

Normal weight. Constant velocity means no acceleration — no change in apparent weight.

Summary table

The key insight

Apparent weight depends on the acceleration, not the velocity.

A lift moving downward at constant speed: normal weight. A lift just starting to move upward (accelerating): feels heavier. A lift slowing down as it reaches the top floor (decelerating = accelerating downward): feels lighter.

This is why you feel a slight stomach drop when a lift starts descending, and a slight heaviness when it slows to a stop at the bottom.