G-force and weightlessness — apparent weight
Control the lift's acceleration. The scale shows the apparent weight Q=m(g+a): upward — g-force, downward — reduced weight, and in free fall (a=−g) the weight disappears. That is exactly why astronauts in orbit are weightless.
I will give you the lift acceleration a — identify the person's state on the scale (no slider). g = 9.81 m/s².
What just happened?
A scale in a lift does not measure the true force of gravity, only how hard you press on the floor — the apparent weight. When the lift accelerates downward at , the normal force vanishes and the scale reads zero: that is weightlessness.
Apparent weight:
— the faster the lift accelerates upward, the greater the normal force. m — mass (kg), g — gravitational acceleration (≈9.81 m/s²), a — lift acceleration (positive upward). The g-force factor .
Three cases:
At rest or in uniform motion → ordinary weight. Rocket launch (upward acceleration) → g-force. Free fall → weightlessness.
Why are astronauts weightless?
Not because "there is no gravity" — in orbit it still has about 90% of its surface value. The station and the astronaut fall freely around the Earth with the same acceleration, so the mutual normal force vanishes: .
Why you need this for the exam:
Problems about a lift, a rocket launch or a state of weightlessness come down to a single formula . Trick: set the direction of the acceleration (upward positive), substitute and compute.
Remember: a scale measures the normal force, not gravity — Q = m(g+a). Upward acceleration means g-force, free fall means weightlessness.
Theory & formulas
Apparent weight in a lift
The scale shows the normal force the body exerts, i.e. the apparent weight. When the lift accelerates with an acceleration directed upward:
Three cases
- g-force (starting upward, ): ,
- reduced weight (starting downward, ): ,
- weightlessness (free fall, ): .
Weightlessness in orbit
The astronaut and the station fall freely toward the Earth with the same acceleration — gravity is still acting, but the normal force on the floor (the apparent weight) is zero.
Notation: — apparent weight (normal force), — mass, — gravitational acceleration, — lift acceleration (positive upward).
Frequently asked questions
›Why is an astronaut in orbit weightless?
Because the station and the astronaut fall freely toward the Earth with the same acceleration — gravity is still acting, but the apparent weight (the normal force on the floor) is zero.
›What is apparent weight?
The normal force a body exerts on the floor or a scale, Q=m(g+a); it differs from the true weight mg when the system accelerates.
›When do we feel g-force?
When the acceleration is directed "upward" (a rocket launch, the bottom of a loop) — then Q>mg.
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