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1.2.25 · D5Newton's Laws & Dynamics

Question bank — Weightlessness — true (free fall) vs apparent

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True or false — justify

An astronaut in the ISS experiences almost zero gravity.
False — at ~400 km, , about 89% of surface gravity; they float because they are in free fall, so .
A body in free fall has zero weight.
Mixed — its apparent weight () is zero, but its true weight is unchanged; gravity is fully on, which is exactly why it falls.
A scale in an elevator always reads .
False — a scale reads the normal force ; it equals only when the support's acceleration .
If you move downward you become lighter.
False — only acceleration affects , not velocity; moving down at constant speed gives and (fully normal).
Weightlessness requires the surroundings to fall at the same rate as you.
True — if support and body share the same acceleration, neither presses on the other, so .
In deep space far from all masses, a body is weightless.
True — but this is true weightlessness (), a different cause from free-fall (apparent) weightlessness where .
Feeling "heavy" in a lift means gravity got stronger.
False — true weight is unchanged; the lift accelerates upward (), so and the extra push on your feet feels like extra weight.
Two bodies of different mass in the same free-falling lift both read .
True — regardless of , since the mass factors out; both fall with the same acceleration .

Spot the error

"The cable snapped, the lift falls, so and ."
The sign is wrong — with up positive, a downward acceleration is , giving . Pick the up-positive convention and keep it (see Newton's Second Law).
"Astronauts float because the ISS is beyond Earth's gravitational field."
Earth's field extends indefinitely; at ISS altitude . They float from continuous free fall, not absence of gravity.
"The scale measures how hard Earth pulls you, so it reads ."
The scale can only sense the contact force it exerts on you, i.e. (apparent weight); by Newton's Third Law you push back equally, and only in equilibrium.
"In free fall gravity is cancelled by an upward force, so net force is zero."
Nothing cancels gravity — gravity is the net force, which is why you accelerate at . There is simply no contact force left, so you feel nothing.
"Weightlessness means the body has no acceleration."
Backwards — a free-falling weightless body has the maximum downward acceleration ; it is the contact force that vanishes, not the acceleration.
"A lift decelerating as it goes down makes you lighter because it's going down."
Decelerating downward means acceleration points up (), so — you feel heavier, not lighter.
"Orbit needs no gravity, otherwise the station would fall."
The station is falling — gravity supplies the centripetal acceleration inward; its sideways speed just keeps it missing the ground.

Why questions

Why does a bathroom scale, not gravity, decide what you "feel"?
Your nerves sense pressure/contact forces; gravity acts on every atom uniformly with nothing to push against, so only the support force (apparent weight) registers as "weight."
Why does mass cancel out when checking weightlessness?
In , setting gives for any ; every mass free-falls with the same acceleration, so none presses on its support.
Why is orbital weightlessness the "same physics" as a falling lift?
In both, the body and its support share one acceleration ( down in the lift, inward in orbit), so the relative normal force is zero — just a straight fall versus a curved one.
Why does velocity direction never enter ?
Newton's second law relates force to acceleration , not velocity; a body can move any direction at constant speed and still have , hence .
Why can we treat the falling lift as a place where "gravity vanishes"?
In the lift's accelerating (non-inertial) frame a pseudo-force appears and cancels real gravity — see Non-inertial Frames & Pseudo-forces; inside, everything behaves as if .
Why does an upward acceleration () increase the scale reading?
To accelerate you up, the floor must push harder than gravity pulls, so ; that extra push is what the scale reports and your legs feel.

Edge cases

Lift at rest on the ground — apparent weight?
, so ; apparent weight equals true weight exactly, the only case where the two coincide.
Lift accelerating downward faster than (say , rocket-driven).
, i.e. formally negative; a floor can't pull you down, so you'd lift off the floor and press against the ceiling instead.
A person floating mid-air inside a free-falling lift, not touching anything.
They are weightless with trivially (no contact), and still accelerating downward at — gravity acts, nothing pushes back.
At the exact instant the cable snaps, before any speed builds up.
drops to immediately, because it depends on acceleration ( at once), not on how much velocity has accumulated.
A body in deep space () sitting on a scale that isn't accelerating.
True weightlessness: because itself is zero — same reading as free fall but a fundamentally different cause.
Astronaut at ISS altitude but momentarily at rest relative to Earth (not orbiting).
They would fall straight down at (support-free) and still be weightless (); orbiting only adds the sideways speed that prevents impact.
Standing in an elevator moving up at constant velocity.
, so — perfectly normal weight; constant velocity in any direction is indistinguishable from being at rest for the scale.

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