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Learn9709Paper 4 · MechanicsNewton's laws of motionLifts and vertical motion
Newton's laws of motion · Subtopic 4 of 4

Lifts and Vertical Motion

Why you feel heavy as a lift sets off upwards and light as it slows: the floor pushes with R=m(g+a)R=m(g+a). The same F=maF=ma handles cables, parachutes and anything else moving up or down.

Cambridge 9709 Paper 4Edexcel 9MA0 Paper 3AQA 7357 Paper 2≈ 30 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Apply F=maF=ma vertically, choosing the direction of acceleration as positive.
  • Find the reaction between a lift floor and a passenger, and the tension in the cable.
  • Interpret "apparent weight" as the normal reaction.
  • Solve vertical problems with ropes and air resistance.
Pause and think

You stand on bathroom scales in a lift. The lift starts moving down. Do the scales read more or less than your weight? What about when the lift slows to a stop at the bottom?

Section 2 of 14

Core idea

Start hereHeavier in a lift

Stand on bathroom scales in a lift. As it starts upward the reading jumps; as it slows at the top it drops. Your mass hasn't changed: the floor is pushing harder or softer to accelerate you.

The big idea

Scales read the normal reaction RR. With up positive, R−mg=maR-mg=ma: accelerating up ⇒ R>mgR>mg; down ⇒ R<mgR<mg; constant velocity ⇒ R=mgR=mg.

1. A person in a lift

A 60 kg person in a lift accelerating upwards
R600 Na = 2 m/s²
R−600=60(2)R-600=60(2), so R=720R=720 N. The scales show about 7272 kg.
Worked example60 kg person

Find RR for acceleration 2 m s⁻² up, 2 m s⁻² down, and constant speed.

Goal
Three values.
Strategy
R−600=60aR-600=60a.
  1. a=2: R=720a=2:\ R=720
    Up.
  2. a=−2: R=480a=-2:\ R=480
    Down.
  3. a=0: R=600a=0:\ R=600
    Steady.
Answer720720, 480480, 600600 N.
✓ CheckScales show "72 kg", "48 kg", "60 kg" ✓.
Scale reading R for a 60 kg person
−10−8−6−4−2242004006008000acceleration of lift, up positive (m/s²)R (N)R = m(g + a)steady: 600 Nfree fall: weightless
At a=−10a=-10 (falling freely) the floor no longer pushes: you would float.

2. The cable

Worked exampleCable tension

A 500 kg lift carries the 60 kg person, accelerating up at 2 m s⁻². Cable tension?

Goal
TT.
Strategy
Whole system.
  1. 560 kg, 5600 N560\text{ kg},\ 5600\text{ N}
    Total mass and weight.
  2. T−5600=560(2)⇒T=6720T-5600=560(2)\Rightarrow T=6720
    F=maF=ma.
Answer67206720 N.
✓ CheckLift alone: T−5000−720=500(2)T-5000-720=500(2) ✓ (person pushes down 720720 N).
Pause and think

The cable snaps. Scale reading?

Summary

  • R−mg=maR-mg=ma.
  • Whole system for the cable.
Key words
Apparent weight
The reaction force felt.
HistoryEinstein's happiest thought. In 1907 Albert Einstein realised that a person falling freely would not feel their own weight. He later called it "the happiest thought of my life": it led to the idea that gravity and acceleration are locally indistinguishable, the starting point of general relativity. A lift is exactly the thought experiment he used.
Fun factAstronauts are not weightless. On the International Space Station gravity is still about 90%90\% as strong as on the ground. Astronauts float because they and the station are in free fall together around the Earth, so the floor pushes on them with R=0R=0. Training aircraft fly parabolic arcs to give the same feeling for about 2020 seconds at a time.
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