A lift is pulled up by the tension T in its cable and down by its weight mg. Resolve in the direction of the acceleration: T − mg = ma when it accelerates upwards.
For a 250 kg lift accelerating up at 0.25 m/s²: T − 250 × 9.8 = 250 × 0.25, so T = 2450 + 62.5 = 2512.5 N. When accelerating downwards, mg − T = ma. A person standing in the lift feels a reaction force from the floor found the same way.
Worked example
A 550 kg lift moves down with acceleration 1.75 m/s². Find the tension. Use g = 9.8.
- Down is the direction of acceleration: mg − T = ma.
- 5390 − T = 962.5.
Answer:T = 4427.5 N
Key words
- tension
- the pulling force in a cable or string
- weight
- mg
- reaction
- the push from a surface
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