Tension Calculator
T = m(g + a) — why lifts feel heavy then light.
Work out Tension. T = m(g + a) — why lifts feel heavy then light. Shows the working, not just the answer.
Positive upward, negative downward. −9.807 is free fall.
Tension in the cable
98.066 N
Static — tension equals weight
T = m(g + a). A lift accelerating upward puts more than the static weight in the cable and accelerating downward puts less, which is exactly the heavy-then-light sensation of a lift ride — your apparent weight is the floor's normal force, and it follows the same equation. In free fall the tension reaches zero and everything inside is weightless. That is what an orbiting spacecraft is doing continuously: not escaping gravity, just falling freely inside it.
How the Tension Calculator works
Enter a mass and an acceleration for the tension in the supporting cable and the apparent weight. Accelerating upward adds to the tension, downward subtracts from it, and free fall takes it to zero.
Also known as: cable tension calculator · rope tension formula · elevator tension calculator · apparent weight calculator
Frequently asked questions
How do I calculate cable tension?
T = m(g + a), with acceleration positive upward. Hanging still it reduces to T = mg, the plain weight.
Why do I feel heavier when a lift starts up?
Because your apparent weight is the floor's normal force, and it follows the same equation. Accelerating up, the floor must push harder than your weight to produce that acceleration.
What is the tension in free fall?
Zero. With a = −g the equation gives exactly nothing, which is why everything inside a freely falling frame is weightless — including an orbiting spacecraft, which is simply falling continuously.
Does tension change along a rope?
Not in an ideal massless rope, which is the usual assumption. In a real heavy cable the tension is higher at the top, because it also carries the weight of the cable below it.
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