Rope Tension Calculator (Hanging Mass)
Find the tension in the rope or ropes holding a hanging mass — a single vertical rope, two symmetric ropes at an angle, or a mass in an accelerating lift.
How it works
One rope: T = m·(g + a) · Two symmetric ropes: T_each = m·g ÷ (2·cos θ)
For a mass hanging still from a single vertical rope, the tension simply equals the weight, T = m·g. If the rope accelerates the mass (as in a lift), Newton’s second law gives T = m·(g + a): accelerating upward increases tension, downward reduces it. When two symmetric ropes share the load, only the vertical components hold the weight, so each rope carries m·g / (2·cos θ) — and the tension grows without bound as the ropes approach horizontal.
Worked example
A 15 kg mass on two ropes, each 30° from vertical: weight = 147.15 N, and each rope carries 147.15 ÷ (2·cos30°) = 147.15 ÷ 1.732 = 84.96 N. On a single vertical rope it would be the full 147.15 N.
Sources: Tension (physics) — Wikipedia
Frequently asked questions
Why is the tension higher when the ropes are spread apart?
Only the vertical component of each rope’s tension supports the weight. As the angle from vertical grows, cos θ shrinks, so each rope must pull harder to keep the same vertical component — which is why a tightrope pulled nearly horizontal experiences enormous tension.
Does tension equal weight for a hanging mass?
Only when the mass is in equilibrium on a single vertical rope. If the system accelerates, T = m·(g + a); and if two or more angled ropes share the load, each carries a different amount set by its angle.
What happens to rope tension in a falling lift?
If the lift accelerates downward at a, tension is m·(g − a). In true free fall (a = g) the tension drops to zero and the mass feels weightless.
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This calculator is for educational purposes. Double-check important results before acting on them.