How this calculator works
A taut massless rope transmits tension along its length. For two supports, horizontal components cancel and vertical components add to weight. A single tilted rope requires an additional horizontal constraint, such as a smooth wall, to balance its sideways component. For a pulled chain, each connecting rope accelerates only the masses beyond it, so tensions decrease toward the free end.
Formula
W = mg; single T = W/cos(theta) with theta from vertical. Two ropes: Tleft = W cos(beta)/sin(alpha+beta), Tright = W cos(alpha)/sin(alpha+beta). Chain a = F/sum(mi); Ti = a sum(masses beyond rope i).
Worked example
A 10 kg mass at g = 10 m/s² needs 100 N from a vertical rope. Pulling masses 2, 3 and 5 kg with 20 N gives 2 m/s² acceleration and successive tensions 20, 16 and 10 N.
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Frequently asked questions
Are both support angles measured from the ceiling?
Yes, both two-rope angles are measured above horizontal. The one-rope angle is measured from vertical.
Why do shallow ropes carry large forces?
Only a small part of each tension points upward, so a much larger total tension is needed to support the weight.
Can I include pulley friction or rope mass?
No. Those effects require a more detailed free-body model and can make tension vary along a rope.