CalcElfCalcElf › 2 m rope, 100 N limit: the breaking speed
2 m rope, 100 N limit: the breaking speed
A ball of mass 0.5 kg on a smooth horizontal table moves in a circle at constant speed on a string 2 m long; the string can stand a maximum tension of 100 N. Find the speed of the ball when the string is just about to break.
Answer
Speed when the rope snaps 20 m/s
Step-by-step
- T = mv²/r → v = √(Tr/m) = √(100×2/0.5) = 20The rope's tension provides the centripetal force; it snaps at maximum tension
Why it works
For circular motion on a smooth table the tension supplies the whole centripetal force, T = mv²/r, so the breaking speed is found by setting T equal to the greatest tension the string can bear.
Common mistakes
- Forgetting the square root and reporting T·r/m as the speed.
- Mixing up r and m when rearranging T = mv²/r.
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