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0.8 m rope, 64 N limit: the breaking speed
A ball of mass 1 kg on a smooth horizontal table moves in a circle at constant speed on a string 0.8 m long; the string can stand a maximum tension of 64 N. Find the speed of the ball when the string is just about to break.
Answer
Speed when the rope snaps 7.1554 m/s
Step-by-step
- T = mv²/r → v = √(Tr/m) = √(64×0.8/1) = 7.1554The rope's tension provides the centripetal force; it snaps at maximum tension
Why it works
The tension is the centripetal force, T = mv²/r, so a longer radius needs a smaller speed for the same tension, while a heavier ball or a stronger string changes the limit in proportion.
Common mistakes
- Thinking a longer string breaks at a higher speed, when the required force actually falls as r grows.
- Using T = mv²r and multiplying by the radius instead of dividing.
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