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0.4 m rope, 64 N limit: the breaking speed
A ball of mass 2 kg on a smooth horizontal table moves in a circle at constant speed on a string 0.4 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 3.5777 m/s
Step-by-step
- T = mv²/r → v = √(Tr/m) = √(64×0.4/2) = 3.5777The rope's tension provides the centripetal force; it snaps at maximum tension
Why it works
On a smooth table the tension is the only force pointing to the centre, so it is the centripetal force: T = mv²/r. The string breaks when the speed is large enough to demand a centripetal force equal to its greatest tension.
Common mistakes
- Doubling the mass and the tension cancel out, so wrongly concluding the answer does not depend on r either.
- Reporting mv²/r as a speed instead of solving for v first.
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