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Rope breaks at 36 N: speed of the ball
A ball of mass 2 kg on a smooth horizontal table moves in a circle at constant speed on a string 0.5 m long; the string can stand a maximum tension of 36 N. Find the speed of the ball when the string is just about to break.
Answer
Speed when the rope snaps 3 m/s
Step-by-step
- T = mv²/r → v = √(Tr/m) = √(36×0.5/2) = 3The rope's tension provides the centripetal force; it snaps at maximum tension
Why it works
The tension in the string is the centripetal force keeping the ball on its circle, T = mv²/r. The tension rises with the square of the speed, so the string snaps the moment the required centripetal force reaches what the string can stand.
Common mistakes
- Writing the centripetal force as mv²r instead of mv²/r.
- Taking T·r/m as the speed and forgetting to take the square root.
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