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Rope breaks at 20 N: speed of the ball
A ball of mass 0.5 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 20 N. Find the speed of the ball when the string is just about to break.
Answer
Speed when the rope snaps 4 m/s
Step-by-step
- T = mv²/r → v = √(Tr/m) = √(20×0.4/0.5) = 4The rope's tension provides the centripetal force; it snaps at maximum tension
Why it works
In horizontal circular motion on a table the rope tension alone provides the centripetal force, T = mv²/r; the normal force balances the weight, so gravity does not enter the answer.
Common mistakes
- Adding the weight mg into the tension, even though on a horizontal table the normal force balances gravity.
- Using the ball's mass or the tension as the radius in T = mv²/r.