CalcElfCalcElf › Rope breaks at 25 N: speed of the ball
Rope breaks at 25 N: speed of the ball
A ball of mass 1 kg on a smooth horizontal table moves in a circle at constant speed on a string 1 m long; the string can stand a maximum tension of 25 N. Find the speed of the ball when the string is just about to break.
Answer
Speed when the rope snaps 5 m/s
Step-by-step
- T = mv²/r → v = √(Tr/m) = √(25×1/1) = 5The rope's tension provides the centripetal force; it snaps at maximum tension
Why it works
The tension in the string is the centripetal force, T = mv²/r, so the speed grows until the tension reaches what the string can stand; that is the moment it breaks.
Common mistakes
- Writing the centripetal force as mv²r instead of mv²/r.
- Taking T·r/m as the speed and forgetting the square root.