A certain string can withstand a maximum tension of 30Nwithout breaking. A child

Question

A certain string can withstand a maximum tension of 30Nwithout breaking. A child ties a 250g stone to one end of thestring. While holding the other end the child whirls the stone in acircle of radius 75cm and slowly increases speed until the stringbreaks. If the circle is horizontal, what is the speed of the stonewhen the string breaks? If the circle is vertical, what is the speed of the stone whenthe string breaks? A certain string can withstand a maximum tension of 30Nwithout breaking. A child ties a 250g stone to one end of thestring. While holding the other end the child whirls the stone in acircle of radius 75cm and slowly increases speed until the stringbreaks. If the circle is horizontal, what is the speed of the stonewhen the string breaks? If the circle is vertical, what is the speed of the stone whenthe string breaks?

Explanation / Answer

r = 75cm=0.75m, T = 30N, m=250g=0.250kg when it move horizontally, we have: T = ma=mv2 / r when T = 30N, the string will break, => v = (Tr/m) = (30N*0.75m/0.250kg) =9.49m/s when it move vertically, at the lowest point, we have: T-mg = ma = mv2/r =>v = [(rT-mgr)/m] =[(0.75m*30N-0.250kg*9.8m/s2*0.75m)/0.250kg]=9.09m/s .

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