Answer to Question #5752 in Mechanics | Relativity for Melanie
when you have a rock on a string spinning it around, if you have a original tension with a radius and velocity, how would you find the breaking strength of a string if the problem also states a second radius and velocity but not the tension?
Let's make the following denominations:
F1 - the original tension R1 = original radius V1 = original velocity R2 = second radius V2 = second velocity M - the mass of a rock
We need to find the mass of a rock at first. Using the first case we have that the centripetal acceleration of a rock is Ac1 = V1²/R1. Now let's use the second Newton's law: F1 = M*Ac1 ==> M = F1/Ac1 = F1/(V1²/R1) = F1*R1/V1².
Now let's find the breaking strength of the string. In the second case we have that the centripetal acceleration of a rock is Ac2 = V2²/R2. So, we can find the breaking strength usind the second Newton's law again: F2 = M*Ac2 = (F1*R1/V1²)*(V2²/R2) = (F1*R1*V2²)/(V1²*R2).