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Answer on Mechanics | Relativity Question for Melanie

Question #5752
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?
Expert's answer
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).

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