How Do You Calculate Tension in a Two-Rock System in Circular Motion?

[quickclick330]

Its just one of those days where my brain needs a bit of a jump start, if anyone could help me it would be greatly appreciated!Thanks!

Problem:

A rock of mass m1 = 0.4 kg is tied to another rock with a mass m2 = 0.58 kg with a string of length L1 = 0.14 m. The rock m2 is tied to another string of length L2 = 0.19 m, and the pair of rocks is swung around in uniform circular motion, making 2 complete revolutions in one second. In this problem, you should neglect gravity and assume the motion is in the horizontal plane.


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a) What is T2, the tension in the string that is connected to the rock with mass m2?


My attempt
I tried taking v = (2*pi*0.33)/.5 seconds = 4.14 m/s
then: T = ((0.58 kg + 0.4 kg)*(4.14 m/s)^2)/0.19 = 88.40 N
but it was wrong...help! thank you!

 

[berkeman]

Think of it as two separate problems, and then add the tensions. What is the tension in a string L1+L2 long that has m1 at the end, with the angular frequency 2x2PI radians per second? And what is the tension in a string L2 long with the mass m2 at the end, with the same angular frequency? (BTW, I'm assuming that one end of L2 is what is being held to swing the system around.)

What is the equation that gives the force (tension) required for uniform circular motion of a mass, in terms of the mass m, the angular frequency omega, and the radius R?