# Finding a Tension Ratio

• Gman24
In summary, two clay balls with masses m and 2m collide inelastically, with the first ball initially at rest and the second ball approaching with a speed of sqrt(2gL) on the same plane. After the collision, the balls stick together and the tension in the string becomes T1. When the combined balls are at their maximum angle X, the tension in the string is T2. Using momentum conservation and energy conservation, it can be determined that T2/T1 = 5/17.

## Homework Statement

A clay ball of mass m hangs from a string with length L. When a second clay ball with mass 2m approaches it with a speed of sqrt(2gL) on the same plane. The collision is completely intelastic so that the balls stick together after the collision. Let T1 be ethe tension in the string immediately after the collision and T2 be the tension in the string when the combined balls are at their maximum angle X. Find T2/T1.
The known quantities are m, g, and L

the answer is supposed to be : 5/17

## Homework Equations

m1V1+m2V2=(m1+m2)Vimp
E1 + Work Non Conservative= E2
any Force summations

## The Attempt at a Solution

ok so I started out with momentum conservation.
since the mass m is at rest I threw that out of the left side of the eqn.
so I get:
2m(rt[2gL]) = (3m)Vimp
so I conlculded that the impact velocity (Vimp)= 2/3of(rt[2gl])

I then did FBDs for the initial and at the top of the swing.
at the bottom I got that
T1-3mg = (3mVimp/L)
and at the top of the swing
T2-3mgcosX = 0 (im not sure about this but I don't think it's accelerating radially if it hits absolute max swing angle since it would be at rest would it not at that instance?"

I then did energy conservation:
E1+Wnc=E2
I defined my y=0 to be the plain that the initial balls were traveling in. I got the ff:
E1 + Wnc:
K=(1/2)3mVimp^2
U=0
W=T1Lcos0 (again not sure)
E2:
K=0
U= 3mg(L-LcosX)

I don't know how to approach the problem given what I've found out. Thank you soo much for your guys' help in advance. Oh and sorry for the crazy notation I am using. I've had to make some compromises since I don't know how to do greek lettering and such on the comp :).

sorry for the double post but I don't know if this will help but here is the visual. Its problem number 2 on my practice test. Thanks again

#### Attachments

• PracticeTest4.pdf
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anybody? I really need help on this one. I have a test in 2 hours.