• Support PF! Buy your school textbooks, materials and every day products Here!

Finding a Tension Ratio

  • Thread starter Gman24
  • Start date
  • #1
3
0

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 dont 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 Im using. I've had to make some compromises since I dont know how to do greek lettering and such on the comp :).

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
3
0
sorry for the double post but I dont know if this will help but here is the visual. Its problem number 2 on my practice test. Thanks again
 

Attachments

  • #3
3
0
anybody? I really need help on this one. I have a test in 2 hours.
 

Related Threads for: Finding a Tension Ratio

  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
9
Views
3K
Replies
1
Views
6K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
5
Views
473
  • Last Post
Replies
2
Views
814
  • Last Post
Replies
1
Views
7K
Replies
3
Views
17K
Top