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June 22nd, 2015, 07:52 PM   #1
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Three Connected Balls

Three identical balls with mass M and connected by ropes with lenght L are laying on a flat table (Picture below). No friction between balls and table.

A. Initially, a guy poked the topmost ball till it has a velocity of Vo at time t=0. Determine the acceleration of three balls at an instant when the guy poked the topmost ball!

B. Initially, a guy poked the topmost and the lowest balls at the same time till both balls have a velocity of Vo. Determine the acceleration of three balls at an instant when the guy poked the topmost and the lowest balls!

I don't where to start, perhaps from the angular momentum of the system?
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June 23rd, 2015, 03:21 AM   #2
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I think that's a good start
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June 23rd, 2015, 03:34 AM   #3
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I think that's a good start
I only came up with the idea. But I don't know to model this case in an equation. The system seems complex.
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June 29th, 2015, 08:37 AM   #4
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Hello again! I've been thinking about this problem a lot... it's deceptively tricky. The problem is that when you have light inextensible strings, you have to define the forces without referring to some sort of physical mechanism that is well known (like gravity, drag, etc). Instead you just have to impose constraints on the problem (such as the distance between two connected particles cannot exceed the length of the string) and solve the problem based on that.

After a quick chat with a friend of mine, he suggests looking at Lagrangian mechanics. I'll delve into it and see if I can come up with something for you.
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July 25th, 2015, 11:00 PM   #5
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A. Balls 2 and 3 move orthogonal to the direction of motion of ball 1 due to centripetal force:

mv² / l / 2 / 2

B. Ball 2 does not accelerate.

Last edited by steveupson; July 25th, 2015 at 11:00 PM. Reason: syntax
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