Conservation of energy with springs and rotational motion

AI Thread Summary
The discussion revolves around the conservation of energy in a system involving springs and rotational motion. The key equation used is T1 + V1 = T2 + V2, where T represents kinetic energy and V represents potential energy. There is confusion regarding the assumption that the velocities Va and Vb are zero, despite the wheels having some velocity, which is clarified by noting that they only reach zero at a specific angle. Additionally, the concept of "pinned" rods is addressed, emphasizing that this is a defined condition in the problem, indicating frictionless movement at the pin joints. Overall, the discussion highlights the importance of understanding the conditions under which energy conservation equations apply in mechanical systems.
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Homework Statement


KXS8m.png



Homework Equations


T1 + V1 = T2 + V2

T = kinetic energy
V = potential energy

The Attempt at a Solution


I am only confused about how to get T2. Here is how the answer key gets T2:
FHFo0.png


I don't get why Va = Vb = 0. The wheels have some velocity so it doesn't make sense how they are zero. I realize that they won't rotate because there is no friction but I still think there is a velocity.

I also don't get why they can assume that the rods are pinned. How are they pinned when the spring stretches from √2 to 2m in length (this is from the solution as well)?
 
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Va=Vb=0 only when θ = 0. At this angle, AC and CB are horizontal and the maximum separation between A and B has been achieved.

''pinned" is not an assumption, it is expressly given--"All pin joints move without friction". Not sure what the answer key means by like "pinned case".
 
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