Conservation of energy with springs and rotational motion

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SUMMARY

The discussion centers on the conservation of energy principles applied to springs and rotational motion, specifically using the equation T1 + V1 = T2 + V2. Participants express confusion regarding the assumption that the velocities Va and Vb are zero, despite the presence of kinetic energy in the system. Clarification is provided that the rods are pinned, meaning they do not rotate due to frictionless pin joints, which is a critical detail in understanding the mechanics involved when the spring stretches from √2 to 2m.

PREREQUISITES
  • Understanding of kinetic and potential energy concepts
  • Familiarity with rotational motion and pin joints
  • Knowledge of spring mechanics and energy conservation principles
  • Ability to analyze motion in a frictionless environment
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn about the behavior of pin joints in rotational dynamics
  • Explore the mechanics of springs and their energy storage capabilities
  • Investigate the implications of frictionless surfaces on motion analysis
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the dynamics of springs and rotational motion in frictionless 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".
 
Last edited:

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