Springs and Elastic Coollisions

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SUMMARY

The discussion centers on a physics problem involving a 2.5 kg ball colliding with a stationary 4.5 kg ball, utilizing a spring with a spring constant of 1100 N/m. The key questions are to determine the velocities of both balls at minimum separation and the change in total kinetic energy compared to the initial kinetic energy of the system. The relevant equations include momentum conservation (p=mv), Hooke's Law (Fx=kx), and elastic potential energy (Ee=1/2kx^2). Participants are encouraged to apply these principles to solve the problem effectively.

PREREQUISITES
  • Understanding of momentum conservation principles
  • Familiarity with Hooke's Law and spring mechanics
  • Knowledge of kinetic and potential energy equations
  • Basic algebra for solving equations
NEXT STEPS
  • Study the conservation of momentum in elastic collisions
  • Learn about energy transformations in spring systems
  • Explore the concept of minimum separation in collision dynamics
  • Review examples of similar physics problems involving springs and collisions
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of collisions involving springs and energy conservation principles.

fibb
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Homework Statement


A ball of mass 2.5kg is moving to the left along a smooth, horizontal table at 3.5m/s. An idea spring (one that obeys Hooke's Law) with a spring contstant of k=1100N/m, and a relaxed length of 0.3m, is attached to its front. It collides head on with a 4.5 kg ball, initially at rest.
a) What is the velocity of each ball at minimum separation?
b) What is the change in total kinetic energy at minimum separation? as compared to initial K.E. of system?


Homework Equations


p=mv
Hooke's Law: Fx=kx
Ee=1/2kx^2
I know there's more equations needed

The Attempt at a Solution


For a, I found an expression of v1 and v2 with the momentum formula and conservation of momentum and tried to eliminate. But I got stuck at that part.
I don't really know how to do b.
 
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