Convservation of Mech. Energy/Momentum

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SUMMARY

The discussion centers on the conservation of momentum and mechanical energy in collision problems, specifically distinguishing between elastic and inelastic collisions. In elastic collisions, both momentum and mechanical energy are conserved, allowing for the use of both conservation equations to solve for variables such as masses and velocities. In contrast, inelastic collisions only conserve momentum, as some energy is transformed into heat or lost due to friction. The coefficient of restitution is introduced to quantify the energy loss in partially elastic collisions.

PREREQUISITES
  • Understanding of elastic and inelastic collisions
  • Familiarity with conservation laws in physics
  • Knowledge of algebraic manipulation for solving equations
  • Concept of coefficient of restitution
NEXT STEPS
  • Study the principles of conservation of momentum in various collision scenarios
  • Learn about the mathematical derivation of the coefficient of restitution
  • Explore real-world applications of elastic and inelastic collisions
  • Investigate the differences in energy transformation during collisions
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Physics students, educators, and anyone interested in understanding the principles of mechanics, particularly in relation to collision dynamics and energy conservation.

AznBoi
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I have a question about the conservation of momentum and energy in collision problems. What type of situations (elastic/inelastic) can you use the equations to solve for either masses or velocities??

Am I correct?::

Elastic collision: You can use both conservation of momentum + mech. energy to solve for the variables because everything is conserved.

Inelastic collision: You can use only conservation of momentum because some energy is wasted as heat or wasted from friction.

Can someone give me a better explanation or correct me if I'm wrong? Thanks!
 
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Not only can you use energy conservation for elastic collisions, you must use it to solve the problem. An algebraic manipulation can be done to produce a velocity difference equation that can be used instead of the quadratic energy equations for head on collsiions. If a collision is perfectly inelastic, there is only one final velocity for both objects involved.

Some problems fit between these two categories and give a coefficient of restitution that expresses the final velocity difference as a fraction of the initial velocity difference.
 
Yes,you are both right.
conservation of energy can only be used in elastic collision.
And in the inelastic collision the coefficient is
e=(U1-U2)/(v2-v1)
U is former velocity
 

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