Conservation of Kinetic Energy vs Momentum

[ja_tech]

Hi all..

I am getting a little confused between the principles of

1.Conservation of Kinetic Energy; and
2.Conservation of Momentum...


What is the difference between the two (if any) and can we use the idea of elastic collisions in both examples?

Cheers,

ja_tech

 

[Doc Al]

One difference is that momentum is conserved in any collision as a consequence of Newton's laws, but kinetic energy is only conserved in elastic collisions.

 

[ja_tech]

One difference is that momentum is conserved in any collision as a consequence of Newton's laws, but kinetic energy is only conserved in elastic collisions.

Great. Thanks for this

 

[HallsofIvy]

For example, an object, A, of mass M, speed v, strikes an obect, B, which also has mass M but speed 0. How do the move after the collision? We have to consider two unknowns, $v_A$ and $v_B$, the speeds of the two objects after the collision. Conservation of momentum gives us one equation: $Mv= Mv_A+ mv_B$ which reduces to $v_a+ v_B= v$ but is still only one equation in two unknowns.

Assuming a perfectly elastic collision, we also have conservation of energy: $(1/2)Mv_a^2+ (1/2)Mv_B^2= (1/2)Mv^2$ which reduces to $v_A^2+ v_B^2= v^2$. We can solve the first equation for $v_B= v- v_A$, replace $v_B$ with that in the first equation and solve.

In a perfectly inelastic collision, the two objects stick together and so move with the same velocity. We have the second equation $v_A= v_B$ and again can solve for the two velocities.

 

[aeb2335]

One difference is that momentum is conserved in any collision as a consequence of Newton's laws, but kinetic energy is only conserved in elastic collisions.

This trips me up every now and again too...but just to add on to that question what if you knew the coefficient of restitution for the inelastic case would that help you conserve energy? Or is the the only way to do that would be the resilience?

thanks

 

[Doc Al]

This trips me up every now and again too...but just to add on to that question what if you knew the coefficient of restitution for the inelastic case would that help you conserve energy? Or is the the only way to do that would be the resilience?

If you know the coefficient of restitution for a given collision, then you can calculate just how much KE is "lost". That coefficient (plus the initial velocities before the collision, of course) allows you to calculate the final velocities after the collision.