The discussion revolves around the conservation of momentum and energy in a scenario involving a dart colliding with a block. Participants are examining the validity of energy conservation equations in the context of elastic and inelastic collisions.
Some participants have provided insights into the nature of the collision, noting that momentum is conserved while energy is not. There is an ongoing exploration of the implications of these principles in different frames of reference.
There is a focus on the definitions of elastic versus inelastic collisions and the dimensions of the terms used in the energy equations. Participants are also considering the effects of the collision type on the overall problem setup.
Your question is whether the collision between the dart and block is elastic or not?j04015 said:
Because ##\frac{1}{2}mv_0## has dimensions of momentum and not energy.j04015 said:
Whoops, typo. I meant (1/2)(mv0)^2kuruman said:
PeroK said:
If the collision wasn't elastic the entire problem doesn't make sense.PeroK said:
That statement is false!j04015 said:
I see the issue now. Momentum is conserved but not energy. Thanks!PeroK said:
You can see that if you consider what's going on in the center of mass frame. Before the collision, both dart and block move with opposite momenta. Total momentum is zero and the kinetic energy is non-zero. After the collision, the dart and the block are at rest. Total momentum is zero (conserved) and total kinetic energy is also zero (not conserved).j04015 said:
The conservation of energy equations will not be compatible with conservation of energy in any frame if you assume that the dart sticks. However, I agree that considering the com frame makes it very explicit.kuruman said: