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:
The principle of conservation of momentum states that in a closed system with no external forces, the total momentum before and after a collision or interaction remains constant. This means that the sum of the momenta of all objects involved in the interaction will be the same before and after the event.
In mechanical systems, the principle of conservation of energy states that the total mechanical energy (sum of kinetic and potential energy) remains constant if only conservative forces are acting. This means that energy can change forms, such as from kinetic to potential energy or vice versa, but the total amount of mechanical energy remains unchanged.
An elastic collision is a type of collision where both momentum and kinetic energy are conserved. In an elastic collision, the total kinetic energy of the system before and after the collision remains the same, and the objects involved rebound without any loss of speed, assuming no external forces act on the system.
An inelastic collision is a type of collision where momentum is conserved, but kinetic energy is not. In inelastic collisions, some of the kinetic energy is transformed into other forms of energy, such as heat or sound, resulting in a loss of total kinetic energy in the system. Objects in a perfectly inelastic collision stick together after the collision, moving as a single object.
To solve problems using conservation laws in AP Physics C Mechanics, you first identify the type of collision or interaction and the forces involved. For momentum problems, you set up the equation for the conservation of momentum, ensuring the total momentum before the interaction equals the total momentum after. For energy problems, you use the conservation of energy principle to equate the total mechanical energy before and after the event, accounting for any potential energy changes and work done by non-conservative forces if applicable. By solving these equations, you can find unknown quantities such as velocities, heights, or masses.