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 conservation of momentum principle states that in a closed system, the total momentum before an event is equal to the total momentum after the event. This means that the total amount of momentum in a system remains constant, regardless of any internal or external forces acting on it.
Momentum is calculated by multiplying an object's mass by its velocity. The equation for momentum is: p = m * v, where p is momentum, m is mass, and v is velocity. Momentum is typically measured in units of kg*m/s.
In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before the collision are equal to the total momentum and total kinetic energy after the collision. In an inelastic collision, only momentum is conserved, meaning that the total momentum before and after the collision are equal, but the total kinetic energy may change.
The conservation of energy principle states that energy cannot be created or destroyed, only transferred or converted from one form to another. In collisions, energy may be transferred between objects, but the total energy in the system remains constant. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
No, the conservation of momentum and energy are fundamental principles in physics and have been proven to hold true in all observed physical systems. While it may appear that momentum or energy is being lost in a certain situation, it is likely due to external factors that are not being taken into account. In a closed system, these principles will always hold true.