State the quantities that are conserved in one-d and two-d collisions. Give an example of each type of collision.
I looked in my textbook and all i could come up with was that momentum was conserved for both?
Momentum and angular momentum (which you may not have studied) are conserved in all collision. Kinetic energy is only conserved in special cases (like billiards) but is often approximately conserved. Total energy is conserved, but some may end up as internal inergy (heat; light; vibration etc.) It does not matter how many dimensions are involved in the problem; momentum is still conserved.
It seems like a pretty silly question for your teacher to assign. An example of a one-d collision would be a basketball dribbled from above, or a head-on collision where both objects stick together or remain on the same linear path.
You are correct that momentum is conserved in both one-dimensional and two-dimensional collisions. However, there are additional quantities that are conserved in two-dimensional collisions.
In one-dimensional collisions, only momentum is conserved, meaning the total momentum before the collision is equal to the total momentum after the collision. An example of a one-dimensional collision is when two billiard balls collide head-on on a straight pool table.
In two-dimensional collisions, both momentum and kinetic energy are conserved. This means that the total momentum and the total kinetic energy before the collision are equal to the total momentum and the total kinetic energy after the collision. An example of a two-dimensional collision is when two ice skaters collide at an angle on an ice rink.
It is worth noting that in real-world situations, there may be some energy loss due to factors like friction or deformation. However, in ideal scenarios, momentum and kinetic energy are conserved.
Yes, you're correct. Momentum is indeed conserved in both one-dimensional and two-dimensional collisions. However, there are a few additional quantities that are conserved in these types of collisions.
In one-dimensional collisions, where the objects move along a straight line, the following quantities are conserved:
1. Momentum: Momentum is the product of an object's mass and velocity. In a one-dimensional collision, the total momentum before the collision is equal to the total momentum after the collision. This conservation law is known as the Law of Conservation of Linear Momentum.
Example of a one-dimensional collision: Two cars of different masses collide head-on with each other and stick together after the collision. The total momentum of the system before the collision (sum of the individual momenta of the cars) is equal to the total momentum after the collision (momentum of the combined mass of the cars).
In two-dimensional collisions, where the objects can move in multiple directions, the following quantities are conserved:
1. Total Momentum (both components): In a two-dimensional collision, the total momentum in each direction (x-axis and y-axis) is conserved independently. This means that the vector sum of momenta before the collision is equal to the vector sum of momenta after the collision.
Example of a two-dimensional collision: A billiard ball collides with another ball at an angle. Both balls have different masses, and after the collision, they move in different directions. The total momentum in the x-direction before the collision is equal to the total momentum in the x-direction after the collision, and similarly for the y-direction.
It's worth noting that in both one-dimensional and two-dimensional collisions, the total kinetic energy of the system may or may not be conserved, depending on whether the collision is elastic or inelastic. However, momentum is always conserved regardless of whether the collision is elastic or inelastic.