Elastic Collision, Equal Masses

In summary, if you are trying to solve for v1 or v2 in a 2 dimensional elastic collision between two balls, you first need to find the slope and angle of their movement.
  • #1
Cruncher
5
0
Okay, i have a problem here with 2 dimensional elastic collision between 2 balls with equal mass, they are both moving in different directions before collision

what i know:

vx and vy of both balls,
the slope of their movement, which can be converted to an angle with tan-1 x

the problem is all I've got so far is momentum conservation with

m1v1 + m2v2 = m1v1' + m2v2'

but of course we have 2 unknown variables here v1' and v2'

so how do i use slope or angle to get v1 or v2 and then the other is easy to solve for.

thanks

EDIT: could i use impulse (J = Ft) and use a really small number of time and we know that J = p2 - p1

EDIT2: and where could i get the F in impulse from? can't really use Newtons second law of F = ma here because then i would need to know the acceleration of what it hit was which is essentially what finding J does for me... so anyone know of a better method??

cruncher
 
Last edited:
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  • #2
Hints:

- treat it as a 1 dimesional problem along the collision axis (connects centers of the balls). nothing changes perpedicular to it

- m1 = m2 in your case

- use the reference frame of one ball for calculation (one initial v becomes zero)

- use google
 
Last edited:
  • #3
i have searched google, i can't get much that helps me or i don't understand what it means, if i make it a 1d problem along the collision axis, i guess i need to find how much momentum in that direction, using triangles i assume with x and y momentum, but what if both circles are moving the same direction and slightly different angles, and different speeds (obviously cause if they were same speed and direction they wouldn't collide) so it comes and hits it from behind, there is no momentum acting against the other ball,
 

What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the total energy before and after the collision remains the same.

What are the conditions for an elastic collision?

In order for a collision to be considered elastic, the objects involved must be able to bounce off of each other without any loss of kinetic energy. This means that the objects must be perfectly rigid and there can be no external forces acting on them.

How do you calculate the velocities of two equal masses after an elastic collision?

The velocities of two equal masses after an elastic collision can be calculated using the conservation of momentum and the conservation of kinetic energy equations. The velocities can be found by setting the initial momentum and kinetic energy equal to the final momentum and kinetic energy, respectively.

What is the difference between an elastic collision and an inelastic collision?

In an inelastic collision, some of the kinetic energy is lost and converted into other forms of energy, such as heat or sound. In an elastic collision, all of the kinetic energy is conserved and no energy is lost.

Why is it important to study elastic collisions?

Studying elastic collisions allows us to understand and predict the behavior of objects in motion. This knowledge is essential in many fields, such as physics, engineering, and sports, where the interactions between objects are crucial in determining outcomes.

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