Solving Motion Equations for 2D Elastic Collisions

Depending on the initial conditions, you can use this to solve for the final velocities and angles.In summary, The conversation discusses the process of creating a 2D simulation of elastic colliding balls and the difficulty in deriving the motion equations after collision. The speaker asks for help in finding the general equations for determining the new speed and angles of the balls after collision, without the presence of friction or rotation. The response suggests using conservation of energy and momentum to solve for the final velocities and angles, with one free parameter being the angle after collision.
  • #1
cghost
4
0
Hi, I'm trying to make a 2d simulation of elastic colliding balls. I have a hard time deriving the motion equations after collision. For each ball i know the speed, the mass and the angle of movement. Can anyone point me in the right direction to find the general equations for this ? I need the new speed after collision and the new angles which the balls will use as direction. I tried some energy and impulse conservation but i didn't came up with something concrete.
Btw: i don't have friction, rotation or things like this. everything is ideal.
 
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  • #2
Given conservation of energy and momentum, you will have one free parameter, namely the angle after collision.
 

FAQ: Solving Motion Equations for 2D Elastic Collisions

1. What is a 2D elastic collision?

A 2D elastic collision is a collision between two objects in two dimensions where both kinetic energy and momentum are conserved. This means that the total kinetic energy and momentum before the collision are equal to the total kinetic energy and momentum after the collision.

2. How do you solve for motion equations in a 2D elastic collision?

To solve for motion equations in a 2D elastic collision, you can use the conservation of momentum and conservation of kinetic energy equations. These equations involve the masses, velocities, and angles of the objects before and after the collision. By setting these equations equal to each other and solving for the unknown variables, you can determine the final velocities and directions of the objects after the collision.

3. What is the difference between a 2D elastic collision and an inelastic collision?

In a 2D elastic collision, kinetic energy and momentum are conserved, while in an inelastic collision, kinetic energy is not conserved. This means that in an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

4. Can a 2D elastic collision occur in real life?

Yes, 2D elastic collisions can occur in real life, though they are rare. An example of a 2D elastic collision is when two billiard balls collide on a frictionless surface. In most real-life scenarios, there is some loss of kinetic energy due to factors such as friction and deformation of the objects involved.

5. What are the applications of understanding 2D elastic collisions?

Understanding 2D elastic collisions can be useful in various fields such as physics, engineering, and sports. In physics, it helps in understanding the principles of conservation of energy and momentum. In engineering, it is important for designing structures that can withstand collisions without breaking. In sports, it can be used to analyze the impact of collisions in games such as billiards and pool.

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