# 2D Elastic Collision equations

• vip4
In summary, the conversation discusses the equations and principles behind 2D elastic collisions, including conservation of momentum and energy. The conversation also mentions the possibility of solving 2D collision problems using Newton diagrams and suggests further research on 3D collisions. The goal of the conversation is to gain a better understanding of these concepts in order to write a computer program for simulating collisions.
vip4
Does anyone know the equations for 2D elastic collisions.

Don't just learn the equations. Learn the principles behind those equations. You will always have conservation of momentum in any collision. For elastic collisions energy is also conserved. This will give you enough info the solve any collision problem, in principle anyway.

Conservation of momentum:

$$m_1 v_1 \cos \theta_1 + m_2 v_2 \cos \theta_2 = m_1 v_1^\prime \cos \theta_1^\prime + m_2 v_2^\prime \cos \theta_2^\prime$$

$$m_1 v_1 \sin \theta_1 + m_2 v_2 \sin \theta_2 = m_1 v_1^\prime \sin \theta_1^\prime + m_2 v_2^\prime \sin \theta_2^\prime$$

Conservation of energy:

$$\frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 = \frac{1}{2} m_1 {v_1^\prime}^2 + \frac{1}{2} m_2 {v_2^\prime}^2 + Q$$

where $Q$ is the amount of kinetic energy lost in the collision (to "heat" or whatever). For an elastic collision, $Q = 0$.

Thanks for the reply galileo and jtbell. I have done a little reading on conservation of momentum and energy. I also search the internet for the equations and the theories involved in collisions. However i could only find 1D equations.

I would appreciate it if you could point me to any information that could help me to better understand it. I would also like any information on 3D collisions as well. The reason I'm trying to get this information is to write a computer program that simulates collisions.

I remember a neat way to solve 2D collision problems geometrically. Google for Newton diagrams.

## What is a 2D Elastic Collision?

A 2D Elastic Collision is a type of collision between two objects in which both the momentum and kinetic energy are conserved. This means that after the collision, the total momentum and total kinetic energy of the system remains the same.

## What are the equations used to calculate 2D Elastic Collisions?

The equations used to calculate 2D Elastic Collisions are the conservation of momentum equation and the conservation of kinetic energy equation. These equations are used to solve for the final velocities of the objects involved in the collision.

## What is the conservation of momentum equation?

The conservation of momentum equation states that the total momentum before a collision is equal to the total momentum after the collision. This can be written as m1v1i + m2v2i = m1v1f + m2v2f, where m is the mass of the object and v is the velocity.

## What is the conservation of kinetic energy equation?

The conservation of kinetic energy equation states that the total kinetic energy before a collision is equal to the total kinetic energy after the collision. This can be written as 1/2m1v1i2 + 1/2m2v2i2 = 1/2m1v1f2 + 1/2m2v2f2, where m is the mass of the object and v is the velocity.

## What are some real-life applications of 2D Elastic Collisions?

2D Elastic Collisions can be seen in many real-life scenarios, such as billiards, bumper cars, and air hockey. They are also used in physics experiments to study the conservation of momentum and energy. Additionally, understanding these equations is essential in fields such as engineering and astronomy.

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