# Two dimensional Elastic Collision

• CalebB-M
In summary, the problem involves an elastic collision between a helium atom and an oxygen atom. Using conservation of momentum and energy, the final velocities of both atoms can be determined. The approach is to set up a coordinate system and write equations for the components of the velocity. By substituting in the variables for the unknown direction, the magnitudes of the velocities can be found and used to solve the system of equations.
CalebB-M

## Homework Statement

[/B]
The problem statement is: A helium atom traveling at a speed of 240 m/s hits an oxygen atom at rest. If the helium atom rebounds elastically, from the oxygen atom at an angle of 90° with respect to the original direction of motion, what are the final velocities of both atoms. (hint the oxygen is approximately 4 times as massive as the helium.)

## Homework Equations

I understand that Momentum is conserved Pi = Pf thus m*v1i + m*v2i = m*v1f + m*v2f
Energy is also conserved in an elastic collision.
1/2m * v^2 = ke

## The Attempt at a Solution

I can setup the coordinate system with +x being the initial direction of the helium particle. I also tried writing it in vector notation. my initial setup looked like this
M*[ 240x, 0y, 0z] + 0 (because it is at rest) = M*[0x,sin90*|v1f|y, 0z] + 4M*[cos♤*|v2f|x,sin♤*|v2f|y, 0z]
With ♤ being the unknown direction.
I also attempted to find the magnitude of the velocities by CE, I found that 1/2 M *(240)^2 = 1/2M*(v1f)^2 + 2M*(v2f)^2. Canceling out the mass I found that 240^2 = v1f^2 /2 + 2*v2f^2. I am lost on the next step.
Any direction would be helpful thank you!

Hello. You have the correct approach. I think it's easier to do the algebra if you write the components of the velocity as v2x rather than v2⋅cosθ, etc. Thus, get equations for v1y, v2x, and v2y.

CalebB-M
Ahhhh I see it now haha, by substituting V2x for cos♤*V2 and V2y for sin♤*V2 I can find the magnitudes without knowing the theta then I can plug an chug the systems of equations. Thanks!

## 1. What is a two dimensional elastic collision?

A two dimensional elastic collision is a type of collision in which two objects collide with one another in a plane, and both the momentum and kinetic energy are conserved during the collision.

## 2. What is the difference between elastic and inelastic collisions?

In an elastic collision, both momentum and kinetic energy are conserved, meaning that the total momentum and total kinetic energy of the system before and after the collision are equal. In an inelastic collision, only momentum is conserved, meaning that the total momentum of the system before and after the collision are equal, but the total kinetic energy is not.

## 3. How is the velocity of objects calculated after a two dimensional elastic collision?

The velocity of objects after a two dimensional elastic collision can be calculated using the equations for conservation of momentum and conservation of kinetic energy, which take into account the masses and velocities of the objects before and after the collision.

## 4. What is the coefficient of restitution in a two dimensional elastic collision?

The coefficient of restitution is a measure of the elasticity of a collision, and is defined as the ratio of the relative velocity of separation after a collision to the relative velocity of approach before the collision. In a two dimensional elastic collision, the coefficient of restitution is equal to 1, indicating a perfectly elastic collision.

## 5. What real-life examples can be modeled using two dimensional elastic collisions?

Two dimensional elastic collisions can be used to model a variety of real-life situations, such as billiard ball collisions, collisions between particles in a gas, or collisions between molecules in a chemical reaction. They can also be used to study the movement of celestial bodies, such as planets and satellites, in space.

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