Two-Dimensional Elastic Collision

In summary, the particle with speed v1 = 2.64 × 106 m/s makes a glancing elastic collision with another particle that is at rest. Both particles have the same mass. After the collision, the struck particle moves off at 45º to v1. The speed of the struck particle after the collision is approximately 1.9E6 m/s.
  • #1
johnhuntsman
76
0
A particle with speed v1 = 2.64 × 106 m/s makes a glancing elastic collision with another particle that is at rest. Both particles have the same mass. After the collision, the struck particle moves off at 45º to v1. The speed of the struck particle after the collision is approximately...

The answer is 1.9E6 m/s.

I drew a diagram of the scenario. I know that the two final vectors form a right triangle with the initial v1. And I have these equations written out:

v1i = v1f + v2f (since momentum is conserved; the mass can be divided out)

v1i2 = v1f2 + v2f2 (since KE is conserved and 0.5m can be divided out)

The first equation broken up into components:

v1ix = v1fx + v2fx

0 m/s = v1fy + v2fy

What do I do? Maybe I'm the world's least intuitive man, but I don't see how this system of equations can be solved. All I need is someone to tell me where to start and I'll probably be good to go.

[Edit] Am I supposed to put the components in terms of sine and cosine and go from there? [Edit]
 
Last edited:
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  • #2
Write the energy equation in terms of the components.
You now have 3 equations and 4 unknowns (the final velocities, v1x, v1y, v2x, v2y).
There is one more equation you forgot:
v2x = v2y
which comes from the fact that v2 is at 45 degrees to vi.
Now you have 4 equations and 4 unknowns. Have at it.
 
  • #3
frogjg2003 said:
Write the energy equation in terms of the components.
You now have 3 equations and 4 unknowns (the final velocities, v1x, v1y, v2x, v2y).
There is one more equation you forgot:
v2x = v2y
which comes from the fact that v2 is at 45 degrees to vi.
Now you have 4 equations and 4 unknowns. Have at it.

Can you do that? I thought energy didn't have components since it's scalar not vector.
 
  • #4
It doesn't, it's still one equation. You just write it in terms of the individual components instead of the total velocity.
[tex]
v_1^2=v_{1x}^2+v_{1y}^2\\
v_2^2=v_{1x}^2+v_{2y}^2
[/tex]

Another approach would have been to replace every v2y and v2x with v2/√2.
 
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  • #5
Alright thanks. I got it. I appreciate it : D
 

FAQ: Two-Dimensional Elastic Collision

1. What is a two-dimensional elastic collision?

A two-dimensional elastic collision is a type of collision that occurs between two objects in which both conservation of momentum and conservation of kinetic energy are observed. This means that both the total momentum and total kinetic energy of the objects before and after the collision remain the same.

2. How is the conservation of momentum and conservation of kinetic energy observed in a two-dimensional elastic collision?

In a two-dimensional elastic collision, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision. Additionally, the total kinetic energy of the objects before the collision is equal to the total kinetic energy of the objects after the collision.

3. What is the difference between a two-dimensional elastic collision and an inelastic collision?

In an inelastic collision, the total kinetic energy of the objects before and after the collision is not conserved. This means that some of the kinetic energy is lost and converted into other forms of energy, such as heat or sound. In a two-dimensional elastic collision, all of the kinetic energy is conserved.

4. What factors affect the outcome of a two-dimensional elastic collision?

The outcome of a two-dimensional elastic collision is affected by the mass, velocity, and angle of the objects involved. The mass and velocity of the objects determine the total momentum, while the angle of the collision can impact the direction of the objects after the collision.

5. How is a two-dimensional elastic collision represented mathematically?

A two-dimensional elastic collision can be represented using the equations for conservation of momentum and conservation of kinetic energy. These equations take into account the mass, velocity, and angle of the objects before and after the collision to determine the final velocities of the objects.

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