Energy, momentum and elastic collisions

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Homework Help Overview

The discussion revolves around a problem involving a perfect elastic collision between two particles, where one is initially stationary. The original poster seeks to derive three equations relating the masses and velocities of the particles using conservation of momentum and energy principles, while noting that both particles move at 30 degrees from the original path after the collision.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to establish equations based on conservation laws but expresses uncertainty about deriving a third equation. Some participants suggest that the momentum conservation should yield two independent vector equations.
  • There are discussions about the correct resolution of velocity components and the implications of the particles moving at different angles post-collision.
  • Participants question the assumptions regarding the equality of velocity components and the direction of motion after the collision.

Discussion Status

The conversation is ongoing, with participants providing feedback on each other's reasoning and suggesting clarifications. There is a focus on ensuring that the initial velocity is properly split into components and that the post-collision directions of the particles are accurately represented. No consensus has been reached yet, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants are navigating the complexities of vector equations in the context of elastic collisions, with specific emphasis on the angles involved and the need to correctly account for the components of velocity. There is an acknowledgment of the need for clarity in the assumptions being made about the motion of the particles.

yellowfish
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Homework Statement


A particle (of mass m velocity v) makes a perfect elastic collision with a stationary particle. After the collision both particles travel 30 degrees from original path. Use conservation of momentum/energy to obtain 3 equations relating the masses/velocities.

Homework Equations

The Attempt at a Solution


I can get two equations, one from using initial momentum = final momentum, and the other using initial kinetic energy = final kinetic energy, but I am unsure of where the third equation comes from. Any help would be appreciated.
 
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Initial momentum = final momentum is a vector equation and should give you two independent relations.
 
Thanks for your response, so would it be,

Initial momentum = final momentum
m1v = (m1 + m2)(v(y component)/sin(30))
and
m1v = (m1 + m2)(v(x component)/cos(30)) ?
 
No. First of all the x and y components of the original velocity are not equal. Second, the particles are not moving with the same velocity after the collision.

Please expand on your argumentation why you think something. It will help us understand how you think and where you go wrong - and it is usually enlightening to listen to your own arguments as well.
 
Since its an elastic collision and the masses are constant then the initial velocity v = final velocity of particle 1(call it u) + velocity of particle 2(call it s). Resolving those into the x and y components would therefore give for particle 1 u(x component)cos(30) and u(y component)sin(30) and for particle 2 s(x component)cos(30) and s(y component)sin(30).
Would the answer then be for the momentums
m1v = m1u(x component)cos(30) + m2s(x component)cos(30)
m1v = m1u(y component)sin(30) + m2s(y component)sin(30)
Or am I completely thinking about it wrong?
 
You need to split the initial velocity into components too.

The particles are also not going in the same direction after impact.

Edit: In addition, you are both taking the components of the velocities and multiplying with a trigonometric function. This is doing the same thing twice, which is one too many.
 
Okay would it then be

m1(√ [(vcos30)^2+(vsin30)^2] ) = m1ucos30 + m2scos30
m1(√ [(vcos30)^2+(vsin30)^2] ) = m1usin30 + m2ssin30
 
No. Again, you have the same initial velocity component in both directions. This is not the case. In which direction is the particle originally moving? On top of that, you are still working with the assumption that the particles move in the same direction after impact, they are not - one is going at a 30 degree angle to one side and the other in a 30 degree angle to the other side.
 

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