2 dimensional elastic collision

In summary, the conversation involves a person seeking help with solving equations related to the collision of two particles, one with initial speed V1 and the other at rest with mass 3m. After the collision, the particle with mass m is seen moving at a 30 degree angle from its initial direction. The individual is advised to use equations for momentum and energy to solve for the unknowns V1, V, and C, with the final goal being to find the angle of motion of the second particle after the collision.
  • #1
teleport
240
0
Hey, I'm having problems with this:

A particle m with initial speed V1 collides with a particle at rest with mass 3m. After collision, particle with mass m is seen moving 30 degrees from its initial direction. What is the angle of motion of the 2nd particle after collision?

I can get three equations from momentum and energy for three unknowns but I can't solve it. Help?
 
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  • #2
Show me your equations.
 
  • #3
x-component:

V1 = v1cos30 + 3VcosC


y-component:

v1sin30 = 3VsinC


Energy:

V1^2 = v1^2 + 3V^2,

where C is the unknown angle, v1, V are the final velocities of the m and 3m masses.
 
  • #4
That's not exactly how I'd go about it. oops nevermind lol.
 
  • #5
Well you see your equation 1 gives you what V1 is. So you can plug that into equation 3. Now you are only left with 2 uknowns, V and C. Now equation 2 gives you a way of getting rid of V. So now you only have 1 equation and 1 unknown, C.

btw, conservation of momentun does not use angles.

I should say conservation of momentum does not have to use angles. So if it helps, go ahead and use the total conservation of momentum equation.
 
Last edited:
  • #6
that's wrong. Ill explain tomorrow why. Anyways thax.
 
  • #7
Your equation in the y direction needs a negative sign.

Also, you will use angles.
 
  • #8
Please can someone actually help?
 
  • #9
teleport said:
Please can someone actually help?

Your equations seem correct (C will then be a negative angle). What's your problem in solving them ?

You need to solve for the quantities v1, V and C and you have 3 equations.

Try to eliminate v1 and V using the first two equations to write everything as a function of C in the third one, and you'll have an equation for your angle C.
 

1. What is a 2 dimensional elastic collision?

A 2 dimensional elastic collision is a type of collision between two objects in which both kinetic energy and momentum are conserved. This means that the total energy and momentum of the system before and after the collision are equal.

2. How is a 2 dimensional elastic collision different from an inelastic collision?

In a 2 dimensional elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision, only momentum is conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

3. What is the equation used to calculate the final velocities in a 2 dimensional elastic collision?

The equation used is: v1f = (m1 - m2)v1i + 2m2v2i / (m1 + m2) for the first object and v2f = (m2 - m1)v2i + 2m1v1i / (m1 + m2) for the second object.

4. What are some real-life examples of 2 dimensional elastic collisions?

Some examples include billiard balls colliding on a pool table, two hockey pucks colliding on the ice, and two air molecules colliding in the Earth's atmosphere.

5. How can the coefficient of restitution be used to determine if a collision is elastic?

The coefficient of restitution, which is the ratio of the final relative velocity to the initial relative velocity, can be used to determine if a collision is elastic. If the coefficient of restitution is equal to 1, the collision is elastic. If it is less than 1, the collision is inelastic. A coefficient of restitution greater than 1 is not physically possible.

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