Understanding the Coefficient of Restitution in 2-D Inelastic Collisions

In summary, the conversation discusses a collision between two spherical balls with equal mass and radius. The collision is two-dimensional and not completely elastic. The primary ball has a given velocity along the horizontal axis while the secondary ball is initially stationary. After the collision, the speed and components of velocity for both balls are observed. The question at hand is about the coefficient of restitution and the relationship between the variables involved. After further research, it is determined that the speeds along the axis of the collision's normal are used to find the coefficient of restitution. The secondary ball's direction is along the normal of the collision axis, and the ratio between the difference of speeds before and after the collision is used to determine the coefficient of restitution.
  • #1
Sythalist
3
0
Hello,

This concerns a collision between two spherical balls of equal mass and radius. The collision is two dimensional and not completely elastic. The secondary ball begins stationary. The primary ball travels along the horizontal axis with a given velocity. After the collision, the speed and components of velocity of both balls are observed.

u0 = initial velocity of primary ball
v0 = initial velocity of secondary ball = 0

u1x = horizontal component of velocity of primary ball post collision
u1y = vertical component of velocity of primary ball post collision
|u1| = post collision speed of primary ball

v1x = horizontal component of velocity of secondary ball post collision
v1y = vertical component of velocity of secondary ball post collision
|v1| = post collision speed of secondary ball

The question is about the coefficient of restitution. What is, if any, the relationship between all or some of the above variables in terms of the coefficient of restitution? Or how can we determine the coefficient of restitution from the above variables? Thank you!
 
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  • #2
aaah n/m sorry, I just hit a mind block back there, I did more research and figured out you must use the speeds along the axis of the normal of the collision. And that the secondary ball's direction IS along the normal of collision axis. Then you simply find the ratio between the difference of speeds before and after the collision. oops

hehe talking to myself in my ooooown thread
 

1. What is a 2-D inelastic collision?

A 2-D inelastic collision is a type of collision between two objects in which they stick together after colliding and move in a single direction. This means that the total kinetic energy of the system is not conserved and is converted into other forms of energy, such as heat or sound.

2. How is momentum conserved in a 2-D inelastic collision?

In a 2-D inelastic collision, the total momentum of the system is conserved. This means that the sum of the momentum of the two objects before the collision is equal to the sum of their momentum after the collision. This conservation of momentum is a fundamental principle in physics.

3. What is the difference between a 2-D inelastic collision and a 2-D elastic collision?

In a 2-D elastic collision, the objects bounce off each other after colliding, and the total kinetic energy of the system is conserved. In contrast, in a 2-D inelastic collision, the objects stick together and move in the same direction after colliding, and the total kinetic energy is not conserved.

4. How is the coefficient of restitution related to a 2-D inelastic collision?

The coefficient of restitution is a measure of the elasticity of a collision. In a 2-D inelastic collision, the coefficient of restitution is zero, meaning that there is no rebound or bouncing off of the objects after colliding. This is due to the fact that the objects stick together and move in a single direction after the collision.

5. What factors affect the outcome of a 2-D inelastic collision?

The outcome of a 2-D inelastic collision can be affected by various factors, including the mass and velocity of the objects, the angle at which they collide, and the type of materials the objects are made of. These factors can influence the amount of kinetic energy converted into other forms of energy during the collision.

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