Find final velocities after elastic collision

In summary, the conversation is about learning physics through Google and wanting to simulate simple physics programmatically. The person is having trouble solving for velocities after an elastic collision and is considering different scenarios with two objects of the same mass. They are asking for additional information or variables needed to determine the outcome of a collision, and it is suggested that the elasticity of the materials and the impulse (amount of time spent in contact) are important factors. The mentor explains that in an elastic collision, the sum of the kinetic energies before and after the collision remains constant, which is another constraint to consider. The person expresses gratitude and acknowledges the need to brush up on algebra skills.
  • #1
danred99
Im learming physics through google and I would like to be able to simulate some simple physics prgromatically. Having a hard time with solving for velocites after an elastic collision. Consider two objects, each with a mass of 1kg. One at rest and the other with velocity of 1 m/s in the direction of the first. Although total momentum in the system will be conserved after their collision, it seems there are an infinite number of possible velocities of the two objects after the collision that will satisfy the conservation of momentum; e.g., v1=0.5 m/s and v2=0.5 m/s;
or v1=0.25 m/s and v2=0.75 m/s;
or v1=-0.5 m/s and v2=1.5 m/s;
etc.

What additional piece of information or variable do I need to determine the one outcome in a given circumstance? Is it related to the elasticity of the materials? Is it the amount of time they spend in contact (i.e. impulse)?
 
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  • #2
If, as you say, the collision is elastic, then (by definition) the sum of the kinetic energies of the two objects remains constant before and after the collision. That's your second constraint.
 
  • #3
Ignotum per ignotius said:
If, as you say, the collision is elastic, then (by definition) the sum of the kinetic energies of the two objects remains constant before and after the collision. That's your second constraint.

Thanks! guess I'll have to spend more time learning / understanding kinetic energy
Ignotum per ignotius said:
If, as you say, the collision is elastic, then (by definition) the sum of the kinetic energies of the two objects remains constant before and after the collision. That's your second constraint.
Wow! that was simple. now to brush up on my algebra skills

[mentor's note: this post has been lightly edited to fix some auto-correct garbling]
 
Last edited by a moderator:

1. How do you calculate the final velocities after an elastic collision?

The final velocities can be calculated using the conservation of momentum and the conservation of kinetic energy equations. The equations are:
m1v1 + m2v2 = m1v1' + m2v2' (conservation of momentum)
(1/2)m1v1^2 + (1/2)m2v2^2 = (1/2)m1v1'^2 + (1/2)m2v2'^2 (conservation of kinetic energy)
Where m1 and m2 are the masses of the two objects involved in the collision, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities.

2. What is an elastic collision?

An elastic collision is a type of collision between two objects where both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before and after the collision are equal.

3. Can you have an elastic collision between objects with different masses?

Yes, an elastic collision can occur between objects with different masses. In an elastic collision, the masses of the objects do not affect the final velocities, only the initial velocities and the angles at which they collide.

4. What is the difference between an elastic collision and an inelastic collision?

The main difference between an elastic collision and an inelastic collision is that in an elastic collision, both momentum and kinetic energy are conserved, while in an inelastic collision, only momentum is conserved. In an inelastic collision, some kinetic energy is lost, usually in the form of heat or sound.

5. Are there any real-life examples of elastic collisions?

Yes, there are many real-life examples of elastic collisions. Some examples include a game of pool, a game of billiards, or a game of air hockey. In these games, the balls colliding with each other exhibit elastic collisions, where both momentum and kinetic energy are conserved. Another example is a collision between two molecules in a gas, which is also considered to be an elastic collision.

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