Using Special Case of Elastic Collisions in one dimension

In summary, the conversation discusses the use of elastic collisions in one dimension with bodies of different masses. The equation v_1 - v_2 = v_2' - v_1' applies to all elastic collisions, but does not necessarily result in a simple exchange of velocities. Instead, it states that the relative velocity before and after the collision must be reversed. This fact alone is not enough to determine the final velocities, as another relationship, such as conservation of momentum, must also be considered. This information is helpful for gaining insight, but is not actually part of the test.
  • #1
Seydlitz
263
4
Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses?

[tex]v_1 - v_2 = v_2' - v_1'[/tex]
 
Physics news on Phys.org
  • #2
Seydlitz said:
Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses?
The equation you posted--which states that the relative velocity reverses in an elastic collision--applies regardless of the masses. But it does not allow you to conclude that velocities are simply exchanged. (That's even more of a special case.)
 
  • #3
Doc Al said:
The equation you posted--which states that the relative velocity reverses in an elastic collision--applies regardless of the masses. But it does not allow you to conclude that velocities are simply exchanged. (That's even more of a special case.)

Ah okay, so what the above equation actually state? I'm confused with the meaning that the relative velocity is simply reversed.
 
  • #4
Seydlitz said:
Ah okay, so what the above equation actually state? I'm confused with the meaning that the relative velocity is simply reversed.
I'll give an example. Before they collide, say m1 is moving with speed 3 m/s to the east and m2 is moving with speed 4 m/s to the west. Taking east as positive, the relative velocity of m2 with respect to m1 before the collision is: V2 - V1 = -4 - 3 = -7 m/s.

So the relationship expressed in the equation above states that whatever happens during the elastic collision, they must end up such that the relative speed of m2 with respect to m1 after the collision is: V'2 - V'1 = +7 m/s. That's what reversed means. Of course this fact alone is not enough to determine those final speeds. You'll have to combine it with another relationship, such as conservation of momentum.
 
  • #5
Ah now I get it, thank you for the help Doc. :D

This problem does not actually appear in my test today but it is really helpful to gain new insight from this.
 

1. What is a special case of elastic collisions in one dimension?

A special case of elastic collisions in one dimension occurs when two objects collide with no external forces acting on them. This means that the total kinetic energy before and after the collision remains the same.

2. How is momentum conserved in elastic collisions in one dimension?

In elastic collisions in one dimension, momentum is conserved as the total momentum of the objects before the collision is equal to the total momentum after the collision. This means that the sum of the mass of the objects multiplied by their velocities remains constant.

3. What is the equation for calculating the velocities of objects in an elastic collision in one dimension?

The equation for calculating the velocities of objects in an elastic collision in one dimension is m1v1 + m2v2 = m1u1 + m2u2, where m is the mass of the object and v and u represent the initial and final velocities, respectively.

4. What is the difference between elastic and inelastic collisions?

Elastic collisions involve objects colliding with each other and bouncing off with no loss of kinetic energy, while inelastic collisions involve objects colliding and sticking together, resulting in a loss of kinetic energy.

5. How do real-life collisions differ from ideal elastic collisions in one dimension?

In real-life collisions, some kinetic energy is lost due to factors such as friction and heat. This means that the total kinetic energy after the collision is less than the total kinetic energy before the collision, making it an inelastic collision. In addition, in real-life collisions, there may be external forces acting on the objects, making it difficult to apply the laws of ideal elastic collisions.

Similar threads

B Alternative elastic collision formula / physical interpretation
    • Mechanics
Replies
3
Views
712
I Elastic collision between two spheres
    • Mechanics
Replies
6
Views
1K
I Work Done/Energy Transferred in One Dimensional Collision
    • Mechanics
Replies
5
Views
854
B Confused about force body diagram for 2 body collision
    • Mechanics
Replies
6
Views
1K
Why Does Second Collision in Ballistic Pendulum Lead to Initial State?
    • Mechanics
Replies
5
Views
696
B Why is KE not conserved when momentum is?
    • Mechanics
2
Replies
53
Views
2K
B Understanding Physics for Coding Collision of 2 Balls
    • Mechanics
Replies
14
Views
1K
I Exploring Collisions w/ Accelerating Objects
    • Mechanics
Replies
4
Views
926
A Pair of interacting systems, driven coupled harmonic oscillators
    • Mechanics
Replies
7
Views
646
One dimensional Elastic collision of two identical particle
    • Mechanics
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top