What Happens When Two Identical Balls Collide Perfectly Elastically?

In summary, two identical balls, each with an initial velocity of +4.4 m/s, collide along the x-axis in a perfectly elastic collision. After the collision, one ball has a velocity of +1.2 m/s along the x-axis while the other ball has a velocity of 0 m/s. The total energy is transferred to the second ball and since they have equal masses, the velocity of the second ball after the collision is 4.4 m/s. To solve similar problems, use the conservation of momentum and kinetic energy, and for multiple directions, use vectors.
  • #1
mikefitz
155
0
Ball #1 moving at a speed of +4.4 m/s along x-axis collides with an identical ball (#2). The initial velocity of ball #2 is equal to zero. Assume that this is a perfectly elastic collision.

I know that Pbefore = Pafter - but since I'm not given the mass of either ball how am I to know what their velocities are after they hit?
 
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  • #2
I have another problem that asks a similar question, no mass given:

Two balls of equal mass approach the coordinate origin where they collide. Assume that this is a perfectly elastic collision. Before collision, one ball moves along the y-axis at +4.5 m/s and the other ball moves along the x-axis at +4.4 m/s. After they collide, one of the balls moves along the x-axis at +1.2 m/s.

Find the x-component of velocity of the other ball after the collision =

How do I get started on these problems? Thanks
 
  • #3
Identical = equal masses
 
  • #4
Hint 1: use the facts that momentum and kinetic energy are conserved, if the collision if perfectly elastic.

Hint 2: when there are more directions, use vectors, and then deal with their components, in order to keep things more clear.
 
  • #5
ok, for the first question; since they're equal mass and hit directly, total energy is transferred to ball 2. Vball1 = 0, Vball2 = 4.4

Now, for the second problem I'm supposed to be using vectors to find the x and y components. I will attempt this one later - thanks.
 
  • #6
mikefitz said:
ok, for the first question; since they're equal mass and hit directly, total energy is transferred to ball 2. Vball1 = 0, Vball2 = 4.4

Your notation is inconsistent - what exactly do you need to find in 1) ? The velocity of the second ball after the collision?

Edit. Actually, if the solution is correct, It doesn't matter.
 
Last edited:

What is an elastic collision of a ball?

An elastic collision of a ball is a type of collision in which the total kinetic energy of the system is conserved. This means that the energy before the collision is equal to the energy after the collision. In other words, the ball bounces off another object or surface without losing any energy.

What factors affect the elasticity of a ball?

The elasticity of a ball can be affected by factors such as the material of the ball, the surface it is bouncing off of, and the speed and angle of the collision. In general, balls made of materials that are more elastic, such as rubber, will have a higher elasticity. A smooth, hard surface will also contribute to a more elastic collision.

How does the mass of a ball impact the elastic collision?

The mass of a ball does not directly impact the elasticity of a collision. However, a heavier ball will have more inertia and may bounce differently than a lighter ball due to its higher mass. Additionally, the mass of the ball will affect the amount of force applied during the collision, which can impact the trajectory and speed of the ball after the collision.

Can a ball experience an inelastic collision?

Yes, a ball can experience an inelastic collision. In an inelastic collision, some of the kinetic energy is lost during the collision, typically in the form of heat or sound. This means that the ball will not bounce back with the same velocity as before the collision and some deformation may occur.

How is the elasticity of a ball measured?

The elasticity of a ball can be measured by calculating the coefficient of restitution, which is the ratio of the final velocity to the initial velocity after a collision. A higher coefficient of restitution indicates a more elastic collision, while a lower coefficient of restitution indicates a more inelastic collision.

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