Do Balls X and Y Conserve Momentum and Energy in an Elastic Collision?

In summary, Two balls X and Y collide elastically with their speeds before and after the collision shown. The correct equation for this situation is Ux- Uy = -Vx+Vy, based on the conservation of momentum. This is because it is an elastic collision, meaning the overall speeds are equivalent before and after the collision. By letting the direction of Ux be positive and Vx be negative, the conservation of momentum is upheld. This conclusion is supported by the conservation of energy as well.
  • #1
Herzbog
5
0
Two balls X and Y collide elastically. Their speeds before and after collision are as shown.
Before

After
Which of the following equations is correct?

A Ux +Uy = Vx +Vy
B Ux +Uy = Vx - Vy
C Ux - Uy = Vx +Vy
D Ux - Uy = Vx - Vy
 

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  • #2
the picture is attached
 
  • #3
What do you think? What can you say about elastic collision?
 
  • #4
Ux- Uy = -Vx+Vy

Ux- Uy = -Vx+Vy
I think this is the right equation.
 
  • #5
Why? What's your reasoning? What physics principle or result are you appealing to? (Hint: The directions of the velocities are given; Treat the U's and V's as positive numbers.)
 
  • #6
The conservation of momentum.
It is elastic collision. Overall speeds are equivalent before and after the collision.
 
  • #7
Let the direction of Ux be positive and thus that of Vx is negative.
 
  • #8
Herzbog said:
The conservation of momentum.
It is elastic collision.
Good.
Overall speeds are equivalent before and after the collision.
I don't know what this means. Hint: Conservation of momentum and energy leads to a very specific conclusion about velocities before and after the collision.

Herzbog said:
Let the direction of Ux be positive and thus that of Vx is negative.
OK.
 

FAQ: Do Balls X and Y Conserve Momentum and Energy in an Elastic Collision?

What is momentum?

Momentum is a physical quantity that measures the motion of an object. It is calculated by multiplying an object's mass by its velocity.

What is the difference between momentum and velocity?

Momentum is a measure of an object's motion, while velocity is a measure of how fast an object is moving and in which direction. Velocity is a vector quantity, while momentum is a vector quantity.

How is momentum conserved in a system of two balls?

Momentum is conserved in a system of two balls if there is no external force acting on the system. This means that the total momentum of the two balls before and after a collision will remain the same.

Does the mass of the balls affect their momentum?

Yes, the mass of the balls does affect their momentum. Objects with larger mass will have a higher momentum than objects with smaller mass, assuming they have the same velocity.

What is an elastic collision?

An elastic collision is a type of collision in which both kinetic energy and momentum are conserved. This means that the total kinetic energy and total momentum of the two balls before and after the collision will be the same.

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