Why Isn't Momentum Conserved on All Axes in a Bouncing Ball Scenario?

In summary: If the collision occurs between two balls, momentum should be conserved in all directions. Why is it that it isn't? It's because the reaction force between the balls is considered an external force. The momentum of the balls is being smacked by the ground, so it's not being conserved.
  • #1
ZxcvbnM2000
64
1
Hello everyone , here we go :

I understand that momentum is always conserved as long as no external forces act on a given system . I also understand that the law of restitution applies to the axis perpendicular to the line of impact between two objects .However i have a problem .

For example . A ball hits the ground at an angle of 45 degrees and bounces up at an angle of 30 degrees.

So from the law of restitution : e= - ( Vball*sin30 - Vground)/(Uball*sin45 - U ground) , the ground does not move therefore Uground = Vground=0 so

e = - Vball*sin30/(Uball*sin45).

My question is , why can't we apply momentum conservation on the y-axis ? Is it because the reaction force when hitting the ground is considered an external force ?

I am very confused please explain :S

Thank you !
 
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  • #2
ZxcvbnM2000 said:
My question is , why can't we apply momentum conservation on the y-axis ? Is it because the reaction force when hitting the ground is considered an external force ?
Exactly. If you look at the ball itself, its direction reverses when it bounces. So obviously, momentum of the ball is not conserved--it's being smacked by the ground!

If you expand your 'system' to be 'ball + ground/earth', then momentum will be conserved again. (The force between ground and ball would then be an internal force.)
 
  • #3
So my restitution formula is wrong and the only thing i have in my "system " is the ball , no ground etc . So it should be e= - V*sin30/(u*sin45) but e can't be negative ...argh ! :S
 
  • #4
Let's assume that two balls(m1=m2=m ) collide with one another .

The first ball is traveling at a speed u while the second ball is stationary.The first ball strikes the second one at an angle θ to the line of impact.If the coefficient of restitution is e , find the angle at which the second ball travels after the impact.

What i don't understand in this case is why isn't momentum conserved both along the line of impact and on the axis perpendicular to it as well ? I mean , both balls are part of our system so there are no external forces ?!

Could you please solve this exercise and explain each step thoroughly so i can finally understand ? Thank you very much !
 
  • #5
ZxcvbnM2000 said:
What i don't understand in this case is why isn't momentum conserved both along the line of impact and on the axis perpendicular to it as well ? I mean , both balls are part of our system so there are no external forces ?!
Why would you think that momentum isn't conserved in all directions?
 

What is the Law of Restitution?

The Law of Restitution, also known as the Law of Momentum, states that when two objects collide, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision. This means that no momentum is lost or gained during the collision, it is simply transferred between the two objects.

How is the Law of Restitution calculated?

The Law of Restitution is calculated using the equation e = (vf - vi) / (ui - uf), where e is the coefficient of restitution, vf and vi are the final and initial velocities of the objects, and ui and uf are the initial and final velocities of the objects after the collision.

What is the coefficient of restitution?

The coefficient of restitution, represented by the letter e, is a measure of how much kinetic energy is conserved during a collision. A value of e = 1 indicates a perfectly elastic collision, where all kinetic energy is conserved. A value of e = 0 indicates a perfectly inelastic collision, where all kinetic energy is lost.

How is the Law of Restitution applied in real-world situations?

The Law of Restitution is commonly used in sports such as billiards, where the trajectory of the balls after a collision can be predicted using the coefficient of restitution. It is also used in engineering and automotive industries to design safer vehicles and predict the outcome of collisions between objects.

What are some limitations of the Law of Restitution?

While the Law of Restitution is a useful concept, it has some limitations. It assumes that all collisions are perfectly elastic, which is not always the case in real-world situations. It also does not take into account external forces, such as friction, which can affect the outcome of a collision. Additionally, it only applies to collisions between two objects and does not account for multiple collisions or complex systems.

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