Basic theory behind conservation of momentum and impulse.

In summary, the conversation discusses the conservation of momentum in a scenario where a rod strikes a table. The equation for conservation of momentum does not hold true due to the eccentricity of the impact and the approximation used for the change in velocity of the table. The approximation is necessary due to the large mass and small velocity of the table. The conversation concludes with the understanding that this approximation can be used to solve for the final velocity of the ball in the scenario.
  • #1
theBEAST
364
0
Conservation of momentum does not hold true?

Homework Statement


Here is the problem. State 2 is shown in the picture, it is right before impact. State 3 is after impact.

Wx4wt.png


I used conservation of momentum of the entire system (rod and table. However as you can see it shows us that the rod has the same momentum before and after the impact. This is impossible because e=0.6. Why is it that my conservation equation does not hold?
 
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  • #2
Because you have said the speed of the table does not change. In reality, it would change. This makes the equation for v3 more complicated, but luckily you can use an approximation. Think about the mass of the table compared to that of the rod. What approximation should you use?
 
  • #3
Hmmm I'm not sure what approximation to use. I thought that linear momentum is not conservated because the impact
Is eccentric (the line of impact
does not cross the center of gravity).
 
  • #4
momentum is conserved. For the approximation, think about a real-life situation where something strikes a table. Is the change in velocity of the table significant? The answer to this suggests what your approximation should be. Don't be surprised is momentum is not conserved in the approximated equation. (That is because the equation is only approximately true).
 
  • #5
BruceW said:
momentum is conserved. For the approximation, think about a real-life situation where something strikes a table. Is the change in velocity of the table significant? The answer to this suggests what your approximation should be. Don't be surprised is momentum is not conserved in the approximated equation. (That is because the equation is only approximately true).

Alright, so the mv3_table term should not be zero. Because you have a huge mass and a tiny velocity. And thus you make the approximation that velocity is zero so you can solve for the final velocity of the ball using the restitution constant equation? Am I right?
 
  • #6
exactly :)

Edit: yep, so that gives you the velocity of the edge of the rod after impact, so then you can use this to answer part a
 

1. What is the conservation of momentum?

The conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time. This means that the total amount of momentum before a particular event or interaction is equal to the total amount of momentum after the event or interaction.

2. How is momentum defined and calculated?

Momentum is defined as the product of mass and velocity. It is calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity. Momentum is a vector quantity, meaning it has both magnitude and direction.

3. What is the relationship between momentum and impulse?

Impulse is a change in momentum, and it is equal to the force applied to an object multiplied by the time it is applied. This means that a larger force applied for a longer time will result in a greater change in momentum. The conservation of momentum can also be applied to impulse, meaning that the total impulse before an event is equal to the total impulse after the event.

4. How does the conservation of momentum apply to real-world situations?

The conservation of momentum is applicable to a wide range of real-world situations, from collisions between objects to rocket propulsion and even the movement of planets in the solar system. It is a fundamental principle in understanding and predicting the behavior of physical systems.

5. Are there any exceptions to the conservation of momentum?

The conservation of momentum is a well-established principle in physics and has been verified through numerous experiments and observations. However, there are certain situations where it may appear to be violated, such as in cases involving external forces or when considering the effects of relativistic speeds. In these cases, the conservation of momentum can still be applied, but with the inclusion of additional factors.

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