Basic theory behind conservation of momentum and impulse.

[theBEAST]

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.

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?

 

[BruceW]

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?

 

[theBEAST]

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).

 

[BruceW]

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).

 

[theBEAST]

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?

 

[BruceW]

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