Work Energy/Momentum Problem - Why is there a loss of energy?

theBEAST

1. The problem statement, all variables and given/known data
Here is the question with the solution




3. The attempt at a solution
First off, where is the energy loss going into? What causes the system to lose energy?

Secondly what is the term I circled in red? The one with 0.22948, where does that come from?

Thanks!

TSny

1. What type of collision takes place at point B? Elastic or inelastic?

2. For the red circled term, do you understand the term before it? The red circled term is similar. What principle is being expressed by the equation that contains these terms?

theBEAST

1. I'm not sure if it's elastic or inelastic, don't you need the coefficient of restitution to know? Which means you need to know the initial and final velocity. In this case we are missing e and the final velocity.

2. The term before it is the angular momentum at B about the center of mass right? I see it on the diagram on the bottom left corner of the solution. But I don't see the other term any where on the diagram. The principle is conservation of angular momentum.

TSny

The ball is assumed to remain in contact with the corner at B during the collision at B. If the collision were elastic, it would bounce off B.
If you study the term before the red-circled term, you can see that it represents just the part of the angular momentum due to the horizontal component of the velocity of the center of the ball at time t₂.

theBEAST

1. Alright so essentially we have energy lost because it is an inelastic collision. Some energy goes into heat and some into sound right?

2. OHHHHHHHHHHH I think I got it. I think you mean vertical component of the velocity right. Because sin6.892 of the momentum is the vertical component. That would explain why it is negative since r x (mv) is into the page and thus clockwise.

Also thanks a lot for you help!

TSny

Right.
Well, I was speaking of the term before the red-circled term. But, yes, the term that you circled would correspond to the vertical component. Good!