Chapter 11.1 Notes
11.1 Kinetic and Potential Energy
This chapter discusses energy. Energy is an amazing concept. It is almost like magic because we can't always see it, just it's effects and manifestations. For example, consider something as simple as a baseball that was just pitched.
I want you to figure out what the ball has received that it manages to keep, even after it has left the pitcher's hand!
The explanations and answers are tricky and sometimes nebulous as we still don't fully understand how all energy behaves. We can look at some of the simpler concepts though, and give ourselves a little better understanding of how our lives work! So, here we go.. hold on to your pencils!
Let's return to the baseball thing. What did the pitcher do TO the ball?
Take a look at some of these formulas that apply:
We remember the impulse-momentum theorem as Ft = mv , so
The work done on the ball is W = Fd, but we just saw that so substituting into the work formula we get
This stuff all seems ok. There is work done on the ball, and there was an impulse Ft. But that was all before the ball left the pitchers hand. I want to know what the ball has AFTER it leaves the pitcher's hand that allows it to keep going.
Check out that last work formula (2.) again.
In that same work formula, what values are given on the right side of the equation that the ball will STILL have after the ball leave's the pitcher's hand?
When something accelerates (like the ball in the pitcher's hand), it's velocity changes according to the formula
If the ball starts from zero velocity (vi) and ends up travelling at some final velocity (vf) just as it leaves the hand, then
(4. ) because vi was zero. And,
These values d and a in equation (5.) all have to do with what is going on in the pitcher's hand except the final velocity vf
substitute for "d" in the work formula (2.) and you get
That got rid of the distance! I still don't want that acceleration in my formula, because I want to examine only those properties the ball has after it leaves the pitcher's hand, and acceleration happened IN the pitcher's hand. BUT.. that v/t in the formula.. what;s that? That's also the acceleration! so..
and the a's cancel out.. which is cool, because after the ball leaves the pitcher's hand, it shouldn't be accelerating anymore anyway! The ball is now clear of the acceleration and this leaves us with
THE MAIN POINT IS RIGHT HERE:
Doing work on the ball has given it kinetic energy, and if you followed the derivation,
You try: do practice problems 1-3 on page 251
Gravitational Potential Energy
Elastic Potential Energy
Set #2. Do problems 38-47
Set #3 Do problems 48-56