6.2: Kinetic Energy and the Work Energy Theorem
This is a short section, but understanding it is very important to understanding reality.
We established last time that work is force times distance. So, when you slide along the floor in your socks and nothing else because your wife is away this week, work is equal to the force of friction at any given point in your slide, times the distance you go. Work in this case is negative, in that the force goes in the direction opposite the direction of motion.
Now, we get to an even bigger concept: kinetic energy.
Say you’re in space and you want to kill your fellow astronaut because looking into the void of space opened your eyes to the void in your soul and now life seems like a pathetic yet heavy burden. You say “hey, let’s go for a spacewalk.” He says “sure, buddy!” You grab a wrench.
When you get out, you hurl the wrench at him. It smacks him in the chest. He goes flying into the vast starry oblivion. But, let’s look at that in physics terms.
First, you accelerate the wrench. You do this by applying force to it with your arm. The wrench moves through space with a force on it, so we say it does a certain amount of work. As it leaves your hand, it ceases accelerating. However, clearly its behavior has been altered by the force you put on it. If you’d put a different force on it or applied that force for a shorter distance, it’d have a different velocity.
Second, the wrench flies in a straight line through space at the other astronaut. Intuitively, you know that for a given wrench, higher speed means it’ll shove the other astronaut harder. This is because you’ve conferred a quality called Kinetic Energy onto the wrench.
Third, the wrench smacks into the astronaut. The wrench decelerates, so you know a force is acting on it. Namely, it’s the force of the astronaut’s body. So, there’s also a force on the astronaut’s body, which shoves him off into space. The wrench does work on the astronaut.
Fourth, the astronaut flies off into space with a velocity determined by how much work the wrench did on him.
You can see a nice quality here emerging – work confers kinetic energy on the object, which then can do work on another object, which then acquires kinetic energy. Cool!
And, you should also see there’s a sort of equivalence between the work you do on the wrench and the new kinetic energy the wrench has.
Let’s do the math.
The book provides a derivation for you that spits out:
That is, work is given by the change in the quantity, one half mass times energy squared.
You’ll note that for an object that starts at rest (like our wrench), one of those terms disappears. The remaining quantity is killed Kinetic Energy:
So, you can see then that there is a clear relation between work and energy given by:
Work equals change in kinetic energy.
Here, the book gives a brief discussion of units of energy. For macroscopic stuff, energy is typically given in Joules. Joules are a very nice unit which I wish we used more in regular life. Instead we get our power bills in “killowatt-hours,” which is like saying “energy divided by time times time.” But, I digress…
Now, the important thing is that you have a conceptual understanding of kinetic energy. Here’s how I like to think of it:
We’ve talked about force as the tendency to change velocity. That is, something happens to an object to tell that object “CHANGE YOUR MOTION!” That is, force is information given to an object about how to move.
Kinetic energy can be thought of us the quality of the object that has been made to move. That is, although it no longer has a force applied to it, it carries that information along, and can deliver it to other objects, just as the wrench did in the example above.
This is the case because of conservation of energy, which we’ve discussed. Energy is conferred to an object. That object moves as a result. When that object smacks some other object, it transfers energy out.
At the end, the book makes a point of noting that we are of course working with idealizations. Conservation of energy holds, but real life systems are more complex than two particles interacting. Imagine, for example if you threw the wrench poorly and hit the astronaut’s hand. The same amount of energy might be transferred to him, but he’d spin around instead of flying off. And the really freaky part is you could get that energy back out by letting the spinning astronaut smack the wrench. So, although the information in 6.2 is very good, so far you’ve only learned how it works in the simple case where two idealized particles smack each other.
But soon… soon your physics might will grow…
Next stop: Work and Energy with Varying Forces
I got to check out newly opened bar/restaurant 
