OBJECTIVE: I *must* be able to differentiate between positive and negative work during today's class.

I *should* be able to define the term "conservative force" during today's class.

I *should* be able to derive the expression equating force to potential energy starting with our definition of work (calc version) during today's class.

WORDS O' THE DAY:

• Work (Force through displacement)
• Dot Product ("scalar product")
• Work ("Newton meter (Nm)" or "Joule (J) ")
• RESTORATIVE force (results in acceleration in the opposite direction of the applied force)

FORMULAE OBJECTUS:

• Work = fdcosθ (including the integral form)
• F = -kx (note the negative sign)
• Potential Energy of a spring = 1/2kx²
• Kinetic Energy of an object = 1/2mv²
• Gravitational Potential Energy = U = mgh
• F_x=-dU/dx (relationship between force in one dimension and the change in potential energy in that dimension). The AP usually writes this equation as a partial derivative F_x=-∂U/∂x. For our purposes we will treat them as one and the same

WORK O' THE DAY:

What does Kahn Academy have to say about positive and negative work?

What does that leave out?

I'm curious if anyone did any further research on that? (I did!)

The key here is the SOURCE of the force. We say gravity is a conservative force (it is!). That means it doesn't matter HOW we get to the top of the mountain, we still have accumulated mgh amount of potential energy <since the SOURCE of the force is gravity).

However, if we are the source of the force and we are lifting books AGAINST gravity, the work that we do is negative by lifting books)

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Let's review what we know about work and energy so far...

Work with your crew to come up with an elegant, concise, succinct (etc) group definition for positive and negative work.

What is the DEFINING feature of a conservative force.

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RANT BEGINS: Take a gander... especially: scroll down to

"In the emerging countries, the hidden face of the crisis"

The bottom line is that India & China crank out somewhere north of one million engineers a year.

They are very, very good at very, very boring stuff....

They KNOW they need to work on their imagination... but they are not quite there yet.

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HOMEWORK

WORK study guide is available on our study guides page here

Ya know, I need to emphasize that each problem should be some sort of learning experience, not a *doing* experience. Towards that end, please make a brief notation at the end of each problem, indicating the intent of the problem (what was the problem trying to teach you).

Also indicate the learning you gained from the problem (they are NOT mutually exclusive).

You may not want to do that, but I'll ask that you do that nonetheless as reflecting on the material is an excellent tool for understanding the material (really! honest! I'm not joking!)

• Check out the following on page 209
• Problem 52 a & c (ignore b)
• Problem 54 (ignore c)
• READY TO KICK SOME BUTT? Try 63

ANSWERS: