OBJECTIVE:  

I will be able to relate the area under a curve/line to the integral of the function that describes the curve/line during today's class.

I will be able to relate the slope of a line or the instantaneous slope of a curve to the derivative of that curve during today's class

WORDS FOR TODAY:

Derivative: instantaneous slope of a curve

Integral: area under a curve

WORK O' THE DAY: 

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Introduce yourself to your groupmates and take a few moments to discuss the following quote from a famous biochemist and science fiction writer Isaac Asimov:

"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together."”

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Let's have some fun with this...

• Let's come up with a clever teashirt: (Varsity Physics?) Someone needs to take point on that ('cause I won't)
• We will dress up on test days (like the sports folks do)
• You WILL meet with your collaborative team after school

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Summer work: Thank you SO much for everyone who jumped on that

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You should have already read about my grading policies...any questions?

You should be able to do ALL of these, we won't practice them in class:

SI UNITS

	Distance	Mass	Time	Volume
SI UNITS	meters (m)	kilogram	seconds	liters
English Units	feet	slugs (really!)	seconds	gallons

UNITS: This class will ALWAYS use Standard International Units

You should have figured those out over the summer... I won't practice these in class

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METRIC SYSTEM: You MUST know the prefixes in yellow:

	milli	centi	deci	base	deca	hecta	kilo
exp	10-3	10-2	10-1	100	101	102	103
deci	.001	.01	.1	1	10	100	1000

You should have figured those out over the summer... I won't practice these in class

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SIGNIFICAN FIGURES (AKA sig figs, siggy figgies etc...):

The AP folks tell me that for AP Physics C that you have a 'get out of free' approach to sig figs:

"In general, two to four significant digits are acceptable."

However I don't know what engineering program you're going to enroll in next year, so I want to make sure you are exposed to sig figs. Let's do some practice!

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Dimensional Analysis

Here's where all you chemistry fans have a leg up on the rest of us... RAILROAD TRACKS. We won't spend too much time on these, but I want you to at least be exposed to the methodology.

Railroad Tracks

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Doing calculations the physics way: Ya know, I've never taught math, so I can't address how they do things there. However, here are two rules to keep in mind:

1) When it comes to calculus, whatever Ms Paine & Mr. Millard sat is right.

2) Save the math for last:

To wit:

Introduction to the FULL WOLGEMUTHIAN method.

Sorry folks, but this is an absolute requirement-- which is to say you have 0, nada, ixnay, NOT A WIT of leeway on this.

You absolutely, positively, MUST show your work at length and ad nauseum.

For too often, many of us have treated math/science problems as a task (hereafter Tasque) to accomplish.

It ain't.

It's not about doing, it's about the showing...

In order to show your understanding in science, you have to build a foundation to assure your reader (that woud be ME or the AP Test Reader) that you know your stuff.

So... here we go. The Full Wolgemuthian Method:

1. List initial conditions both implicit or explicit
2. Show appropriate formulas (hereafter: "Formulae Objectus")
3. Isolate and Substitute (you are absolutely FORBIDDEN to substitute numeric values until you have completed this step)
4. Substitute (now you add in numerics)
5. Solve

Let's say we're doing a simple calculation to determine the force exerted on an object being pulled at 30 degree angle to the floor.

The simple formula that governs this interaction is:

W = Fcosθ · d

Let's say we have the following initial conditions:

Work = 130. Joules

F = (unknown)

θ = 30.0 degrees

d = 3.00 meters

We might be tempted to just plug and chug:

130 J = F cos (30 degrees) · 3.00 meters

NO NO NO NO NO

SAVE THE MATH FOR LAST... ALWAYS

W = Fcosθ · d

W/(cos θ · d) = F

NOW insert numbers and solve!

130 J/(.866 x 3.00 meters) = 50.0 N

You might not agree, but trust me, it will make life a WHOLE lot better.

Also, notice use of the · "dot". Never, ever use the " · " operator to mean multiplication unless you are doing a 'dot' product. Ever. (We'll learn about that when we study work, power & energy in a month or so)

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Fun With Graphs --

• Describe the slope during each of the four different stages of motion exhibited by this object in a full sentence (for each!)
• How do we get the slope using calculus?
• How do we find the area under curve for each of the last 3 sections?
• How do we do that using calculus?
• What aspect of motion do we find from the slope (or derivative) for this graph?
• What aspect of motion do we find from the area-under-the-curve (or integral) for this graph?
• How would we generally describe the velocity of the second section? How do you know that?

HOMEWORK:  Please go to my website and review the learning targets for this unit. Come prepared tomorrow to comment on at least two of those.