LEARNING OBJECTIVES:

I will be able to demonstrate (with sketches and written phrasing) the following 3 Newton's Laws:

• An object will continue doing whatever it is currently doing unless and until it is subjected to an unbalanced force (Newton's First Law)

• The sum of the forces acting on an object is equal to the mass of that object mulitplied by the acceleration it experiences as a result of those forces:

∑F = ma (Newton's Second Law)

• An object will exert an equal and opposite force on any object that exerts a force upon it! (Newton's Third Law)  -- I usually teach this to my freshmen as force/object pairs: <force 1 object 1, force 2, object 2>

  For example:

  Bat hits ball, ball hits bat (NOT bat hits ball, ball sails into the outfield)

  Similarly

  Bug hits 747, 747 hits bug. Both forces are equal and opposite but the results are NOT equal... we'll discuss this in detail due to much misconceptionage.

• I will be able to do simple differential equations after today's class

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WORDS O' THE DAY:

1. Newtons ("a unit of force" with units of (kg)(m/sec²) (Newtons are vector quantities so the direction in which the force is exerted on an object is crucial)

2. Normal Force ("Perpindicular Force")

3. Weight ("mass multipled by gravity") weight is NOT equal to mass, this takes some getting used to.

4. • Therefore my (Mr W) weight on Earth (~85 kg)(9.81 m/s²) = 833 Newtons.
   • However my weight on the moon (85 kg)(1.6 m/s²)= 136 N

     (which is substantially less due to a much lower gravitational acceleration on the moon)

   • NOTE: although weight is often written as w = mg (weight = mass x gravitational acceleration) notice that is actually a special case of F=ma!

   Sidebar (if you are interested, you don't need to know about slugs and such): The english unit of weight is the pound and is analogous to the SI Unit "Newton".

   A common misconception is that mass (SI Units = kg) and weight are the same. They are very definitely NOT. The English unit for mass is the slug (really!)

CALENDAR: Labs are due one week from the last day we work on the lab. If your group is struggling collecting data, please come after school today or tomorrow so I can assist.

WORK O' THE DAY:

Let's pick someone to give us a gentle presentation on how:

• They go t stumped on the test
• How they worked around that particular problem
• Their takeaway from that problem

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Remember, the VERY BEST way to study for the AP test is to actually do AP Test problems... we'll talk about that as we go. 

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Speaking of which... let's learn about Diff Eq's (if you want to be hip you really MUST refer to those as "diffy cues")

I want to give a very basic understanding of those so we can build on that learning as we go:

Consider the case of the following equation that shows the velocity of a particle moving in the x direction over time:

v = t² + 2

However

We know that velocity is also the first derivative of position so we can rewrite it as:

dx/dt = t² + 2

Here's where it gets REALLY interesting--- Using our basic math skills, we can rewrite that equation thusly:

dx = (t² + 2) dt

"HOLD THE BUS" (you say!), that looks like one of them thar integrals we just learned about so let's see where THAT gets us:

∫dx = ∫(t² + 2) dt

taking the integral of both sides we get:

x = t³/3 + 2x

We'll practice like this fairly easily for a while and THEN get to the NASTY stuff

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Now let's take a few moments to review Newton's Laws of Motion... it is critical that you understand these laws qualitatively. Towards that end I have rephrased them a bit to emphasize the qualitative nature of those laws (see Work o' the Day above).

DO NOT fall into the trap of mindlessly quoting 3rd Law-- "for every action..." BLECHHH... that will NOT help you.

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