WORDS O' THE DAY:

• Work (Force through displacement)
• Dot Product ("scalar product")
• Work ("Newton meter (Nm)" or "Joule (J) ")
• Hooke's Law (F = -kx)
• Work done by or done on a spring = 1/2k_ix² - 1/2k_fx²
• Kinetic energy of an object in motion = 1/2mv²
• Potenial energy in a compressed spring = 1/2kx²

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
• ∆E = 0: Conservation of Energy
• ∆E = ∆KE + ∆U
• ∆KE = Work
• -∆U = Work

WORK O' THE DAY:

There are so many formulae type things in this unit that it is really a whole lot better to make sure you understand the physics of the situation and THEN apply the appropriate math.

Please work with your crew to come up with a *working* mathematical model that allows you to account for situations:

• No energy added, just transformed
• Energy is lost to the system
• Energy is gained by the system

We'll practice putting your model to the test today. I've also assigned a whole slew (slough?) of practice problems to stress your model.

Please revise your model and be prepared to present it/defend it on MONDAY

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Balloon Scenario:

Consider the energy present in a balloon that you've just blown up. Write an equation that shows the energy present there.

Now imagine that a candle is *carefully* introduced to the situation so that the air inside the baloon is heated.

Now do an energy equation for that.

Now please work with your group to come up with a general understanding/equation that will account for situations where:

• Energy is neither added nor lost from a system
• Energy is taken away from a system
• Energy is added to a system.
• The relationship between ∆E and KE, ∆E & U (think WORK!)

Try some BASIC thought experiements that involve Ug, KE and US and permutations thereof. K.I.S.S. for the most part please

For Monday:

Problem #12 (a lot of analysis here), #14 (on page 237), #19, #21 (part a only) , #23 , 26 (on page 238)

PLEASE ANNOTATE each of your answers with an analysis of the 'hook' of the problem (what was the problem trying to teach you) or your insight iinto doing the problem (they are not necessarily the same)

ANSWERS