OPENING QUESTIONS:
What are the units of measure for the spring contant k?
How do we usually refer to them?
Why is there a discrepancy?
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LEARNING OBJECTIVES:
I will develop a working knowledge of a 'restorative' force during today's class.
I will be able to relate work to a transfer (or change) in energy 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:
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Work = fdcosθ (including the integral form)
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F = -kx (note the negative sign)
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Potential Energy of a spring = 1/2kx2
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Kinetic Energy of an object = 1/2mv2
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Gravitational Potential Energy = U = mgh
A change and/or transfer of energy requires WORK, or to put it perhaps a bit more succinctly, WORK is defined as a transfer of ENERGY
WORK O' THE DAY:
HW #19b is a bit cheesy... why?
If you struggled a bit with HW #24 (There's a lot going on there), I'll post my solution after school today, please take a gander.
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By the by, we've defined WORK to be a transfer of Energy, so what does that mean the units of ENERGY are defined to be?
The kinetic energy of an object is found to be 1/2 mv2
The Work done on a particle results in a change in kinetic energy of that particle:
Work = 1/2 mvf2 - 1/2 mvi2
Once again, notice the similarity to the work done in/by a spring
Work = 1/2 kvf2 - 1/2 kvi2
Learn these formulas SOONEST... these relationships will weave in and out of our discussions for the rest of the semester (they relate to the concept of
The Conservation of Energy
which we will discuss in a week or so)
Now let's take a gander at example 7.6:
NOTICE that the problem also asks you to solve this problem using the ideas that we learned about in Newton's Laws...
Learning how and when to apply the principles of Work/Energy as opposed to Forces/Acceleration are very, VERY important as we move forward.
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Potential Energy means just that: An object with POTENTIAL energy can be at rest -- an apple hanging from a tree at a height (h) above the ground for example, is said to have potential energy because it will fall to the ground if its connect to the tree is lost.
A spring is said to have POTENTIAL energy when it is stretched our coiled, because when the force holding it in that position is released, the spring will respond.
We can safely skip through most of section 7.6 except to note the definitions of gravitational potential energy (mgh) -- (mass) x (acc of gravity) x (height)
and that work must be done to change the gravitational potential energy of an object:
Work = ∆U
Be prepared to speak articulately on THIS:
Yesterday's HW Solutions are below:
- Take a LONG look at the quick quiz in 7.6 Try to answer the question qualitatively. Then support your thoughts with mathematical examples. Does that change your thinking?
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- Work *ahem* through 7.8
- Do problems 38 & 40 on page 207