monday, november 30, 1998

Monday, November 30, 1998

Results from Exam #3Overall Grades Thus FarSketch of Remainder of the SemesterChapter 13: Hooke’s Law (again!)

Simple Harmonic Motion

Generally, most ofyou did WAY

better this time!

I guess it really was a pretty EASY test…As you’ll be able to tell from the gradedistribution which sits about 14 pointshigher than either of the two previousexams!

You should have been able to reallyENJOY your turkey dinner!

Exam #3Mean = 80.7 Stddev = 15.2

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0 8 16 24 32 40 48 56 64 72 80 88 96

Score

Nu

mb

er

AD C BIf I had toput lettergrades onthis exam...

(As seen on the Physics 111 web site…)

I have compiled overall grades up throughand including Exam #3. I have dropped yourlowest homework grade (as promised) buthave NOT dropped your lowest exam score(yet). I will do the latter at the end of thesemester. You will find your current overallaverage marked on your test in purple crayon.

Overall AverageMean = 77.1 Stddev = 11.9

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If your averageis below 70, youmight like to stopby and visit me.

Our final exam period is scheduled for thevery last possible day of finals’ week:

Friday, December 18, 1998!

Please, do not leave town early…you’ll

just make my life …ahem…

….miserable???...

(Is that pathetic enough?)

This 2-hour exam period will contain TWO exams.

The first 50 minutes will be used for an examon the material that we cover over the next twoweeks. It will be structured very much likeExam #3 (three sections, one of which will bemultiple choice---you do two of the three). Youwill be permitted to use the usual 3”X5” notecard.

Final Exam: 1 hour plus comprehensive

5 sections, you do 4 (one will be multiple choice)

Each section somewhat shorter (25 points)]

8.5”X11” crib sheet + 3”X5” notecard fromExam #4

I will give you math & constants but notphysics formulae

Exam #4 (during the first 50 minutes of our final exam period) counts the same as the previous 3 exams (the best 3 scores from Exams #1 - 4 count 15% each).

If you are REALLY happy with your performance on the first 3 exams, simply notify me and you will be permitted to SKIP Exam #4. In this case you may show up 50 minutes into the exam period.

(I’m guessing there won’t be too many of YOU!)

Everyone MUST take the Final Exam.

You cannot pass this class without completing the final exam.

The final exam counts for everyone andis worth 20% of your final grade.

There will be TWO morehomework assignments: - due Monday, December 7 - due Friday, December 11

There will be two more meetings of Lab:- Thursday, December 3 (Lab 10)- Thursday, December 10 (Lab Final=Party?)

We are going to skip Chapter 12 -- not that thematerial in Chapter 12 isn’t important, but I thinkthe time is better spent on waves and sound(Chapters 13 and 14).

Vibrations and Waves

We’ve already studies some vibrational motion,when we we examining the curious behaviorof springs and objects that interact with them.We will expand our studies to objects thatbehave similarly to our spring, such as thependulum and rotating objects.

We’re going to start by reviewing someof the basic properties of springs.

You may recognize this stuff…These arethe same notes I used back in Chapter 5!

So let’s go through them quickly justto refresh our memories -- especiallyafter that long Thanksgiving Break!

However, if we compress or stretch the springby some amount x, then the spring is observedto exert a Force in the opposite direction.

Hook discovered this force could be modeledby the mathematical expression

F = - kxNotice that this force operates along a linear line!

l x

Which means that if we looked at the plotof Force versus compression/stretching x...

Force

x

Slope of this lineis -k, where k isthe spring constant.

Force

x

Notice that the force is always in theOPPOSITE direction of the displacement.

We call such a force a

Because the force actsto “restore” the particleto its original position.

Force

x

If we look at the work done by an appliedforce which compresses the spring througha distance (-x1)...

-x1

F1W F s Fx F x 1

1

2 1 0( )

W k x x kx 1

2 1 11

22( )( )

Work done BY theexternal force ONthe spring.

This energy is stored in the spring...

PE kxspring 1

22Potential Energy of a spring is

So, for spring problems, we have a newTOTAL MECHANICAL ENERGY given by

KE PE PEg spring

And it is THIS quantity which will be conservedabsent other, outside forces.

A wealthy socialite,bored of countinghis gold coins, decidesto play with his newspring toy.

Predict the motionof the mass at thebottom of thisspring as explicitlyas possible.

Assume no friction andno air resistance.

Now, sketch a plotof the height of theblock above the flooras a function of time.

h

What kind ofmathematicalfunctions (withwhich you’refamiliar) result insuch a pattern?

Height of Block vs Time

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Time (s)

Hei

gh

t (m

)

Equilibriumposition

Amplitude

period

Amplitude

This type of oscillatory behavior is known as

An object in simple harmonic motion displaysan acceleration that is proportional to thedisplacement and in the opposite direction.

Not simpleharmonica

music!