Midterm 2

Believe it or not it's time to think about the next midterm on Nov. 9

Here are the room numbers:

D100 12:30—13:50 SUR 5380
D200 15:30—16:50 SUR 5280

The format will be the same as before with 10 multiple choice questions and 4 written problems. The total will be worth 50 points for 15% of the final mark. One difference is that we may use Exam Booklets and Bubblesheets so that our printing load will be less. This is due to a possible staff shortage in the Surrey "Document Solutions" service.

All units up through Unit 10 are fair game for this exam. I suggest studying the calculations you did in the activity guides and be prepared for variations of those types of calculations. Make sure you understand the reasons they were done the way they were. Also it would be good to  study the problem examples in the textbook and textbook problems similar to those assigned in homework.

As usual bring a pencil, pen, simple scientific calculator, ruler and a protractor for vectors. You can bringyour own activity guides and homework.

Update
Please turn in your Unit 10 homework and Activity Guide after the exam.

Friction

Tomorrow's session will deal with friction. It's not my favourite topic, it's not really fundamental physics and the treatment at this level is a little fictitious.

As a challenge you can review your results of the inertial mass measurement in Unit 5 Session 3.  (You measured the accelerations of a fan-cart with and without a bar of known mass on it.) The mass you calculated was systematically wrong because friction was neglected.

Try to figure out how to take friction into account...

1. How would you experimentally measure the coefficient of kinetic friction in the movement of the fan cart?
2. How can you correct the mass calculations using the measured coefficient of kinetic friction?
3. How could you have modified the expriment of Unit 5 so that the systematic error due to friction would have been reduced?

Decimal Time, Republican Calendar and other Lost Causes

A decimal clock face made shortly after
 the French revolution. (From Wikipedia)

The decimal time system that was the subject of the first problem on the midterm was actually used for about 2 years after the French Revolution. It's mandatory period of use was less than a year: 22 September 1794 to 7 April 1795. Here is a clock face from the wikipedia article on decimal time.

Republican Date on the door.
(From Wikipedia)

The Republican Calendar lasted a little longer: 12 years. This calendar system had weeks that were 10 days long. One month was three republican weeks. Thus 12 Republican months made for 360 days and there were several holidays at the end of the year to fill out the rest of the 365 or 366 days. Evidence of its use can still be seen on public buildings in France. For example, the door of the famous École Normale Supérieure displays the date 9 Brumaire III, the date of its establishment decree.  (The building was built later.)  Despite the best of intentions, the system was not popular, probably because a 9-day work week replaced one of 6 days.

Can you image the confusion that we would be experiencing if only part of the world had actually adopted--and stuck with--the decimal time and calendar systems? For example the date of the midterm exam, Oct. 8, 2010, would have been called 17 Vendémiaire CCXIX.

All attempts after the French revolution to change units of measurement were based on the premise that dividing units into tens or hundreds makes calculating easier in our base-10 number system. 

But hold on. There's a society that wants to change our number system to base 12! Why?

There are several reasons discussed on the  Dozenal Society website. Here's a hint: in decimal the fraction 1/3 is 0.3333333... and goes on forever. In the dozenal system it's just 0.4.  Exactly.  Wonderful!

Definitely worth the trouble to switch.

Finally, here's in intriguing book: The Measure of the World: A Novel. It tells the story of the project to establish the value of the metre by accurately triangulating the distance from Dunkirk to Paris to Barcelona from hilltop to church steeple to hilltop etc.  Two expeditions set out to do it ---- and they did. We still use the value they determined. (This book is a novelization based on the real project.)

Midterm Exam Grades

Update
The midterm grades are posted in the webct gradebook.  There are four parts: labelled "Midterm 1 MC", "Midterm 2 probs" and "Midterm 1 response". These report the following:

• "Midterm 1 MC": The Multiple-choice score out of 20, 
• "Midterm 2 probs": The Problem score out of 30, 
• "Midterm 1 total": The total out of 50.  Y
• "Midterm 1 response": Your multiple choice responses and the correct answers. 
• The format is [NNNN]xxxxxxxxxx{yyyyyyyyyy}, where NNNN is the version of the exam, yyy... are the correct answers and xx...x is either a dot if you got it right, or your response if it is wrong.

Class average is 34.2/50 with at standard deviation of 7.65.

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Earlier post

I'm going to grade these exams myself so it may take a day or so. I'll try to get them done by Tuesday.

In the meantime, please enjoy the Thanksgiving holiday.

Unit 6 AGs and Homework are due on Tuesday.  (sorry)

Midterm Exam Rooms

         
Phys140 D100    10/08/2010  F     12:30 PM       SUR 2600 
Phys140 D200    10/08/2010  F     03:30 PM       SUR 5240  

The Gravity Conspiracy

The last part of Unit 6 Session 1 was dancing around a really interesting coincidence in our world: There are two ways to measure mass. Even though they are completely different, the values the two ways give just happen to be the same. Coincidence? 

All measurements of mass depend on comparing an unknown mass to a standard one. The two ways are

Comparing masses two ways: gravity and inertia.
The mass of a certain volume of water could be
used as the "standard".

1. Put the object you're measuring on a scale and compare the force of gravity on it to the force on another standard mass.
2. Try to accelerate it with a force that you can reproduce and compare the acceleration that you get to what you get when you try to accelerate a standard mass with the same force.

These two measurements always give equivalent results. This is so surprising that it has been checked over and over again to high accuracy. When such coincidences seem to occur in nature it's probable that it's not a coincidence, but there is something behind it. That's what Einstein thought and he managed to figure out a logical connection.

To understand the basic idea of Einstein's theory of gravitation imagine that you had a little laboratory in a box with no windows. You can put this laboratory on earth and do experiments with balls and carts and pendulums....whatever.  Then you could put this imaginary lab-in-a-box in a ship and floating far from any gravitational pull and you'd expect the balls not to fall, the pendulums not to swing etc etc, But now fire up the rockets and make the lab accelerate at 9.8 m/s/s and all your experiments would turn out exactly like they would on earth. Einstein took this as a postulate which he called the principle of equivalence.

Experiments on an accelerating rocket ship would seem the same as if gravity were present.
(Figure from Wikipedia)

So gravity acts just like the "fictitious" force that you would feel in an accelerating frame of reference. Similarly the forces you feel on a carousel or centrifuge are proportional to mass, just like gravity — and, in fact, you can use a spinning device to measure mass.

Somehow, mass creates something like an acceleration.  This is accomplished by having mass cause space to warp.  Everything travels in a straight line -- which means the path of shortest distance between two points -- but the space is warped by mass so that the lines are not straight in the Euclidean sense. 

To see how this works in 3 dimensions we have to imagine it in 2D where we can visualize warped space. Then the analogy to 3D can be accepted.  Formally what is done is that the mathematics of warped space is developed that can be used in any number of dimensions so we won't have to be able to visualize what's going on in order or predict what's happening.

So in 2 dimensions a flat universe would have familiar properties as postulated by Euclid: Parallel lines never meet, the interior angles in a triangle add up to 180° and so forth.  Now imagine that the flat space is warped somewhat like a fabric that is poked with your finger.

Mass causes the space near it to warp.
This is a 2D model to help you imagine what's going on in 3D.
(Figure from Wikipedia.)

In this case, draw a triangle, add up the angles and the sum is not 180°. What's important here though is that the shortest distance between two points tends to bend to conform with the curvature of the fabric. The line of shortest distance is called the geodesic and is familiar on our spherical earth as what is called the great circle route that airplanes take when trying to navigate.  In Einstein's universe the curvature of space depends on the mass that is present in the space and the trajectory of an object following the geodesic in the curved space is about the same as what Newton's law of gravitation predicts.

Notice I said "about" the same. Actually there are some small differences between Newton's gravity and Einstein's.  One example is the precession of the perihelion of Mercury's orbit.  The orbit of Mercury does precess as Einstiein's theory predicts and Newton's does not.

Another prediction is that light should be pulled by gravity. Imagine a little hole in one wall of the lab in the rocket ship. If light comes in that hole while the ship is accelerating then the light will hit the other wall a little lower down because of the ship's acceleration. The light beam will seem to "fall".  So by the principle of equivalence, gravity should cause light to "fall". A very careful observation of the light of stars that comes close to the sun shows that this light does bend because the sun's gravity attracts it. This observation has to be done during a total eclipse of the sun and the first time it was done was during an expedition organized by Sir Arthur Eddington in 1910 to test Einstein's prediction.  The bending was confirmed in that the stars whose light came near the sun seemed to shift position from where they should have been.

If you're interested in more about this on a popular level look at the references below --- they're probably in the public library or university library.  If you want to understand the rigorous theory, keep studying physics and math.

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References

1. Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimens ion, Michio Kaku
2. One Two Three . . . Infinity: Facts and Speculations of Science, George Gamow
3. Mr Tompkins in Paperback (Canto imprint) (containing Mr. Tompkins in Wonderland and Mr. Tompkins Explores the Atom), George Gamow
4. The Universe and Dr. Einstein, Lincoln Barnett (introduction by A. Einstein)