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## 10 physics misconceptions, explained poorly

[This blog post was written by a guest columnist, a D-student in freshman physics who will remain anonymous]

10.         It’s winter because we’re far from the Sun

Everyone knows that it’s cold in January because, well, we’re farther from the Sun that usual.  The orbit of the Earth is elliptical, so in the Summer we’re closer to the Sun, like Mercury.  I have no idea why the seasons are reversed in Australia…maybe it’s because they’re upside-down?

9.            Force is non-reciprocal

I tug on a rope with a force of 100 N.  On the other end of the rope is a football player; let’s say Greg Olsen (TE for the Carolina Panthers, of course, but you knew that I’m sure).  With what force is Greg Olsen pulling on the rope?  It must be much more than 100 N, because a football player is stronger than me.

8.            Areas and volumes have the same conversion factors as linear units

If 100 cm = 1 m, then 100 cm2 = 1 m2.  This is so obvious it doesn’t merit comment.  Another way to look at it is that a meter and a square meter are, basically, the same thing.

7.            Acceleration is the same as speed

Acceleration is, like, how fast you’re going.  So if I throw a ball straight up, at the top of its arc, its speed is zero, so its acceleration must be zero.  Can I have some of those Cheetos?

Best comic ever?

6.            Weight and mass are the same

I was asked in lab the other day to find the weight of a brass cylinder.  So I did:  I weighed it, and got that its weight was 250 g.  I was then asked to find the force due to gravity on the object, but I don’t know how to do that.  Oh, I have to go; I’m rushing Phi Upsilon.

5.            There’s a magical force that appears whenever you move in a circle

So, I was driving the Tail of the Dragon on my scooter the other day, and almost got pulled off the road because of centrifugal force.  That’s another kind of force; you know, like gravity, friction, drag, spring force…centrifugal force.  It appears whenever you move in a circle.  It’s directed outward.  It is a repulsive force, the opposite of gravity.

4.            Objects have a memory of circular motion

If you spin a circle with a ball in your hand, then let go, the ball will spiral outward (obviously) because by the 1st Law objects in motion stay in the same kind of motion that they had before: circularly moving objects keep moving in a circle, etc.  I might then wonder why my scooter didn’t keep going in a circle in spite of centrifugal force, but luckily I don’t ever experience cognitive dissonance.

3.            There’s no gravity in space

Here’s a spoiler in case you didn’t see Gravity with Sandra Bullock and George Clooney.  In the scene where Sandra Bullock is knotted up in some ropes, she tries to hold on to George Clooney, but lets go.  Of course then George Clooney plummets towards the Earth, because of gravity.  They must have been right at the invisible border between space and not-space, where gravity suddenly drops to zero.

2.            g stands for “gravity”

The formula for weight is w = mg, which stands for mass times gravity.  g is gravity.  It’s like a force or something.  I have no idea why my instructor winces every time I say this.

1.            No net force means no movement

This is the most obvious one of all.  On one of our homework problems, there were only two forces acting on a box: 50 N up, and 50 N down.  The net force is clearly zero.  So the box cannot be moving!  Therefore v = 0 (duh!)  But my professor marked this wrong.  She said that v might be 50,000 m/s for all we know.  That makes no sense!  Physics is too hard.

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If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  Publication of the first installment will be January 2015; further details will be released on Facebook, Twitter, or via email: SargassoNova (at) gmail.com.

## The Franck-Hertz ice cream truck

Imagine that there’s an ice cream truck parked near a school.  It’s 3pm; class is dismissed and a steady stream of kids approach the truck.  For simplicity, let’s stipulate the following rules:

1. If a kid has enough money, he or she will buy an ice cream cone;

2. A kid will only buy one ice cream cone;

3. A kid will buy the most expensive ice cream cone he or she can.

After the kids buy ice cream (or not) they continue on their way, having whatever leftover money they might have in their pocket.

My question is this: by seeing how much money kids have left, what can you determine about the prices of ice cream cones?  (Astute observers will note that this toy model has many similarities to the Franck-Hertz experiment of 1914, but we’re not there yet.)

Let’s look first at some hypothetical data.  Here we have plotted L (money left over in a kid’s pocket) as a function of M (how much money a kid started with) for a school with 11 kids:

There doesn’t seem to be a pattern.  Maybe we don’t have enough data?  Let’s increase the number of kids to 42:

The sawtooth form of the function is characteristic of problems of this type, and can be understood intuitively.  First of all, notice that the function is linear to begin with, with a slope of exactly one; this means that below a certain threshold value of M, a kid can’t afford any ice cream, so he/she ends up with the same amount of money he/she started with.  Eventually, if M ≥ \$1, a kid can buy a cone; L then plummets because the kid has spent a dollar.

It seems obvious from the graph, then, that ice cream cones are priced at \$1, \$2, and \$3; beyond that we don’t have any data so can’t draw more conclusions.

Now, if we relax the stipulation that kids only buy one cone, then our data is ambiguous.  Maybe the cones are priced \$1/\$2/\$3, or maybe cones are always just \$1, and kids are buying more than one cone if they can.  We can’t distinguish between these cases; that’s why I put the original stipulation there to begin with.

Let’s try a more challenging graph:

This graph is much harder to interpret.  The first peak is much bigger than the others; there is also a very tiny peak on the right-hand side.  It helps if you know where the jumps are: L jumps down to zero whenever M is equal to \$0.67, \$1.02, \$1.34, \$1.69, \$2.01, and \$2.04.  If you want to work out the ice cream cone prices for yourself, feel free.  I’ll wait.

The solution?  A little trial and error will give you two different prices for ice cream cones: A= \$0.67 and B=\$1.02.  Then the jumps occur at A, B, 2A, A+B, 3A, and 2B.  If we were doing physics, we’d make a prediction: we would expect the next jump to occur at \$2.36, which is B+2A.  Observing this would support our hypothesis.  But if the next jump occurred at \$2.22, say, then we’d have to revise our theory and posit a new ice cream C priced at \$2.22.

What does any of this have to do with physics?

I use this example when I introduce the Franck-Hertz experiment to my students.  This experiment was first performed in 1914 (an auspicious year!) and provided support for Bohr’s idea that atoms have specific (quantized) energy levels.  Electrons are accelerated and shot towards mercury atoms (in a vapor).  The electrons may then give energy to the atoms (exciting them) or they may not, bouncing off without loss of kinetic energy.  We look at how much energy the electrons have to start with, and how much they end up with, and thereby deduce the energy levels of the mercury atoms.

How is that possible?  In terms of the analogy, make the following transformations:

kids –> electrons

ice cream truck –> Hg atoms

kids buying ice cream at certain prices –> electrons giving certain amount of energy to Hg atoms

prices of ice cream cones –> energy levels of Hg

M (initial amount of money) –> V (proportional to initial kinetic energy of electron)

L (leftover money) –> I (proportional to final kinetic energy of electron)

If energy levels of an atom are truly quantized, then we would expect a graph of I vs. V to look like our graphs above, with an increasing sawtooth pattern.  Where the drops occur will then tell us the specific energy levels of the Hg atom.  (Incidentally, why do we use V and I?  Well, in the actual experiment the easiest way to measure initial kinetic energy is by measuring the voltage used to accelerate the electrons; the easiest way to measure final kinetic energy is to measure the current of the electrons after they have passed through the Hg vapor.)

How did the experiment go?  Here are the results:

It should be obvious that atomic energy levels have specific “prices”, and that there’s a minimum amount of energy that an electron must have in order to “buy” an atomic transition (exciting the atom at the expense of the electron’s kinetic energy).  It remains for the experimenter to do some elementary unit conversions, to translate I and V into final and initial kinetic energy.

[Note for advanced students and/or physicists: it is interesting to ponder the following questions, which highlight the fact that the ice cream analogy is not perfect: (1) why is the I vs.V graph not linear at low voltage? (2) After “spending” kinetic energy to cause the first excited state, why does the electron’s energy not drop all the way down to zero?]