Tag Archives: physics

A Furry Friction Funny

Q. Two cats are sitting on a roof.  Which one slides off first?

A. The one with the smaller mu!


Of course this joke assumes that the cat in question is totally complacent to slide off the roof, making no effort to maintain his position.  Strange cat.

Anyway, “mu” is pronounced like “mew“, as in the sound made by a cat.  It is a Greek letter, usually represented by the following symbol: µ.  Mu must be the favorite Greek letter of mathematicians and scientists; it pops up in fields as diverse as computer science, number theory, physics, orbital mechanics, chemistry, and pharmacology.  In this joke, µ is meant to represent the coefficient of friction, about which more in a moment.

What is friction?  To greatly oversimplify things, friction is a force that resists relative motion between two surfaces, or between a surface and a fluid.  When you experience resistance while pushing a refrigerator across a tile floor, you’re working against friction.  When you rub your hands together to warm them up, friction is your friend.  Friction is an even greater friend to the skydiver; when she opens her parachute, fluid friction against the atmosphere reduces her speed from a spine-shattering 120 miles per hour to a totally survivable 10 miles per hour.)

Here’s an interesting side note about friction; scientists used to think that the friction was caused by microscopic grooves and bumps that tended to lock surfaces together, requiring extra force to break their grip and get the surfaces sliding past each other.  Now, scientists think that friction is caused by chemical bonds forming between the atoms in the adjacent surfaces.  That’s a strange thought; merely by touching something, you bond with it.  In a way, you become a part of it and it becomes a part of you.  Deep, man.  Deep.

But I digress.  Mathematically, the friction between two surfaces – such as, say, a roof and a cat’s butt – can be expressed using the following formula:

Ff = µ * m * g * cosθ

Ff represents friction, which is measured in units of force called newtons.  The letter m represents the mass of the cat in kilograms, g is the acceleration due to gravity (On Earth, that’s about 9.8 m/s/s) and cosθ is cosine of angle theta, where theta (another Greek letter strongly favored by the academic elite) is the angle that the roof makes with the ground.

Just to have some numbers to play with, let us assume that the cat’s mass is 3 kilograms, giving her an Earthly weight of about 6.6 pounds.  Now let us assume that the roof has a pitch of, say, 30º.  To find the friction between the cat’s derriere and the rooftop, we would substitute and multiply:

Ff = µ * m * g * cosθ

Ff = µ * 3 kg * 9.8 m/s/s * cos(30º)

Ff = µ * 25.5 newtons

I have not yet specified the roof-feline coefficient of friction, because frankly, I don’t know what it is.  My search of the literature has been fruitless.  For the sake of argument, let’s assign a completely arbitrary value of 0.6 to µ, and see what that gets us.

Ff = 0.6 * 25.5 newtons

Ff = 15.3 newtons (about equal to 3.4 pounds of force)

So there you go; there are 15.3 newtons of friction preventing the cat from sliding down the roof.  Whether the cat actually slides or not depends on whether the gravitational component pulling the cat down the roof is greater than the friction holding the cat in place.

But let us assume that the coefficient of friction between the cat and the hot tin roof were smaller, perhaps because the cat had just finished grooming and her fur was unusually even and smooth.  Instead of 0.6, let’s say the coefficient of friction were only 0.3, giving the cat a static friction of only about 7.7 newtons.  Naturally, with a smaller coefficient of friction – a smaller mu – the cat would be less able to hold its position on the roof and more likely to start sliding downward.

So there you have it: the cat with the smaller mu is the one that starts sliding first.  Next time somebody tells you this joke, they’ll be met with less friction, because you’ll understand it purr-fectly.

Okay, I’ll go now.


On The Stoicism of Helium

Helium walks into a bar. The bartender tells him “Sorry, we don’t serve noble gases here.” Helium doesn’t react.


Helium (symbol: He) is the second element – both in terms of atomic number and abundance in the universe. It sits at the top right corner of the periodic table.

Helium is the lightest member of the element family known as the noble gases. The noble gases also include neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn), and maybe element 118. The noble gases are unique among the elements in that they all have low melting and boiling temperatures (which explains why they are all gases at room temperature). Also, the noble gases are very unreactive; they do not tend to form compounds with other elements.

I could stop right now and you would understand the joke. Helium doesn’t react because it’s a noble gas, and noble gases don’t react. But there’s much more to tell, so please indulge me while I bore you to tears explain why noble gases are the way they are. This is your last chance to log off before you learn about electron configurations.


Still here? Good.

We’ve already discussed how the electrons in atoms are arranged into concentric shells (or energy levels) around the atomic nucleus. Actually, it’s a little more complicated than that. Each energy level can be further divided into sublevels. The sublevels are given odd names like sharp, principle, diffuse, and fundamental, but we’ll just call them s, p, d, and f.

The first energy level – that is, the one closest to the atomic nucleus – has only one sublevel. It’s an s-type sublevel, so it’s called 1s (read that as “one-S”). All s-type sublevels can hold 2 electrons, so the entire first energy level can hold 2 electrons.

In atomic physics there’s a guideline called the Aufbau principle. Aufbau is a German word meaning construction. It says that the electrons in atoms fall to the lowest-energy sublevel that is available. Once a sublevel is filled with electrons, the next highest sublevel begins to fill, and so on.

If an atom has one or two electrons, the 1s sublevel is perfectly capable of accommodating them. However, if an atom has 3 or more electrons, it must tap into higher-energy sublevels.

The second energy level is made of two sublevels. It also has an s-type sublevel (in fact, all energy levels contain an s-type sublevel) but it also contains a p-type sublevel. These two sublevels are called 2s and 2p (or not 2p? That is the question!)

Like the 1s sublevel, the 2s sublevel also holds 2 electrons. The 2p sublevel can hold 6 electrons. All told, the second energy level can hold up to 8 electrons.

And so it goes. As the electron population grows, so does the number of sublevels and energy levels. If you’re assigning homes to an atom’s electrons, you continue adding energy levels and sublevels until you run out of electrons. The last sublevel may or may not be full, but every sublevel prior to the last one must be full (except for a few special cases that we’re not going to discuss right now).

Sublevels

The sublevels don’t necessarily get filled in the order you might expect. 1s, 2s, 2p, 3s, and 3p fill with electrons in order, but the next sublevel to be filled after 3p is 4s, not 3d. The 3d sublevel fills after 4s, then comes 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, etc, etc. This arrangement may seem bizarre, but it plays a major role in determining if and how an atom will react with other atoms.

See, the most important electrons in any atom are the valence electrons. Valence electrons are the electrons that inhabit the highest energy level – the one farthest from the nucleus. Atoms that have one through seven valence electrons will generally react with other atoms, either by losing, gaining, or sharing electrons. Atoms that have eight valence electrons, however, are special…eight valence electrons is a very stable arrangement. Why? Because when an atom has eight valence electrons, its highest s-type and p-type sublevels are just filled. Let’s take a look at the arrangement of electrons in each of the noble gas atoms:

Helium (2): 1s2
Neon (10): 1s2 2s2 2p6
Argon (18): 1s2 2s2 2p6 3s2 3p6
Krypton (36): 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6
Xenon (54): 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p6
Radon (86): 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 6s2 6p6

For each element, the number in parentheses tells you the total number of electrons. The raised numbers tell you the number of electrons in each sublevel. I’ve color-coded the sublevels to make it easier to see which electrons are grouped together in an energy level. Take a look at each of the noble gases (except for helium). Notice how they all have a total of 8 electrons in their outermost energy levels, distributed between the outermost s-type and p-type sublevels.

These arrangements are really stable. Because noble gases have full s– and p-type sublevels in their outermost energy levels, they tend not to gain, lose, or share electrons under normal conditions. That’s why we say that noble gases don’t react with other atoms.

Now of course the joke is about helium, and you’ve probably noticed that helium does not have 8 valence electrons; in fact, helium doesn’t have 8 electrons at all. Regardless, helium still has a complete 1s sublevel, which confers its own kind of stability. Chemically, helium reacts (or more appropriately, it doesn’t react) more like the noble gases than like any other family of elements, and so it is considered to be one of them.


Here are two other interesting tidbits about helium which won’t enhance your understanding or appreciation of the joke, but might give you something to think about.

  1. The name helium comes from the word Helios, who was a Sun god in Greek mythology. The element was so named because it was discovered first in the Sun, via an anomalous spectral signature in sunlight, 25 years before it was isolated on Earth.
  2. Despite helium’s abundance in the universe, we’re running out of it on Earth. The looming helium shortage has implications far beyond birthday party balloons.

Hamburger Humor

Q. Why does hamburger have less energy than steak?

A. It’s in the ground state.


English is kind of a funny language (not funny ha-ha…funny strange). When you say ground in reference to beef, you’re using the past participle of the word grind. Why is ground the past participle of grind? Who knows? It just is! Deal with it!

And then of course there’s the ground, that huge surface outside that pilots spend their careers avoiding. Interestingly (or maybe not), that ground has very little to do with grinding, etymologically speaking. Like I said: English = funny.

Because the ground has great fundamental importance to almost everything we humans do, the word ground has permeated many disciplines, including chemistry and physics. There, the word refers to the absolute lowest level of something. In atomic physics, the phrase ground state is the lowest energy configuration in which an atom’s electrons can exist. When an atom’s electrons are in their ground state, they have no capacity to give off energy.

So let me back up just a bit. The electrons of an atom are arranged into concentric shells, sort of like Russian nesting dolls except less creepy and a whole lot smaller. These shells are also known as energy levels. The closer a shell is to the nucleus, the less energy its electrons have. Electrons can move from shell to shell, but they must absorb and release the appropriate amount of energy as they do so.

The most desirable real estate in an atom – as far as electrons are concerned – is close to the nucleus. Just as water tends to flow downhill, the electrons in an atom will rush “downhill” to find a slot as close to the nucleus as they can. (Space is limited in each shell) In an atom with only one electron (hydrogen), the electron naturally tends to fall into the first shell. When this happens, the hydrogen atom is in its ground state.

If you zap the hydrogen atom with just the right amount of energy, the electron can be temporarily bumped into a higher energy level. In this case, we say that the hydrogen atom is excited. An excited atom is unstable; it soon allows its electron to pay back the bolt of energy (usually in the form of light) and fall back to the ground state. It’s kind of like a sugar crash, but with less crankiness.

One presumes that if you zap a slab of hamburger beef with a bolt of energy, the beef can be simultaneously ground and excited. What a state that would be!


Cuckoo for Cross Products

Q: What do you get when you cross a mosquito with a mountain climber?

A: You can’t cross a vector and a scalar!


Man, that is one nerdy joke. To be honest, I had to do a little review so I could confidently discuss it.

See, it’s a pun! Actually, it’s a triple pun, because it relies on the multiple meanings of three words: vector, scalar, and cross. Prepare for MAXIMUM NERDAGE as we fearlessly leap across disciplines!

What is a vector?


Biologically speaking, a vector is an organism that transmits diseases from one animal or plant to another; a mosquito, e.g. Mosquitos can transmit malaria, West Nile virus, dengue fever, yellow fever, and a bunch of other germs you really don’t want.

In mathematics (and its beautiful child, physics) a vector is a quantity that has both a magnitude and a direction. If I tell you that I am driving east at 80 kilometers per hour, I have given you a vector: specifically, my velocity. Velocity is a vector quantity because it has both a magnitude (80 km/hr) and a direction (east). Other examples of vectors are acceleration, force, and momentum.

What is a scalar?


To scale a mountain is to climb it, so a mountain climber might be called a scalar (or would it be spelled scaler? I’m not sure, but the joke doesn’t work if you spell it with an e, so I’ll stick with scalar).

A scalar is also a quantity that has a magnitude but not a direction. Speed is an example of a scalar quantity. If I tell you that I am driving at 80 kilometers per hour – but neglect to mention which way I am driving – I have told you my speed. That’s the difference between speed and velocity: velocity has a direction; speed does not. Other examples of scalar quantities are: mass, distance, and energy.

What does it mean to cross two things?


There are lots of jokes that start with “What do you get when you cross X with Y?” I’ve always assumed that this crossing was some sort of ethically questionable breeding program being conducted in a secret laboratory deep beneath a mad scientist’s mansion. Think about that the next time somebody asks you a joke like this one. It’ll make you cringe a little and not feel so sure you want to know the answer.

In math/physics, crossing is a specific mathematical operation that can be performed on two vectors in three-dimensional space. That doesn’t make a bit of sense, I know, so let’s back up. Imagine that vectors are arrows…that’s how most scientists think of them anyway. Now imagine two arrows pointing outward from a single location, sort of like this:

Two vectors diverged in a yellow wood...

Two vectors diverged in a yellow wood…

We’ll call the green vector A and the red vector B. The cross product of A and B is written as A x B (read as “A cross B”) and is calculated using the following formula:

A x B = |A| |B| sinθ n

In this formula, |A| is the magnitude (or length) of vector A. |B| is the length of vector B, θ (theta) is the measure of the angle between A and B, and n is a unit vector, which helps you figure out which way the cross product points in three-dimensional space. And what exactly is the cross product of A and B, I hear you asking? It’s a third vector (really, a pseudovector…don’t ask) that is perpendicular to both A and B. The blue arrow below represents the cross product of the green and red vectors.

Hot cross vectors

Hot cross vectors

You’re probably thinking “Great…so what?” Well, the cross product has a lot of practical uses, particularly in the field of engineering. Cross products are used in some calculations involving torque, a force that causes things to spin. Yes, despite what sounds like a lot of made-up mathematical nonsense, it does have real world value.

Now then, on to the heart of this joke: why can’t you cross a vector with a scalar? Because you specifically need two vectors – two quantities that have directions. Since a scalar has no direction, you cannot cross a vector with a scalar. Insert uproarious laughter.

Now that you thoroughly understand vectors and cross products, here’s a follow-up joke to send you on your way. Enjoy!


Q: What do you get when you cross an elephant with a banana?

A: |elephant| |banana| sinθ n


Heisenberg Hilarity

Werner Heisenberg is pulled over by a police officer. After checking his license and registration, the cop asks “Do you have any idea how fast you were going?”

“Not at all,” replies Heisenberg, “but I know precisely where I am.”

The cop says “I clocked you doing eighty miles an hour.”

“Oh great!” says Heisenberg. “Now I’m lost!”


Werner Heisenberg was a central figure in the development of quantum mechanics, the branch of physics that deals with the strange comings and goings of the subatomic realm. His name is connected most frequently with the Uncertainty Principle; more about that in a moment.

There’s a lot of history behind the development of the modern atomic theory and quantum mechanics, not all of which is relevant to this joke. Still, I would be remiss not to include some links so you can refresh your knowledge about how scientists know what they know about impossibly tiny subatomic particles.

  • First, spend four minutes with this video to get acquainted with the origins of quantum mechanics.
  • atomictimeline.net has an incomplete “Who’s Whom?” of atomic philosophers and physicists spanning from ancient Greece to modern times.
  • David Harrison of the University of Toronto provides a brief but somewhat academic narrative of the birth of quantum mechanics through the work of Heisenberg and Erwin Schrödinger, with a smattering of Eastern philosophy thrown in for good measure.
  • Todd provides a decent introduction to some principles of quantum mechanics.
  • And finally, if you don’t feel like reading the rest of this article (or even if you do!) spend four more minutes with this video that brilliantly demonstrates the Uncertainty Principle in a simple experiment.

In the first decades of the 20th century, physicists were making enormous strides toward understanding how protons, neutrons, and electrons work together to make atoms. It was becoming apparent, however, that subatomic particles still had a few closely-guarded secrets. Werner Heisenberg, a German theoretical physicist and the star of today’s joke, voiced an argument that there was a theoretical limit to how precisely we can measure the speed and position of an electron (or any other particle, for that matter). According to the Uncertainty Principle, the more precisely we know an electron’s speed, the less precisely we will know its position, and vice versa.

Unlikely press conferences, Figure 1.

Unlikely press conferences, Figure 1.

The reason for this intractable uncertainty has nothing at all to do with scientists’ instruments. Even if scientists could use perfectly precise instruments (which don’t exist anyway), they would never be able to break past this barrier. No matter what, nature prevents us from knowing both the speed and location of an electron with exact certainty.

Unlikely press conferences, Figure 2

Unlikely press conferences, Figure 2

Of course Heisenberg couldn’t really use his Uncertainty Principle to claim ignorance about the location or speed of his car. The Uncertainty Principle doesn’t really apply to objects above the atomic scale. Heisenberg would have known this: I think he was just trying to get out of a ticket.