# The Franck-Hertz Experiment

This picture is from a class (Experiments in Modern and Applied Physics) that I took at Rutgers back in my junior year.

It’s not a spaceship or alien technology; it’s a special mercury vapor triode I was using to recreate the famous Franck-Hertz experiment.

You can enjoy it as it is, or read further for an explanation of the physics behind the picture.

# Back To School

Classes have started up again, so posts will probably become a little less frequent than before. In case you’re wondering, most of my time in the next few weeks will be spent doing this.

# Rippled Ice

My current blog header is a crop from this photo, which was taken after a snowstorm at Rutgers in early February 2011. I wanted to get pictures of the snowy campus, but by the time I got out of class, everything had begun to melt. I walked by a wooden handrail and found this: some very thin rippled/bubbly ice floating on a slightly less thin layer of melted water. (The dark lines are the spaces between painted wooden boards.) There are a few spots where you can see air bubbles trapped between the ice and the water below it. I don’t know what physical processes produced this interesting texture, but I sure would love to. Does anyone have some insight?

# The Missing Link: Point Particles, Extended Objects, and the Center of Mass

I’d like to make one more post about Newton’s Laws of Motion before I temporarily abandon them. There are two closely-related issues that I want to address:

1. There is a glaring problem with Newton’s Laws as I have portrayed them in my last two posts (Why Are Newton’s Laws of Motion Important? and Variations on Newton’s Laws of Motion).
2. Many students in introductory physics classes get the impression that physics cannot possibly apply in the real world because we always replace real objects with point particles.

In the process of addressing the problem with Newton’s Laws, I will simultaneously show that the aforementioned physics students could not be further from the truth; Newton’s Laws of Motion do apply to objects in the real world, and this is true because of the fact that we can replace extended objects with point particles (not in spite of it)!

Continue forward to see what allows me to make these claims!

# Variations on Newton’s Laws of Motion

I would like to explore Newton’s laws in a bit more detail, especially the connection between the two different versions that I introduced in my previous post. Whereas that post focused on “higher-level” aspects of Newton’s laws, this one will explain some of the supporting details. (I’m also sort of making this post for the sake of completeness: I made a claim in my previous post, and I want to prove it. You shouldn’t believe anyone’s claims unless they have proof, including me.)

Just as a reminder, Newton’s Laws of Motion are:

1. If there is no net force on an object, it will have no acceleration.
2. If there is a net force ${\bf F}$ acting on an object with momentum ${\bf p}$, then ${\bf F} = \dot{\bf p}$.
3. If object 1 exerts a force on object 2, then object 2 exerts a force on object 1 with the same magnitude but opposite direction.

I plan to turn them into:

1. The other two laws are valid in only in inertial reference frames. These special frames really do exist, and they are easy to identify.
2. There is an equation (${\bf F} = m {\bf a}$) that can determine the position and velocity of an object at any time in the past or future.
3. The momentum of a system is conserved if no forces act on it.

# Why Are Newton’s Laws of Motion Important?

Isaac Newton first published his three laws of motion in 1687, and physics students have been learning about them in class ever since. I’m sure more than a few of them have wondered: “Why are they teaching me this stuff?” This is an important question that is, unfortunately, not usually addressed in physics classes. I can think of four main reasons:

• They work!
• They represent mankind’s first great success at describing diverse aspects of nature with simple mathematical formulas.
• They form the most intuitively appealing physical theory.
• They lay the groundwork for later physics developments.

Now I’ll explain what I mean.

# Glossary

Sorry, but this is not a very exciting post. I’m just going to go over some physics notation and other basic principles so I can reference this in my other posts. I don’t know why the LaTeX stuff looks so weird. I guess I’ll blame wordpress.

# Notation

• A bar over a letter (e.g., $\bar{v}$) denotes an average value.
• A boldface letter (e.g., $\bf r$) denotes a vector.
• A dot above a letter (e.g., $\dot {\bf r}$) denotes a time derivative, i.e., $\dot {\bf r} = \frac{d}{dt}{\bf r}$.
• A derivative of a vector (e.g., $\dot {\bf r}$) denotes derivatives of each of its components, i.e., $\dot {\bf r} = \dot{r}_x \hat{\bf x} + \dot{r}_y \hat{\bf y} + \dot{r}_z \hat{\bf z}$
• $\sum_{\beta}$ denotes a sum over all values of $\beta$. For example, if $\beta$ is allowed to be any integer between 1 and $N$, then $\sum_{\beta}$ is equivalent to $\sum_{\beta=1}^{N}$
• $\sum_{\beta \neq \alpha}$ denotes a sum over all values of $\beta$ except $\alpha$.
• $\sum_{\beta > \alpha}$ denotes a sum over all values of $\beta$ that are greater than alpha $\alpha$.

# Basic Principles

• We can measure an object’s average velocity ($\bar{\bf v}$) during a time interval $\Delta t$ by measuring the change in its position ($\Delta {\bf r}$) and then computing $\bar{{\bf v}} \equiv \frac{\Delta {\bf r}}{\Delta t}$.
• The natural generalization of average velocity is instantaneous velocity ($\bf v$). To find it, we use ${\bf v} = \dot{\bf r}$.
• We can measure an object’s average acceleration ($\bar{\bf a}$) during a time interval $\Delta t$ by measuring the change in its instantaneous velocity ($\Delta {\bf v}$) and then computing $\bar{{\bf a}} \equiv \frac{\Delta {\bf v}}{\Delta t}$.
• The natural generalization of average acceleration is instantaneous acceleration ($\bf a$). To find it, we use ${\bf a} = \dot{\bf v} = \ddot{\bf r}$.