I was looking through some of my books and saw this — it’s a great experiment and I couldn’t resist making a little geogebra model:

]]>

If this simple but inconvenient truth were kept at the forefront of the mind, many of the major crimes of the physics class room would be eliminated. The student in the back row, as well as the student in the front row, should see and hear what is going on. The instructor must examine critically every experiment to be demonstrated with this thought in mind; he should consider the value of an experiment by judging what the student sees and understands rather than by his own personal enjoyment and satisfaction in performing an operation that may be perfectly clear from his vantage point but perfectly invisible to most of the students in his class.

If you have to have a physics degree to understand the experiment, you’re on the wrong track. Likewise, if you can’t see it clearly, you can’t hope to comprehend the action.

After an experiment is set up you may be astonished to see what it looks like from the back of the room. Large scale apparatus, using cameras to magnify the action, clearly visible indicators, and readable charts and drawings are essential. Simplicity (but not crudity) of arrangement and manipulation is paramount. Teachers often avoid simple experiments, favoring those which require elegant and elaborate facilities. By such displays, the student may be impressed and even overawed, but they may in equal parts be being trained that physics happens only in the hallowed halls of the laboratory and through the use of exotic materials - it would also be a mistake to consider that he is better instructed.

The student deserves to see as much of the working arrangement of every experiment as they can understand without being confused by unnecessary detail. It might be stated as a corollary that the experimental arrangement should be more easily understood than the concept that it is designed to illuminate. The foremost purpose of any demonstration experiment is to clarify a physical principle or to show some interesting application of a principle.

If, at the same time, it can amaze and intrigue the student and cause him to do some independent thinking, it more than fulfills its mission. But its primary purpose is not to mystify. Whenever a physics instructor presents a demonstration, they can become a showman; some of the experiments are as clever as any magician’s tricks, and one should make the most of their “show” qualities when appropriate.

Our purpose, however, is very different from any magician’s: the latter makes every effort to conceal and to mystify; the former makes every effort to expose and to clarify the underlying physical principles. Of the many principles taught in elementary physics courses, almost every one is reducible to a mathematical statement that involves three or four symbols only. Yet students constantly stumble over these mathematical expressions which might be made vivid and meaningful if illustrated concretely by simple experiments.

One instructor suggests that a good experiment involves a maximum of manipulation and a minimum of explanation. He goes so far as to suggest giving a demonstration lecture of selected experiments without saying a word! The inspirational value of experiments depends so much upon the manner in which they are presented that the instructor cannot give too much attention to planning his experiments so that they will be given in the proper setting. There is an appropriate time at which to perform an experiment: to show it too soon is to find a class unprepared to appreciate its importance; to delay it by prolonged explanation is to diminish its effectiveness. Thought should be given to exposition, and the lecture should move steadily forward toward some climax. The physics instructor needs to develop a sense of what on the stage is called “timing.‘’

]]>Reading through some science and maths papers this morning - this is my favourite so far and yes, that's all of it! pic.twitter.com/SYpaDjO0F1

— Joe Rowing (@JRowing) October 21, 2023

]]>this led me to hunt out the shortest paper published: pic.twitter.com/ZpE53U0xih

— Joe Rowing (@JRowing) October 21, 2023

But this video is a favourite;

]]>There was a time when the AEB had a multiple choice paper - here’s a few of those that are worth a look:

I’ve built single stage, multi-stage and large volume roakets like this on on the cover of the NPL booklet:

Water rocket challenge

Fin template:

There’s a great video here: by an American physicist explaining how to set up the visualization, and then use a combination of weights and marbles to explain everything from gravity’s basic mechanics to how gravity lets us plot return trajectories from the moon.

In fact - here I am doing this very activity with the fantastic Ben Sparks (Ben Sparks | mathematician musician speaker) at a physics CPD event:

]]>I thought this might be useful to someone - I have taken to building this with my students from scratch as a lesson activity - I think it’s a really nice mathematical follow-up from using a stretchy lycra sheet to get a feel for potential wells (See Fabric of time and Space).

]]>*from the AQA A-level physics specification (September 2015 onwards)*

Stefan’s law and Wien’s displacement law

General shape of black-body curves, use of Wien’s displacement law to estimate black-body temperature of sources.

$$\newcommand{\SI}[2]{{#1}~\mathrm{#2}} \newcommand{\si}[1]{\mathrm{#1}} \renewcommand{\vec}[1]{\mathbf{#1}} $$

Bodies which absorb all incident radiation are known as black bodies and stars are very good approximations to black bodies. The intensity of the light we get from stars at different wavelengths has a distinctive shape and can be measured to determine its black-body temperature.

The flux $F$ (power per unit area of a black body is given by $$F\left(\equiv \frac{P}{A}\right)=\sigma T^4,$$ where $\sigma$ is the Stefan–Boltzmann constant (its value is $\sigma = 5.67\times 10^{-8}\mathrm{~W~m^{-2}~K^{-4}}$).

The Stefan–Boltzmann Law shows how the *total* power emitted depends on temperature. The Wien displacement law gives the way in which the wavelength of maximum intensity—the peak of the curve—shifts with temperature.

It is found that the peak wavelength, $\lambda_\mathrm{peak}$, is inversely proportional to temperature $$\lambda_\mathrm{peak}T=2.90\mathrm{~mm~K}.$$

The shape of black-body curves is given by the Planck radiation law, which gives the energy density as a fuction of wavelength (the Stefan–Boltzmann law and Wien’s displacement law follow immediately from it: by integrating over all $\lambda$ and finding the peak value of $\lambda$ respectively).

Max Planck in 1901 published an equation which fitted the experimental results for black-body radiation, but he could only derive it by quantizing the vibrations allowed in the oscillators within such bodies. This, together with Einstein’s paper quantizing light in 1905, established *quantum theory*, a cornerstone of modern physics.

The Planck radiation law gives the spectral emissive power of a black body as $$e_{\lambda b}=\frac{2\pi h c^2 \lambda^{-5}}{\exp(hc/\lambda k T)-1}.$$

In [2]:

```
import numpy as np
import matplotlib.pyplot as plt
# Constants
from scipy.constants import c
from scipy.constants import h
from scipy.constants import Boltzmann as kB
from scipy.constants import Wien
```

In [4]:

```
def planck (wavelength, temp):
e = 2*np.pi*h*c**2 / (wavelength**5*(np.exp(h*c/(wavelength*kB*temp))-1))
return e
wavelength = np.linspace(100e-9,2000e-9,100)
#Maxima line
peak = 2*np.pi*h*c**2/(wavelength**5*(np.exp(h*c/(kB*Wien))-1))
temps=np.array([2000,2500,3000,3500,4000,4500,5000,5500])
#Plotting from here on in
fig = plt.figure(figsize=(6, 4))
ax = fig.add_subplot(111)
plt.rcdefaults()
ax.plot(Wien/temps, planck(Wien/temps,temps), 'ko', ms=10, mfc='none')
ax.plot(wavelength, planck(wavelength,3500), 'k-')
ax.plot(wavelength, planck(wavelength,4000), 'k-')
ax.plot(wavelength, planck(wavelength,4500), 'k-')
ax.plot(wavelength, planck(wavelength,5000), 'k-')
ax.plot(wavelength, planck(wavelength,5500), 'k-')
ax.plot(wavelength, peak, 'k--')
ax.set_ylim(0,7e13) # note this has to come after plotting of data
ax.set_xlim(left=0,right=2e-6)
ax.set_xlabel(r'$\lambda / \mathrm{m}$')
ax.set_ylabel(r'$\mathrm{spectral\;radiance}\,/\,\mathrm{W}\,\mathrm{m}^{-3}$')
#ax.set_title('Black body radiation curves')
from matplotlib import ticker
formatter = ticker.ScalarFormatter(useMathText=True)
formatter.set_scientific(True)
formatter.set_powerlimits((-1,1))
ax.xaxis.set_major_formatter(formatter)
ax.yaxis.set_major_formatter(formatter)
ax.text(Wien/3500+1e-8, planck(Wien/3500,3500)+18e11, r'$3500\;\mathrm{K}$')
ax.text(Wien/4000+1e-8, planck(Wien/4000,4000)+18e11, r'$4000\;\mathrm{K}$')
ax.text(Wien/4500+1e-8, planck(Wien/4500,4500)+18e11, r'$4500\;\mathrm{K}$')
ax.text(Wien/5000+1e-8, planck(Wien/5000,5000)+18e11, r'$5000\;\mathrm{K}$')
ax.text(Wien/5500+1e-8, planck(Wien/5500,5500)+18e11, r'$5500\;\mathrm{K}$')
plt.show()
```

The Wien displacement law tells us the region of the spectrum in which thermal radiation is most intense for sources at different temperatures: room temperature, $\lambda_{\text{peak}}\approx\SI{10}{\mu m}$, far infra-red; sun’s surface ($\SI{5800}{K}$), $\lambda_{\text{peak}}\approx\SI{480}{nm}$, blue; etc. It is obvious that the colour with which a hot body seems to glow will change with the temperature of the body. Between about $\SI{500}{^\circ C}$ and $\SI{1500}{^\circ C}$, the temperature of a body may be judged quite accurately by eye.

$t / ^\circ\mathrm{C}$ | colour |
---|---|

500 | red, just visible in daylight |

700 | dark red |

900 | bright red (“cherry” red) |

1100 | orange |

1300 | yellowish-white |

1500 | dazzling white |

Hotter stars produce more of their light at the blue/violet end of the spectrum and appear white or blue-white. Cooler stars look red, since they produce more of their light at longer wavelengths.

In [6]:

```
%load_ext version_information
%version_information numpy, matplotlib, scipy
```

The version_information extension is already loaded. To reload it, use: %reload_ext version_information

Out[6]:

Software | Version |
---|---|

Python | 3.6.1 32bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] |

IPython | 5.3.0 |

OS | Linux 3.2.98 smp i686 Intel R _Pentium R _4_CPU_2.40GHz with slackware 14.0 |

numpy | 1.12.1 |

matplotlib | 2.0.2 |

scipy | 0.19.0 |

Thu Apr 26 19:32:26 2018 GMT |