(Versuchsbeschreibungen s. unten.)

(Experiment descriptions see below)

Die anderen Versuchsbeschreibungen folgen.

The other descriptions are coming soon!

The task here is, to get a tiny hole into a coin, without completely destructing it.

To do so, there is various stuff, which could be used.

The solution idea is to freeze a banana with the liquid nitrogen. (This must not be done by the students but by one of the tutors.) Then, the banana can be used as a hammer.

Then, a fixing pin can be sticked into a cork. Now, this can be used as „nail“.

With the banana-hammer, the pin-cork-nail can be used to get a tiny hole into the coin.

To confuse the students a little more, other stuff will be there.

The goal here is, to let the students think about creative solutions for this pretty uncommon probem in style of MacGyver.

There is no need for a final presentation of the „master solution“, because the students may also find no result, which is not too seldom in physics.

The task of this experiment will be to measure the width $ d $ of tiny objects (like hairs) with a monochromatic laser of given wavelength $ \lambda $. To do this, one profits from the fact, that the position of the diffraction minima is the same as in a single-slit experiment whith a slit of the same width $ d $. (Indeed, the basic goal in this experiment is, to understand why.)

A simpe derivation of the corresponding formula $d\,\sin\theta_{n} = n\lambda$ (in Fraunhofer approximation) can be found here: http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction

To see, why the minima are at the same positions, consider three systems. First, consider the singe-slit, which we will indicate by $ s $, second, consider the hair ($h$) and finally, consider a free system, where the light ray is propagating without any barrier ($f$).

Let us denote the light's amplitudes on the screen in system $i$ as $A_i(\theta)$. Then, by the principle of superposition,

$A_f(\theta)=A_s(\theta)+A_h(\theta)$.

Assuming the light ray's diameter to be smaller than the position of the first minimum (which can always be gained by moving the screen away from the laser), we have

$A_f(\theta\geq\theta_1)=0$,

because outside the ray, there must be a vanishing amplitude. This implies

$A_h(\theta\geq\theta_1)=-A_s(\theta\geq\theta_1)$.

As what we can see are not amplitudes but intensities $I_i\propto A_i^2$, we can take the square of this equation and get finally

$I_h(\theta\geq\theta_1)\propto I_s(\theta\geq\theta_1)$,

which implies, that the positions of the minima (and indeed, all other critical points) are the same.

This derivation shall be presented to the new students in approximately 5 minutes. If they ask, one should spend another 2 minutes to explain the minima formula for the single-slit.

But the most important thing is to make clear, that we cannot observe the amplitudes directly, but the intensities.

This experiment is probably the one with the biggest part of physics.

The task is to measure Earth's gravity constant $g$ in the usual constant approximation close to the surface.

To do this, the students shall use a pendulum, constructed by a string and some screw nuts.

This system can be approximately described by the differential equation of the harmonic oscillator (Which can be derived by a force ansatz [driving component of gravity] and a Taylor expansion $\sin\varphi\approx\varphi$):

$0=\ddot\varphi+\frac gl \varphi$,

where $\varphi$ is the angle coordinate and $l$ is the length of the pendulum. Of course, this description neglects friction and is ony valid in the usual small-angle approximation.

In this case, the angular frequency $\omega$ is given by

$\omega^2=\frac gl$

which leads to

$g=\omega^2 l$.

(This can for exampe be shown by inserting $\varphi(t)=\hat\varphi\sin{\left(\omega t+\phi\right)}$ into the differential equation.)

The students shall also think about the error on $g$. So, not only the previous part has to be discussed, but also the basic formula for the propagation of errors:

$\sigma_y^2=\sum\limits_i \left(\frac{\partial y}{\partial x_i}\right)^2\sigma_{x_i}^2$

There is no need to derive this formula, but one should present the derivation of the special case of relative errors.

Assuming $y=\prod\limits_i x_i^{\nu_i}$, we have (by the error propagation formula):

$\sigma_y^2=\sum\limits_i \left(\nu_i\cdot x_i^{\nu_i-1}\prod\limits_{j\neq i}x_j^{\nu_j}\right)^2\sigma_{x_i}^2$

Division by $y^2$ then yieds:

$\left(\frac{\sigma_y}y\right)^2=\sum\limits_i \left(\nu_i\cdot \frac{\sigma_{x_i}}{x_i}\right)^2$

With this in mind, the students shall estimate $g$ and $\sigma_g$ as precisely as possible and the shall also think on how to improve their measurement.

For example, a smaller amplitude $\hat\varphi$ leads to a better justification of the small-angle aproximation and measuring $N$ instead of one period reduces the error on the corresponding time $T_N$, which will be dominated by the reaction time of the person who controls the chronograph, by a factor of $\sim N$.

The students shall also think about any other effects that could disturb their measurement. (For example, the string wil not be perfecty rigid and thus, the length $l$ could vary a little bit. And there is also friction!) They shall try to quantify the errors and get a feeling for the dominant ones.

More on the topic can be found here: http://en.wikipedia.org/wiki/Pendulum

The presentation of the differential equation and the related quantities should not take more than 4 minutes. The error propagation formula and the derivation of the relative-error propagation formula could take another 3 minutes.

In this experiment, the challenge is, which studentgroup can build the best balloon rocket.

The idea is to bend a balloon to a straw which is fixed on a long cord. Who reaches the furthest point, wins.

The material, the students get, is:

• a balloon per group

• tape

This is just a fun experiment. Some physical backgrounds can be found here: http://en.wikipedia.org/wiki/Water_rocket

It is not neccessary to discuss the whole principle of recoil in a too precise manner. One can give some keywords like:

• The pressure in the water is equivalent to some potential energy.
• When it is allowed to relax (i. e. the mounting is removed), the water will be „shot“ out of the bottle and carry a momentum $p$.
• Due to the principle of momentum conservation, the bottle also has to carry a momentum, namely $-p$.

Apart from this, the students shall have fun and if they wish, they can have a competition on who reaches the biggest shooting distance.

A flask is filled with water and leads to a thin hose which goes upwards and is filled with water up to a height of approximately 1.5 meters. The flask is heated by a Bunsen burner, but the water does not simply boil. Suddenly, the 'gusher' erupts and the water escapes in a fontain that reaches a height of 1 to 2 meters.

Due to the 1.5 meters of water in the hose, the pressure in the flask is higher than usually. (For an atmospheric pressure of 1013 mbar, the pressure in the flask is approximately 1150 mbar.) A look at the phase diagram of water shows a boiling temperature of roughly 104 °C.

So, it takes 'longer', until the water boils, but when it happens, small bubbles of water vapor. Those bubbles escape in the hose and 'push' some of the liquid water out of it. But when the water has left the house, the pressure in the flask becomes normal, again.

This happens very quickly and since the water in the flask still has a temperature of 104 °C, it cannot stay liquid anymore and thus, becomes to gas in an explosion.

The first thing to do is, to fill the water into the hose and to boil it. When this is done, the freshmen shall discuss about what will happen.

Unfortunately, one cannot predict precisely, if and when the gusher is going to erupt. (If there is too much wind, it takes longer.) Thus, if nothing happened after 10 to 15 minutes, the idea of the experiment shall be explained and the freshmen shall learn how to use and to interpret the phase diagram of water. If the gusher erupts in time, the explanation follows later.

This is a fun station. The task is to build an bridge over a gap of approximately 50-80cm. To do this, the students get nothing but 10 pages of paper. The winner is the one who builds a bridge on which one can put the most tealights. The second task is to build a ship out of paper which can carry the most tealights. Meanwhile, the ship has to swim on water. Again, the students get nothing but 5 pages of paper. The use of glue or any other aid is forbidden. They may only use for example scissors to cut the paper or some aid to fold it.

This experiment is about having fun with electrostatics.

The new students will get two tasks with a van-de-Graaff band generator. (Additional information can be found here: http://en.wikipedia.org/wiki/Van_de_Graaff_generator)

The voltage for the motor can be varied from $0 V$ up to $\sim 200 V$.

Furthermore, there will be a metal sphere on a metal stick, that shall be connected to earth.

The tasks will be:

• to measure the length of the lightnings as function of the motor voltage
• As many people as possible take each others hands (while they are standing on plastic plates). The first one touches the generator with his second hand. How many people can ruin their hairstyles at the same time?

Do not forget to let everybody touch the earth after the experiment!

At this station the students can get to know that old version of a camera and take some pictures.

There are two pinhole cameras, photographic paper and the chemicals that you will need to develop the pictures. The freshmen are going to take pictures and develop them on their own.

This experiment has no real task that must be solved. At the beginning you should tell the freshmen about the idea, that light is deflected by gravity. That idea is recorded at least since the late 18. century and later Einstein approached it from the other side and derived this deflection from his Relativity Theory.

Now here is the question the freshman should answer: Why (and in which way exactly) is a pinhole camera a suitable device to proof this prediction? Why would you prefer a pinhole camera over a regular one with lenses?

This station actually needs some preparation that we can hardly do for you, but it's pretty easy. The chemicals are in 26C 102 on the table as well as four containers.

• The two slim plastic containers should be filled with distillated water up to a height of about 6 cm. They will be needed to wash the remaining chemicals off of the photographs.
• The round container will be used for the developer. Mix 20ml of developer with 180ml of distillated water.
• The big, rectangular container will be used for the fixer. Mix 30ml of fixer with 120ml of distillated water.

Here is the routine of taking pictures with the pinhole-cameras:

• Find a good position for the camera to take your picture.
• Get into the shaded room, close the doors, stick photographic paper onto the visor and put the visor back into place. Close the camera. Make sure that the seeker and the aperture are covered.
• Put the camera back into place.
• Uncover the aperture to take the picture.
• Cover aperture again and take the camera back into the darkroom. Now you can take out the photographic paper for development.

Developing pictures works as follows:

• Hold photograph into the developer-solution (use tweezers and avoid touching the solution) and move it slightly to make sure it is covered with solution evenly. Development time should be about 90 seconds, but if you use the developing-lamp (orange, sits on the table), you can just observe the process and take it out when it's dark enough.
• Wash off remaining developer in the first water-container.
• Put the picture into the fixer (tweezers!) and move around for about 30 seconds. Rinse in the second water-container and that's it!

The freshmen can go through all this on their own. Just make sure that they use tweezers and wash their hands if they should touch one of the two solutions during development.