# 4th Round of 26th year

Series

### 1. ... Who cares about Einstein?(2 points)

Who is your favorite physicist except of Albert Einstein? What were her contributions to physics? Why do you consider her to be so brilliant? Why should she be famous? Write a short essay about her life and the discoveries she made.

### 2. ... Space sclerosis(2 points)

Given that the Earth is 81 times heavier than the Moon, and that its surface gravity is 6 times greater than that of the Moon, calculate the ratio of the volumes of these two objects.

### 3. ... A rubber duck(3 points)

A passanger on a ferry forgot to set the parking brake. Assume that the axis of the car is aligned with the axis of the ferry, and that because of waves the ferry is undergoing a harmonic motion, i.e. $φ$ ( $t$ ) = Φ sin$~\~left$ ( $ωt$ ) . How far from the edge of the ferry can the passenger park the car without worrying about it falling into the sea? Assume that the maximal amplitude of oscillations is slowly increasing from zero to Φ.

### 4. ... Hit it with a hammer(4 points)

Imagine hitting one end of an iron rod and observing the resulting sound waves. Describe (using drawings) the time dependence of the wavefronts in the plane of the rod. We are especially interested in what the wavefronts would look like at two particular moments. The first one is the time when the sound wave reaches the other end of the rod, and the second one is the moment the wave reaches the original end of the rod after reflecting at the other end. Do not forget to describe how did you construct your drawings. You can assume that there are only longitudinal oscillations of the rod, and that its diameter is negligable compared to its length. The ratio of the speed of sound in the rod and in the air is $β$ = $v$_{rod} ⁄ $v$_{air}$~≈~$10.

### 5. ... How to build a bridge(4 points)

Imagine a cross section of a bridge as depicted in the picture. It consists of massless rods attached at the points $\bodA$, $\bodB$, $\bodC$, $\bodD$ and $\bodE$. Determine which rods would exhibit pressure forces and which pulling forces if a car of mass $m$ is placed on the rod $\bodBC$. You should use the picture to estimate the lengths of the rods. Bonus   Assume that the linear density of the rods is $λ$ instead of zero.

### P. ... Mrazík(5 points)

In the fairy tale Mrazik, Ivan fought several bandits, stole their clubs, and threw them so high up into the sky that they did not fall back until half a year later. What is the altitude the clubs had to reach in order to stay in the air for so long? Make a first guess and then go on and improve it. Carefully analyze all the approximations you made and explain why are these estimates most likely wrong. Furthermore, explain why it makes no sense for the clubs to fall back at the same spot where Ivan threw them.

### E. ... Fun with straws(8 points)

You can charge a regular plastic straw by rubbing it with a piece of fabric. This charge can be so large that the straw might even attach itself to a wall or a whiteboard. Explain this phenomena and estimate the charge you can put on a single straw. Hint   You might need to use two straws.

### S. ... More tokamaks(6 points)

* Using the expression for the frequency of impacts from the last part of this series, derive a formula for the diffusion coefficient of classical diffusion and calculate its value for a typical plasma in a tokamak.

• Derive a formula for the dependence of the fraction of captured particles on the ratio of the main and small plasma radius $r$ ⁄ $R$_{0}.
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