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### (10 points)3. Series 36. Year - 5. guitar

Assume you have a guitar that is perfectly tuned at room temperature. By how many semitones (in tempered tuning) will the individual strings be out of tune if we move to a campfire, where it is cooler by $10 \mathrm{\C }$? Will the guitar still sound in tune? The distance between the string attachment points is $d = 65 \mathrm{cm}$. The strings have a density $\rho = 8~900 \mathrm{kg.m^{-3}}$, a Young's modulus of elasticity $E = 210 \mathrm{GPa}$ and a thermal expansion coefficient $\alpha = 17 \cdot 10^{-6} \mathrm{K^{-1}}$.

Honza's guitar is out of tune again.

### (9 points)3. Series 36. Year - P. absurd pendulum

What phenomena can affect the measurement of gravitational acceleration using a pendulum? Estimate how many valid digits your result would have to contain to measure them. Consider also the phenomena that you usually neglect.

Kačka was wondering what she could write in the discussion.

### (12 points)2. Series 36. Year - E. the loudspeaker

Measure the dependence of sound intensity emitted by your loudspeaker/mobile phone/computer on the distance from the source. Furthermore, determine the dependence of sound intensity on the settings of the output volume. Do not forget to fit the data.

Jarda cannot hear much in the back row.

### (12 points)6. Series 35. Year - E. minute

Create a device that can measure one minute as accurately as possible. You are not allowed to use any time measuring devices for calibration when designing your own. After you finalize your device, use a stopwatch to determine „your minute“ accuracy.

Bonus: Measure ten minutes.

Matěj allways arrives at the train station at most one minute before the train's departure, even if it's got a half hour delay.

### (10 points)6. Series 35. Year - P. torrential rain

Is it convenient to hide from the rain in the woods? Create a suitable model describing this issue. Consider, for example, foliage density, and the intensity and duration of the rain. Describe how long after the rain starts, the drops from the leaves start to fall to the ground, as well as how long after the rain ends, it stops raining in the woods, and so on.

Lucka ran through the woods and got completely wet.

### (3 points)4. Series 35. Year - 1. planet dependent units

Units of many physical quantities on Earth are historically tied to the properties of our planet. What would be the units such as meter, knot or atmosphere, if we defined them using the same methodology as on Earth, but while living on Mars? Derive both the ratios between „terran“ and „martian“ units and their values in SI units.

Karel was pondering about non-SI units.

### (12 points)4. Series 35. Year - E. Useful Coin

Measure at least three physical properties of the smallest coin of legal tender in your country. We consider macroscopic dimensions as one property. We evaluate not only the accuracy of the measurement and the detail of the description but also the originality in the selection of quantities.

Karel wanted the participants to observe the money.

### (11 points)4. Series 35. Year - P. winter wonderland

Think about the possibilities for simplification of movement of a human through a landscape during winter. Consider different terrain inclinations, types of snow („powder“, wet snow, melted and resolidified snow, ice, \dots ), and equipment (snowshoes, skis, crampons, ice skates, \dots ). Describe the physical principle behind each type of equipment, and based on this principle, determine which type is best suited for which environment.

Dodo wishes for a proper winter at last.

### (10 points)3. Series 35. Year - 5. blacksmith's

Gnomes decided to forge another magic sword. They make it from a thin metal rod with radius $R=1 \mathrm{cm}$, one end of which they maintain at the temperature $T_1 = 400 \mathrm{\C }$. The rod is surrounded by a huge amount of air with the temperature $T_0 = 20 \mathrm{\C }$. The heat transfer coefficient of that mythical metal is $\alpha = 12 \mathrm{W\cdot m^{-2}\cdot K^{-1}}$ and the thermal conductivity coefficient is $\lambda = 50 \mathrm{W\cdot m^{-1}\cdot K^{-1}}$. The metal rod is very long. Where closest to the heated end can gnomes grab the rod with their bare hands if the temperature on the spot they touch is not to exceed $T_2 = 40 \mathrm{\C }$? Neglect the flow of air and heat radiation.

Matěj Rzehulka burnt his fingers on metal.

### (3 points)1. Series 35. Year - 2. two-second rule

The two-second rule is a driving principle which states that a safe time distance between two vehicles is at least two seconds long. Suppose a traffic junction where a $n_1$-lane road changes into a $n_2$-lane one. The maximum allowed speed in the first section is $v_1$. What is the lowest possible maximum speed $v_2$ that can be allowed in the second section so that there is no traffic jam and everyone can follow the two-second rule? The average length of a car is $l$ and it can change its speed in leaps.

Honza was stuck in the traffic jam for too long.

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