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### (10 points)6. Series 37. Year - S. illuminating units

- There is an isotropic (its properties depend on the direction) light source perpendicularly above the center of a table. The center of the table is illuminated by $E_1=500 \mathrm{lx}$. The edge of the table is $R=0{,}85 \mathrm{m}$ from the center and is illuminated by $E_2=450 \mathrm{lx}$. How far from the center of the table is the light source? What is its luminous intensity?
- Measure the luminous intensity of your favorite lamp using one of the visual photometric methods mentioned in the series. Use a tea candle made of white paraffin wax as the unit of luminosity. Remember to describe your experimental setup and attach a photograph or a diagram. How accurate was your results
- Let's construct the „Earth“ system of units using the values of the mean density of the Earth, the standard atmospheric pressure at sea level, the standard gravity of Earth, and the magnetic induction measured at the Earth's south magnetic pole $B_0=67 \mathrm{\mu {}T}$. Calculate the values of second, meter, kilogram, and ampere in this system and find the values of the speed of light, Planck's constant, gravitational constant, and vacuum permeability in „Earth“ units.

### (10 points)5. Series 37. Year - P. CERN on Mercury?

On the surface of Mercury, the atmosphere is approximately as dense as the vacuum tubes at CERN, in which scientists conduct experiments to investigate particle physics. Would it be a good idea to move the experiments to Mercury and perform them on its surface? Mention as many arguments as you can and elaborate on them.

**Bonus::** Suggest the best place to build an accelerator.

### (10 points)4. Series 37. Year - P. efficient lighting

Describe the basic physical principles of the various methods of producing artificial lighting. Calculate the efficiency for at least three of them, i.e. how much energy supplied is actually converted into visible light. Compare with actual data.

Jarda was replacing his grandmother's lamp switch.

### (3 points)3. Series 37. Year - 1. it's too dry in here

Danka has a humidifier in her dorm room, which evaporates water from its boiling point to create warm steam. The device can hold a maximum of $V = 3,8 \mathrm{l}$ of water, which it uses up in $t = 24 \mathrm{h}$. What is its efficiency, i.e., what fraction of the energy drawn from the electrical grid it uses to convert the water to steam? The input power of the humidifier is $P = 260 \mathrm{W}$, and Danka put water at $T_0 = 20 \mathrm{\C }$ inside. All the necessary properties of water can be looked up.

Danka has to use a humidifier in her dorm room during winter.

### (10 points)2. Series 37. Year - P. height of mountains

Which factors influence the height of mountains on different planets? Make an attempt at a quantitative estimate. You can consider the highest mountains on the Earth, Mars, and other known planets.

Karel was admiring Olympus Mons.

### (10 points)1. Series 37. Year - P. rocket

Using current technology, how much fuel would it take to carry an object of mass $m=1 \mathrm{kg}$ into low Earth orbit?

The leprechaun wanted to save on rocket fuel.

### (3 points)6. Series 36. Year - 1. canoeing mystery

In sunny summer weather, we observe interesting wind behavior on the river during the day. It is cold in the morning at sunrise, and sometimes there is even morning fog. The fog then quickly dissipates, and the air temperature rises. A light wind then blows up the river. In the evening, the situation calms down, and the wind direction turns downstream as the sun lowers toward the horizon. What causes this phenomenon? Explain the ongoing processes in these two cases.

Katarína was floating down the river and observing.

### (7 points)6. Series 36. Year - 4. light faster than light

There is a laser in the distance $L$ from a large screen. Initially, the laser shines on the screen so that the distance from a laser spot on the screen to the laser is $R > L$. Then at the time $t=0 \mathrm{s}$, we begin to rotate the laser at a uniform angular speed $\omega $. Consequently, the distance of the spot on the screen from the laser decreases to $L$ and then increases back to $R$. What is the speed of this laser spot relative to the screen? Is it possible that the spot moves at a speed greater than the speed of light in a vacuum? Is there a limit, can it be infinite? How (qualitatively) does this speed depend on the spot's position on the screen? The whole apparatus is in a vacuum.

Marek J. wanted to verify statements about the apparent surpassing of the speed of light.

### (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.