# 4. Series 31. Year

* Post deadline: 26th February 2018*

* Upload deadline: 27th February 2018 11:59:59 PM*

### (3 points)1. ice-cream

Estimate how many grams of ice-cream is possible to be made out of $5 \mathrm{l}$ of liquid oxygen with temperature $-196 \mathrm{\C }$ and unlimited amount of milk and cream with room temperature $22 \mathrm{\C }$? Let's suppose that ice-cream consists of milk and cream only (same mass of both ingredients) and the temperature of the ice-cream should be $-5 \mathrm{\C }$. Use average heat capacity $c\_m = 3{,}45 \mathrm{kJ\cdot kg^{-1}\cdot K^{-1}}$ for milk and $c\_s = 4{,}45 \mathrm{kJ\cdot kg^{-1}\cdot K^{-1}}$ for cream (despite the fact that changes considerably in this temperature range). Find other needed quantities on the internet by yourself.

Michal got a taste for ice-cream.

### (3 points)2. autism

What is the least number of fidget spinners such that the day on Earth is extended by $1 \mathrm{ms}$ when we spin all of them? Try to guess all the missing quantities.

Matěj wants more time for spinning.

### (6 points)3. weirdly shaped glass

We have a cylindrical glass with a small hole at the bottom of the glass. The surface area of the hole is $S$. The glass is filled with water and the water flows into a second glass by itself. The second glass has no holes. What shape should the second glass have so that the water level grows linearly inside it? The glass is supposed to have cylindrical symmetry.

**Bonus:** The bottom of both glasses is at the same high and the glasses are connected by the hole.

Karel was watching how the glass is being filled.

### (7 points)4. solve it yourself

We have a black box with three outputs (A, B, and C). We know that it consists of $n$ resistors with the same resistance but we don't know the circuit diagram. So we measure the resistance between each pair of outputs $R\_{AB} = 3 \mathrm{\Omega }$, $R\_{BC} = 5 \mathrm{\Omega }$ a $R\_{CA} = 6 \mathrm{\Omega }$. Your task is to find the minimum possible $n$ and calculate the corresponding resistance of one resistor.

Matěj solved it quickly.

### (7 points)5. impossibility of infection

Imagine that we accelerate a usually sized bacteria into velocity $v = 50 \mathrm{km\cdot h^{-1}}$ in the horizontal direction and we let it move freely in air. Estimate the distance traveled by the bacteria before it stops.

The result might be surprising for you. How is it possible to become infected this way with a bacterial infection? Discuss why is it possible despite the result.

Karel was watching TED-Ed on Youtube.

### (9 points)P. Voyager II and Voyager I live!

We have a satellite and we want to launch it out of the Solar System. We launch it from Earth's orbit so that after some corrections of the trajectory it gets a velocity which is higher than the escape velocity from the Solar System. What is the probability that the satellite will collide with some cosmic material with higher diameter that $d=1 \mathrm{m}$ before leaving the Solar System.

Karel was wondering why NASA doesn't consider this possibility…

### (12 points)E. heft of a string

Measure the length density of the catgut which arrived to you together with the tasks. You are forbidden to weigh the catgut.

**Hint:** You can try to vibrate the string.

Mišo wondered about catguts on ITF.