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## relativistic physics

### 6. Series 18. Year - 2. how to make a black hole

When the star is compressed (or any other body) into a sphere of radius $r_{g}$, the black hole is created. So called *Schwarzschild's radius* $r_{g}$ can be interpreted in classical physics as a radius of a body of mass $M$, where the exit velocity is equal to the speed of light $c)$.

Knowing the mass of the star $M$ calculate Schwarzschild radius $r_{g}$ and critical density of the star $ρ$, at which it collapses into black hole. Solve for arbitrary values and then for the masses of Earth, Sun and the galaxy nucleus 100 billions heavier than Sun.

Jarda

### 6. Series 18. Year - E. catch a photon

Measure the speed of light in vacuum. Use any method, for example use microwave oven.

Co jiného dát jak exp do roku fyziky.

### 6. Series 18. Year - P. trip to Stonehenge

Imagine a trip in a rocket over Stonehenge. The Stonehenge is made from stone blocks in the the shape of regular dodecagon (object with 12 corners – see figure 2) of radius 200. You fly above the axis $x$ at the height $z=50$ and are looking in horizontal direction. When you are in the point of coordinates ( $-200$, $0)$ and ( 0$$, $0)$ you see the world exactly as in the image 6 respectively, while both of you have same eyes (at least the view angle:-). Calculate (approximately) the ratio of the speed of the rocket and the speed of light from the images.

Matous.

### 4. Series 18. Year - 3. limousine in the shed

One of the winners of Superstar (equivalent of 'You are a star'/'Eurovision song contest') has suddenly a problem. His new limousine is too long to fit in his old shed. His friend, student of physics and lover of Albert Einstein work, suggested that if the limousine drives fast it contracts in the frame of stationary observer. And if the speed is large enough, it will fit into the shed.

At the beginning and the end of shed are trap doors which fall when the limousine is all inside. But from the point of view of driver the in the limousine, due to the length contraction the shed is shorter and the limousine cannot fit in!

Decide, if is possible to park the limousine in the shed.

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