Search

At the speeds close to speed of light you can observe contraction of objects. On the other hand the objects looks longer, then they are in reality (try to follow and compare light beams from closer and distant part of a body). Calculate, if these two effect will cancel for a sphere.

An rich space-tourist has payed for a trip to the deep space. The Racket flies from the Earth and is accelerating with constant acceleration $a$, which can be verified by dropping a small ball. He is quite bored and therefore is watching disappearing Earth through the back window. After some time (how long it will take?) he starts to see, that something is not right. The Earth is not getting much smaller, and he deduces, that the space ship is slowing down, which does not correspond with the constant acceleration of $a$. However the tourist is not as good physicist and goes to file complain with captain. What should the captain to tell him?

Assume, that the tourist see whole electromagnetic spectrum and will survive the observation.

Rama travels between the stars in such way, that one half of time is constantly accelerating and second half of time is slowing down. Currently the Rama is on parabolic trajectory around the Sun with peak on Earth orbit. It gets energy from Sun light. Its surface absorbs 80 % of incident energy. Will it get enough energy to get to Sirius, which is in distance of 12 light years in less than 24 years?

Two identical charges are at the end of stiff non-conductive rod. What power will be needed to rotate rod at constant angular speed with axis going through the middle of the rod? The friction is negligible

Lets have a lens of focal length $f$. The light source is at optical axis in distance $a>f$ from the lens. The light source starts moving at constant speed towards the lens. Calculate the speed of movement of the image of the light source. Decide, if this speed can be bigger than the speed of light. Would it contradict special theory of relativity?

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.

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

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.

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.