1. Invent it yourself
“Magnetic suspension” may be used in high speed trains of the future. Design and make an experimental model of such a suspension.
Circus actors often perform riding tricks on unicycles. There may be a range of wheel sizes. What is the largest possible diameter of the wheel?
3. The dam
There is a saying in Russian, “money goes like water through sand.” However, sand dams hold water. What should be the thickness of the dam in order to retain water whose level behind the dam is 10 m?
A special swing (trapeze) is used to train air and space pilots. This device is able to make a loop around the horizontal axis. What minimum time is necessary to build up the motion of the swing from the rest at the equilibrium position, to an amplitude of 180°?
5. High jumper
There is a saying in Russian, “one cannot jump over his own head.” But many high jumpers do this easily. Estimate the maximum height a man will be able to get over in high jumps and in pole vaulting, in the year 2000?
What is the minimum necessary mass of “sulfur” in the head of a match to make it blaze up?
7. Steel rod
A steel rod 8 mm in diameter is bent at an angle of 90°. What is the position and value of the maximum local temperature rise?
A tall cylindrical vessel is partly filled with water and is put with its open end into a wide-mouthed vessel which is also filled with water. If we get the water to the boiling point and then cool it down, the level of the water in the cylinder will change. Study experimentally the correlation between the height of the water column in the cylinder and the temperature, under repeated heating and cooling. Explain the phenomena observed.
There is a fountain called Samson in Peterhof. Water spurts out of it to a height of more than 20 meters. Suggest how to construct a fountain YPTon which could provide the maximum height of the spurt at a given power of the pump. What is the height if the power of the pump is 1 kW?
A thin brass wire can be used as a fuse. Find the correlation between the critical current and the wire diameter.
11. Hopfield model
Develop the algorithms for storing images in computer memory and for distinguishing them.
Butterflies find each other by smell. Estimate the “transmitter” strength and the “receiver” sensitivity of butterflies.
13. Topsy-turvy world
Some medical publications state that 0—2 months old babies see the objects around them up side down. Give your arguments “for or against.”
A laser beam is directed perpendicularly to the wall of a transparent glass tank filled with water. If the beam passes through the tank above or below the level of the water in the tank, we can observe a spot on the screen behind the tank. If the beam passes along the level of the water we observe a vertical line. Explain the origin of the line and calculate its parameters.
15. Incandescent lamp
Estimate the amplitude of temperature variations of the spiral filament of a light bulb powered by alternating current.
16. The depth of field
Find experimentally the dependence of the depth of field of a camera on the aperture diameter of the objective. Give the theoretical explanation of the dependence obtained.
17. Rain bubbles
Some people suppose that if there are bubbles on the surfaces of water pools during the rain, the rain will be long, but others think they are a sign of the close end of the rain. Who is right?