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• Jakub's breakfast

Every morning Jakub enjoys his favourite cereals which he pours into a bowl of milk. Assume the bowl is of circulur frustum shape with upper and lower radius $R$ and $r$ respectively ($R$ \geq r$)$, that the cereals are little solid spheres and that before he puts the cereals into the bowl there is milk of height $h$. What is the maximum amount of cereals he can fit into the bowl? You also know that the fraction of volume the cereals occupy inside a fully filled box is $\kappa$.

• Magnetic monopole

Let's have a metal plate magnetized in such a way that the upper and lower sides are the north and south poles respectively. We use these plates to create two semispheres with the outer side being the north pole. Now, if we glue these two semispheres together, we effectively get a magnetic monopole, which, as we know, can not exist in our world. Where did we go wrong?

Lukáš found an old sofa spring of force constant $k$, coil radius $r$, length $l$ and the number of coils $n$. Since he was bored, he connected the spring to electric current $I$. How did the action change the force constant of the spring?

Where does permanent magnet take the energy to lift stuff? We know, that magnetic force cannot do any work. Lorenz equation$\vect{F}$ = q ( \vect{v}\times \vect{B})$ says, that magnetic force is perpendicular to the velocity of moving charge and therefore only change its direction.

[on request you can get a piece of magnet] Measure the dependence of magnetic force between 2 magnets.

Hint: place a piece of paper between magnets and measure the force needed to separate the magnets.