Problems of the Eötvös 2002 Physics Competition

1. We want to estimate the force exerted on the arms of a gymnast in the lowest point if he swings from a handstand into a great circle. Apply the following simple model: Fix at the end of a very long non-elastic rope a homogeneous metal rod of length l and mass m, and release it from its position shown in figure 1.a on page 169. Calculate what force exerted on the rope in the instant shown in figure 1.b. (The mass of the rope is negligible.)

2. In a closed round-bottom flask there is a small amount of water. Turning the flask upside down the water stands at about a 5 cm height in the neck of the flask. (The inner sizes are shown in figure 4 on page 170.)

After this we make the flask spin around its vertical axis in a way, that it turns three times a second. We make sure that the temperature stays constant everywhere along the wall of the flask. After a sufficiently long time a state of equilibrium is reached.

Make a schematic drawing about the position of the water inside the flask.

3. Two insulator hemispheric shells (e.g. two halves of a table-tennis ball) are placed near to each other according to figure 8.a on page 173 in a concentric arrangement. Charge them uniformly with electric charges Q and q respectively.

a) What force do the two bodies exert on each other?

b) Does the result change if the radius of one hemisphere is decreased to its half?