June 25  October 15 

FIRST PHYSTECH INTERNATIONAL OLYMPIAD IN PHYSICS
 Problems
 NOTE: ALL answers must be in SI, System International. Assume g=10 m/s2.

Bucket with fruits is being suspended on two weightless springs in two different configurations.
In the first case the springs are connected to bucket in parallel and exert restoring forces of 20
N and 30 N (configuration pictured on the left). Find forces (in newtons) the springs will exert
when the same bucket is suspended as in the configuration shown to the right (Fig. 1)? Figure 1
The glass with vertical (and very thin) walls is filled with water (see Fig.2). The bottom of the glass
has area S=30 cm2. An iron ball with volume V = 1.5 cm3 is being put into the glass. Find the
increment (in pascals) of pressure due to the ball near the bottom of the glass.
Figure 3
A piston with mass m = 1 kg and area S=50 cm2 covers a cylinder containing air (see Fig. 3). The
piston can slide inside the cylinder without friction. A weight of 6 kg is being put atop of the
piston. In how many times will the volume of the air under the piston shrink after the
thermodynamic equilibrium is achieved?
Caution : be careful with the analysis!
A locomotive accelerates a train of identical railway carts. The carts are numbered consequently
with the cart next to locomotive having the number 1. The tension in the connection between
the carts with numbers 4 and 5 is three times bigger than the tension in the connection
between the carts with numbers 14 and 15. What's the number of the last cart? There is the
resistance to the train's motion.
Figure 4
R1 = 20 W and R2 are resistances in the circuit on the Figure 4. Find the R2 (in W) if the capacitor (to
the left of the 2E battery on the picture) is not charged. Neglect the internal resistances of the
batteries.
Figure 5
A mass m is put atop of a mass M. The mass M vibrates horizontally without friction with the
amplitude A = 8 cm at the end of a horizontal Hookean spring. Find the minimal coefficient of
friction such that m is not moving with respect to M.