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FIRST PHYSTECH INTERNATIONAL OLYMPIAD IN PHYSICS

FIRST PHYSTECH INTERNATIONAL OLYMPIAD IN PHYSICS
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.

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