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Review of Physics 2 - Exam

Semestr: sommer, 2019/20, Tutor: Martin Žáček, Date: 2020-07-03

For every task is for correct general result 1 point, for correct numerical result 1 point and correct way of solution for 3 points, i.e. maximum of possible points is 5 per task and maximum 20 points for the test. Numerical results estimate with the 1-digit of precision.

Task 1 - Water flowing out of a vessel

A vessel is filled with water to the height h=0.5 m. At the bottom is connected a horizontal tube consisting of two parts. The first one has cross-section S1=1 cm2, the second one S2=0.5 cm2 and its end is open so water can flow freely out of the vessel (see picture).

  1. Calculate the speed v of the outflowing water at the end of the tube.
  2. Calculate the pressure p in the first part of the tube.
Calculate with the density of water ρ=1000 kgm3 and the gravity acceleration g=10 ms2.

Task 2 - The seconds pendulum

The seconds pendulum is a pendulum whose length is set so that the period is equal to 2 seconds.

  1. Calculate the length of the seconds pendulum, assume gravitational acceleration as g=10 ms2.
  2. Calculate the total energy of the second pendulum, if the mass is equal m=2 kg and the initial deflection is φ0=2°
  3. What is the ratio of the lengths lE/lM and total energies EE/EM for pendulums located on Earth and the Moon with equal initial deflections φ0=2°? Assume the ratio of accelerations as gE/gM=9.81/1.62=6.0566.

Task 3 - Capacitors

Three capacitors with capacities C1=5 μF, C2=3 μF and C3=2 μF are connected serio-paralell where the first one is connected paralel with the remaining two, which are connected in series (see picture). Initially, the capacitors were not charged. Then was connected to a source with voltage U=10 V.

  1. Calculate the total capacity.
  2. Calculate the voltage at the capacitor C3.
  3. Calculate the total bound charge of all capacitors.

Task 4 - Weight of the atmosphere

From the pressure acting to the Earth's surface calculate

  1. The total weight m of the atmosphere.
  2. The total amount of matter s of the atmosphere.
  3. The total amount of particles N in the the atmosphere.
  4. The teoretical height h of the the atmosphere with assumption that their concentration n=N/V=const.
Assume the behavior of the atmosphere as an ideal gas with the constant pressure p=105 Pa and the constant temperature ϑ = 20\text{ °C}. Calculate with the Earth's radius R = 64\cdot10^5\text{ m}. Relative atomic mass use as 14 and 16 for nitrogen and oxygen respectively; atmosphere take as compoud of two-atomic molecules with the N:O ratio as 4:1; the molar gas constant is R_\text{m} = 8.3\text{ J}\,\text{K}^{-1}\,\text{mol}^{-1} and Avogadro constant is N_\text{A} = 6.6\cdot10^{23}\text{ mol}^{-1}.