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 \(h = 0.5\text{ m.}\) At the bottom is connected a horizontal tube consisting of two parts. The first one has cross-section \(S_1 = 1\text{ cm}^2,\) the second one \(S_2 = 0.5\text{ cm}^2\) 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 \(\rho = 1\,000\text{ kg}\,\text{m}^{-3}\) and the gravity acceleration \(g = 10\text{ m}\,\text{s}^{−2}.\)

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 \(g = 10\text{ m}\,\text{s}^{−2}.\)
  2. Calculate the total energy of the second pendulum, if the mass is equal \(m = 2\text{ kg}\) and the initial deflection is \(\varphi_0 = 2\text{°}\)
  3. What is the ratio of the lengths \({l_\text{E} / l_\text{M}}\) and total energies \({E_\text{E} / E_\text{M}}\) for pendulums located on Earth and the Moon with equal initial deflections \(\varphi_0 = 2\text{°}\)? Assume the ratio of accelerations as \({g_\text{E} / g_\text{M}} = {9.81 / 1.62} = 6.056 \approx 6.\)

Task 3 - Capacitors

Three capacitors with capacities \(C_1 = 5\text{ }\mu\text{F},\) \(C_2 = 3\text{ }\mu\text{F}\) and \(C_3 = 2\text{ }\mu\text{F}\) 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 \(U = 10\text{ V.}\)

  1. Calculate the total capacity.
  2. Calculate the voltage at the capacitor \(C_3.\)
  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 \(n = {N / V} = \text{const.}\)
Assume the behavior of the atmosphere as an ideal gas with the constant pressure \(p = 10^5\text{ Pa}\) 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 \(N_\text{A} = 6.6\cdot10^{23}\text{ mol}^{-1}.\)