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).
- Calculate the speed \(v\) of the outflowing water at the end of the tube.
- Calculate the pressure \(p\) in the first part of the tube.
Task 2 - The seconds pendulum
The seconds pendulum is a pendulum whose length is set so that the period is equal to 2 seconds.
- Calculate the length of the seconds pendulum, assume gravitational acceleration as \(g = 10\text{ m}\,\text{s}^{−2}.\)
- Calculate the total energy of the second pendulum, if the mass is equal \(m = 2\text{ kg}\) and the initial deflection is \(\varphi_0 = 2\text{°}\)
- 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 \(U = 10\text{ V.}\)
- Calculate the total capacity.
- Calculate the voltage at the capacitor \(C_3.\)
- Calculate the total bound charge of all capacitors.
Task 4 - Weight of the atmosphere
From the pressure acting to the Earth's surface calculate
- The total weight \(m\) of the atmosphere.
- The total amount of matter \(s\) of the atmosphere.
- The total amount of particles \(N\) in the the atmosphere.
- The teoretical height \(h\) of the the atmosphere with assumption that their concentration \(n = {N / V} = \text{const.}\)