Review of Physics 2 - Exam, muster
Semestr: sommer, 20XX/XX, Tutor: Martin Žáček, Date: 20XX-XX-XX
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.
\(\)Calculate the difference in the river levels before and after the hydroelectric power station, where the current flow rate is \(I = 400\text{ m}^3\text{s}^{−1},\) the output power is \(P = 2\text{ MW,}\) and efficiency of the power plant is \(\eta=75\text{ }\%.\) Assume gravitational acceleration as \(g = 10\text{ m}\,\text{s}^{−2}.\)
The linear harmonic oscillator with the amplitude of displacement \(y_0 = 12\text{ cm}\) has a period of movement \(T = 40\text{ ms}\). The rigidity of the oscillating system is \(k = 6\text{ N}\text{m}^{−1}.\) Calculate the total mass, maximal velocity, maximal acceleration, and total energy of the oscillator.
Three capacitors with capacities \(C_1 = 1\text{ }\mu\text{F},\) \(C_2 = 3\text{ }\mu\text{F}\) and \(C_3 = 20\text{ }\mu\text{F}\) are connected serial. What is the total capacity? What is the total bound electric charge, if the capacities are charged to voltage \(U = 200\text{ V}\)? how is the voltage divided into individual capacities?
Inside the closed glass tube with a volume of \(V = 3\text{ cm}^3\) is located pure water vapor with the pressure \(p = 2\,000\text{ Pa}\) and the temperature \(ϑ = 20\text{ °C}.\) Calculate their total mass, molar mass, density and number of molecules of the vapor. Relative atomic mass let's assume as 1 for hydrogen and 16 for oxygen; the molar gas constant is \(R = 8.3\text{ J}\,\text{K}^{-1}\,\text{mol}^{-1},\) Avogadro constant is \(N_\text{A} = 6.6\cdot10^{23}\text{ mol}^{-1},\) let's assume the behavior of the vapor as an ideal gas.