This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — Here are the solutions for the questions from Section III, Option 1: 1. (a) (i) The completed diagram showing the energy flow sequence in a hydroelectric power plant is: Gravitational potential energy of water in the reservoir → Kinetic energy of water in the turbine → Mechanical energy of the turbine → Electrical energy from the generator. 1. (a) (ii) Step 1: Convert the volume of water discharged per second to mass per second. Given volume V = 150 cm^3/s. Convert cm^3 to m^3: 150 cm^3 = 150 × (10^-2 m)^3 = 150 × 10^-6 m^3 = 1.5 × 10^-4 m^3 Density of water = 1000 kg/m^3. Mass of water discharged per second (m)/(t) = × (V)/(t): (m)/(t) = 1000 kg/m^3 × 1.5 × 10^-4 m^3/s = 0.15 kg/s Step 2: Calculate the input power (gravitational potential energy per second). Given height h = 38 m and acceleration due to gravity g = 9.81 m/s^2. P_input = (mgh)/(t) = ((m)/(t))gh P_input = 0.15 kg/s × 9.81 m/s^2 × 38 m = 55.803 W Step 3: Calculate the power output from the turbine. Given efficiency = 72\% = 0.72. P_output = P_input × P_output = 55.803 W × 0.72 = 40.17816 W Rounding to three significant figures: The power output from the turbine is 40.2 W. 1. (a) (iii) Fossil fuels are non-renewable energy sources formed over millions of years from the decomposition of ancient organic matter (e.g., coal, oil, natural gas). Bio-fuels are renewable energy sources derived from recently living organisms or their metabolic byproducts (e.g., ethanol from corn, biodiesel from vegetable oils). 1. (b) (i) One advantage nuclear fusion has over nuclear fission is that it produces less radioactive waste with shorter half-lives, and the fuel sources (isotopes of hydrogen) are abundant. 1. (b) (ii) The fusion reaction is: ^2_1H + ^3_1H → ^4_2He + ^1_0n + E Given masses: Mass of ^2_1H = 2.015 u Mass of ^3_1H = 3.017 u Mass of ^4_2He = 4.004 u Mass of ^1_0n = 1.009 u Step 1: Calculate the total mass of the reactants. M_reactants = mass(^2_1H) + mass(^3_1H) = 2.015 u + 3.017 u = 5.032 u Step 2: Calculate the total mass of the products. M_products = mass(^4_2He) + mass(^1_0n) = 4.004 u + 1.009 u = 5.013 u Step 3: Calculate the mass defect ( m). m = M_reactants - M_products = 5.032 u - 5.013 u = 0.019 u Step 4: Convert the mass defect to energy ( E) using the conversion factor 1 u = 931.5 MeV. E = m × 931.5 MeV/u E = 0.019 u × 931.5 MeV/u = 17.7005 MeV Rounding to three significant figures: The energy released is 17.7 MeV. Send me the next one 📸