This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back — missed you this week. Here are the calculations for the tank and its supports: a) The volume of the tank. Step 1: Identify the dimensions of the tank. Length (L) = 8 m Width (W) = 5 m Height (H) = 2 m Step 2: Calculate the volume using the formula for a rectangular prism. V = L × W × H V = 8 m × 5 m × 2 m V = 80 m^3 The volume of the tank is 80 m^3. b) The capacity of the tank. Step 1: Convert the volume from cubic meters to liters. 1 m^3 = 1000 L Capacity = 80 m^3 × 1000 L1 m^3 Capacity = 80000 L The capacity of the tank is 80000 L. c) Mass of the fuel in the tank when full. Step 1: Identify the density of petrol and the volume of the tank. Density of petrol () = 8.8 kg/m^3 Volume of tank (V) = 80 m^3 (from part a) Step 2: Calculate the mass of the fuel using the density formula. m_fuel = × V m_fuel = 8.8 kg/m^3 × 80 m^3 m_fuel = 704 kg The mass of the fuel in the tank when full is 704 kg. d) The total weight needed to be supported by a constructed steel support. Step 1: Identify the weight of the tank and the mass of the fuel. Weight of the tank (W_tank) = 500 N Mass of fuel (m_fuel) = 704 kg (from part c) Assume acceleration due to gravity (g) = 9.81 m/s^2. Step 2: Calculate the weight of the fuel. W_fuel = m_fuel × g W_fuel = 704 kg × 9.81 m/s^2 W_fuel = 6906.24 N Step 3: Calculate the total weight to be supported. W_total = W_tank + W_fuel W_total = 500 N + 6906.24 N W_total = 7406.24 N The total weight needed to be supported is 7406.24 N. e) The tensile stress of the steel support when carrying the tank full of fuel. Step 1: Identify the total weight, number of supports, and dimensions of each support. Total weight (W_total) = 7406.24 N (from part d) Number of supports = 4 Diameter of each support (d) = 32 mm = 0.032 m Step 2: Calculate the force on each support. F_one = W_totalNumber of supports F_one = 7406.24 N4 F_one = 1851.56 N Step 3: Calculate the cross-sectional area of one support. Radius (r) = (d)/(2) = 0.032 m2 = 0.016 m A_one = r^2 A_one = × (0.016 m)^2 A_one = × 0.000256 m^2 A_one ≈ 0.000804247 m^2 Step 4: Calculate the tensile stress on each support. = F_oneA_one = 1851.56 N0.000804247 m^2 ≈ 2302200 Pa ≈ 2.30 × 10^6 Pa ≈ 2.30 MPa The tensile stress of the steel support is approximately 2.30 MPa. Send me the next one 📸