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.
ScanSolve AI Answer
To check the condition of resistance, we need to calculate the stress on the supports and compare it to an allowable stress for the material. Since no allowable stress is provided, we will calculate the stress and state that further verification requires this value. Step 1: Calculate the volume of petrol in the tank. The internal dimensions are length L = 8 m, width W = 5 m, and height H = 2 m. V = L × W × H = 8 m × 5 m × 2 m = 80 m^3 Step 2: Calculate the mass of the petrol. The density of petrol is = 8.8 kg/m^3. m_petrol = × V = 8.8 kg/m^3 × 80 m^3 = 704 kg Step 3: Calculate the weight of the petrol. Using the acceleration due to gravity g = 9.81 m/s^2. W_petrol = m_petrol × g = 704 kg × 9.81 m/s^2 = 6906.24 N Step 4: Calculate the total weight supported by the four supports. The weight of the tank is W_tank = 500 N. W_total = W_tank + W_petrol = 500 N + 6906.24 N = 7406.24 N Step 5: Calculate the total cross-sectional area of the four supports. Each support has a diameter D = 32 mm = 0.032 m. The radius of one support is R = D/2 = 0.032 m / 2 = 0.016 m. The cross-sectional area of one support is: A_one support = R^2 = (0.016 m)^2 = × 0.000256 m^2 ≈ 0.00080425 m^2 Since there are four supports, the total cross-sectional area is: A_total = 4 × A_one support = 4 × 0.00080425 m^2 ≈ 0.003217 m^2 Step 6: Calculate the compressive stress on the supports. Stress is defined as force per unit area. = W_totalA_total = 7406.24 N0.003217 m^2 ≈ 2302390 Pa Converting to megapascals (MPa): ≈ 2.30 MPa Step 7: Check the condition of resistance. The condition of resistance is verified if the calculated stress () is less than or equal to the allowable stress (_allowable) for the material of the supports. _allowable Since the problem does not provide an allowable stress value for the support material, we cannot definitively verify the condition of resistance. We have calculated the stress on the supports. The stress on the supports is approximately 2.30 MPa. To verify the condition of resistance, this calculated stress must be compared to the allowable stress of the support material, which is not provided in the problem statement. What's next?