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
Here are the solutions to Question 7: Given: Diameter, d = 18 mm Load, F = 55 kN Extension, L = 0.190 mm Original length, L_0 = 202 mm Step 1: Convert given values to SI units. d = 18 mm = 0.018 m F = 55 kN = 55 × 10^3 N L = 0.190 mm = 0.190 × 10^-3 m L_0 = 202 mm = 0.202 m 7.1.1 The stress in the bar Step 2: Calculate the cross-sectional area (A) of the bar. The bar is round, so its area is: A = ( d^2)/(4) A = (0.018 m)^24 A = ( (0.000324))/(4) m^2 A ≈ 2.54469 × 10^-4 m^2 Step 3: Calculate the stress () in the bar. Stress is defined as force per unit area: = (F)/(A) = 55 × 10^3 N2.54469 × 10^-4 m^2 ≈ 216130000 Pa ≈ 216.13 MPa The stress in the bar is 216.13 MPa. 7.1.2 The strain in the bar Step 4: Calculate the strain () in the bar. Strain is defined as the change in length divided by the original length: = ( L)/(L_0) = 0.190 mm202 mm ≈ 0.00094059 The strain in the bar is 0.00094059. 7.1.3 Young's modulus Step 5: Calculate Young's modulus (E). Young's modulus is the ratio of stress to strain: E = ()/() E = 216.13 × 10^6 Pa0.00094059 E ≈ 229782000000 Pa E ≈ 229.78 GPa Young's modulus is 229.78 GPa. What's next?