A chandelier of mass 250 kilograms is hung vertically from a ceiling using a 1.25 meters long brass rod of square cross-section of sides 0.4 centimeters each. How much will the rod stretch when the ch

The stretching of the rod can be calculated using the formula for the Young's modulus of elasticity: stress = (force/area) strain = (stress / Young's modulus) where stress is the amount of force exerted on the rod per unit area, and strain is the resulting deformation of the rod. The weight of the chandelier is given by: weight = mass x gravity = 250 kg x 9.8 m/s^2 = 2450 N The force exerted on the rod is equal to the weight of the chandelier, so we can calculate the stress: stress = force / area = 2450 N / (0.004 m^2) = 6.125 x 10^6 Pa The Young's modulus of brass is \approx imately 100 x 10^9 Pa, so we can calculate the strain: strain = stress / Young's modulus = (6.125 x 10^6 Pa) / (100 x 10^9 Pa) = 0.00006125 The minimum breaking load of the rod is given by: breaking load = ultimate tensile stress x area where ultimate tensile stress is the maximum stress the rod can withstand without breaking. The ultimate tensile stress of brass is \approx imately 400 x 10^6 Pa. So the breaking load is: breaking load = (400 x 10^6 Pa) x (0.004 m^2) = 1600 N To calculate the factor by which the breaking load exceeds the weight of the chandelier: factor = breaking load / weight = 1600 N / 2450 N = 0.65 So the breaking load is 0.65 times greater than the weight of the chandelier. Therefore, the rod will stretch by a small amount, and the breaking load is greater than the weight of the chandelier by a factor of 0.65.