numericals on solid mechanics

NAMDEO PHYSICS MECHANICAL PROPERTIES OF SOLIDS (Numerical) A steel wire 3m long when subjected to a tensile load of 40 kg f extends through 6 cm. If Y of steel is 2 × 1011 Nm-2, calculate (i) stress (ii) strain (iii) area of cross section of wire. Two wires are made of the same metal. The length of the first wire is half of the second wire and its diameter is double that second wire. If equal loads are applied in both the wires, find the ratio of increase in their lengths. Calculate the force required to increase the length of a steel wire of cross sectional area 10-6 m2 by 50%. Given Y for steel is 2 × 1011 Nm-2. A rubber cord 12 m long is suspended vertically. How much does it stretch under its own weight? Density of rubber is 1.5 g cm-3 and Y = 5 × 106 g f cm-2. Find the greatest length of a steel wire that can hang vertically without breaking. The breaking stress for steel = 7.9 × 109 dyne cm-2 and density of steel = 8 g cm-3. The diameter of a brass rod is 4 mm. Y for brass is 9.2 × 1010 N m-2. (i) Calculate is SI units the stress and strain when it is stretched by 0.25 % of its length. (ii) What is the force exerted. A solid cylindrical steel column is 4.0 m long and 9.0 cm in diameter. What will be its decrease in length when carrying a load of 80,000 kg? Given Y = 1.9 × 1011. A copper wire and a steel wire of the same diameter and length 100 cm and 200 cm respectively are connected end to end and a force is applied which stretches their combined length by 1 cm. Find by how much each wire is elongated. Given Y for steel is 20 × 1011 dynes cm-2 and Y for copper is Given Y for steel is 12 × 1011 dynes cm-2. Two parallel steel wires A and B are fixed to rigid support at the upper ends and subjected to the same load at the lower end. The lengths of the wires are in the ratio 4:5 and their radii are in the ratio 4:3. The increase in length of the wire A is 1mm. Calculate the increase in the length of the wire B. A platform is suspended by four wires at its corners. The wires are 3 m long and have a diameter of 2.0 mm. Y for the material of the wire is 1.8 × 1011 Nm-2. How far will the platform drop due to elongation of the wires if a 50 kg load is placed at the centre of the platform? Calculate the volume change of a sold copper cube, 40 mm on each edge, when subjected to a pressure of 2 × 1011 Pa. B for copper is 1.25 × 1011 Nm-2. Find the change in volume which 1 m3 of water will undergo when taken from the surface to bottom of a lake 100m deep. Given B for water is 22000 atmospheres. A spherical ball contracts in volume by 0.0098% when it is subjected to a pressure of 100 atmospheres. Calculate its bulk modulus. The compressibility of water is 5 × 10-10 m2 N1. Find the decrease in volume of 100 cm3 of water when subjected to a pressure of 5MPa. Two parallel and opposite force, each 4000 N, are applied tangentially to the upper and lower faces of cubical metal block 25 cm on a side. Find the angle of shear and the displacement of the upper surface relative to the lower surface. η = 8 × 108 Nm-2. A metallic cube whose each side is 10 cm is subjected to a shearing force of 10 kg wt. The top face is displaced through 0.25 dm with respect to the bottom. Calculate the shearing stress, strain and shear modulus. By applying a tangential force of 5 kg to the upper surface of a cube of side 5 cm, the upper surface is displaced by 0.5 cm relative to the bottom of the cube. Find the shearing modulus. A 60 kg motor sits on four cylinder rubber blocks. Each cylinder has a height of 3 cm and a cross sectional area of 15 cm2. The shear modulus for this rubber is 2 × 106 Nm-2. If a sideways force of 300 N is applied to the motor, how far will it move sideways? Find the depth of a lake for which the density of water will be 10% higher than the density at the surface. Compressibility of water is 0.00005 per atmosphere and average density of lake water = 1100 kg m-3. When load on the wire is increased from 2 kg to 4 kg, the elongation increases from 0.5 mm to 0.9mm. If g = 10 ms-2, find the work done during the extension of the wire. A steel wire of 6 m is stretched through 3 mm. The cross sectional area of the wire is 2.0 mm2. If Y for steel is 2 × 1011 Nm-2, find the elastic energy density of the wire and the elastic potential energy stored in the wire. A material has a Poisson’s ratio 0.20. If a uniform rod of the material surfers a longitudinal strain of 2 × 103, then find the percentage change in volume.