Section A
Q1.
(a) A slider-crank reciprocating mechanism has the following data: Radius of the crank = 480 mm Length of the connecting rod = 1600 mm Angular velocity of the crank = 20 rad/s Find the velocity and acceleration of the piston for the crank position of θ = 45\circ from the inner dead centre.
(b) Two pulleys having diameters 640 mm and 480 mm, are used to connect two parallel shafts by a crossed belt drive. The distance between the centre lines of the shafts is 3 m. Determine how much the length of the belt should be changed, if it is desired to alter the direction of rotation of the driven shaft.
(c) A rod of 1 m length is kept at a temperature of 30\circC. Find the expansion of the rod when the temperature is raised to 80\circC. If this expansion is prevented, find the stress induced in the material of the rod. Take E = 100 GPa and α = 0.000012/°C.
(d) The state of stress at a point in a loaded piece of material is given by σ_x = 85 kPa, σ_y = -40 kPa and \tauxy = ± 50 kPa. Find the magnitudes of the principal stresses. Also find the magnitude of the maximum shear stress and the plane on which this acts.
(e) In a simple cubic crystal, draw the following planes: (i) (110) (ii) (111)