Q1.
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1. (a) horizontal plane. The block A is tied with a weightless horizontal cord to a wall. A force P is applied to the block B at 45° to the horizontal as shown in the figure. If the coefficient of friction is 0.25 between the blocks and 0.3 between block B and the floor, determine the tension T in the cord and the value of the force P so that block B is at the point of sliding.
A Cord
P ×
100 N
B
150 N
(b)
(i) Find the maximum flexural stress developed in a steel wire 2.00 mm in diameter, if it is coiled over a drum 0.5 m in radius (it is assumed that the limit of proportionality is not exceeded due to coiling). What is the bending moment to which the wire is subjected? Take E = 200 GPa.
(ii) If the ratio of Young's modulus to the modulus of rigidity is 2.5 for a certain material, find its Poisson's ratio and the ratio of Young's modulus to bulk modulus.
(c) An aeroplane flying at 300 km/h turns towards the left and completes a quarter circle of 80 m radius. The mass of the rotary engine and the propeller of the plane is 500 kg with a radius of gyration of 300 mm. The engine speed is 2000 r.p.m. clockwise when viewed from the nose end (front end). Determine the gyroscopic couple on the aircraft and state its effect whether the nose end is raised or depressed.
(d) Define the following terms for the governor:
(i) Sensitiveness Stability Isochronous Hunting Draw the controlling force (Fc) vs. radius of rotation of balls (r) for
(ii) spring controlled governors for the above conditions.
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(b)
(i) Find the maximum flexural stress developed in a steel wire 2.00 mm in diameter, if it is coiled over a drum 0.5 m in radius (it is assumed that the limit of proportionality is not exceeded due to coiling). What is the bending moment to which the wire is subjected? Take E = 200 GPa.
()
(b)
(ii) If the ratio of Young's modulus to the modulus of rigidity is 2.5 for a certain material, find its Poisson's ratio and the ratio of Young's modulus to bulk modulus.
() (c) An aeroplane flying at 300 km/h turns towards the left and completes a quarter circle of 80 m radius. The mass of the rotary engine and the propeller of the plane is 500 kg with a radius of gyration of 300 mm. The engine speed is 2000 r.p.m. clockwise when viewed from the nose end (front end). Determine the gyroscopic couple on the aircraft and state its effect whether the nose end is raised or depressed.
()
(d) Define the following terms for the governor:
(i) Sensitiveness Stability Isochronous Hunting. Draw the controlling force (Fc) vs. radius of rotation of balls (r) for
(ii) spring controlled governors for the above conditions.
