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Q3. A packing case rests on an inclined plane of 14°. A force of 1400 N acting parallel to and up the plane is applied and just moves the packing case up the incline.

When a force of 1510 N is applied to the same packing case but now horizontal and acting into the plane, the packing case also just moves up the incline. Determine EACH of the following:

(a) The coefficient of friction between the packing case and the plane;

(b) The mass of the packing case.

Q2. A winch motor drives a pinion which has 320 teeth. Friction in the motor bearings is constant at 20 Nm. The pinion meshes with a gear wheel having 640 teeth and this gear wheel drives a winch drum of diameter 340 mm. The winch drum raises an anchor of mass 2 tonne at a steady speed of 0.3 m/s. Assume the efficiency of the gearing is 100%. Calculate EACH of the following:

(a) The total torque to be supplied at the output from the winch motor;

(b) The input power required by the winch motor if the motor efficiency is 85%.

Q1. A single plate clutch with both sides effective has an outside diameter of 380 mm and an inside diameter of 140 mm. The clutch is designed to transmit 12 kW at 600 rev/min. The axial thrust on the clutch faces is provided by six identical springs, each with a stiffness of 8 kN/m. The coefficient of friction at the clutch surfaces is 0.6. Calculate EACH of the following:

(a) The required compression of each spring to deliver the designed power when the clutch is new;

(b) The power transmitted when a total of 2 mm of plate wear occurs and the clutch is worn.

Note: For constant pressure, T =   (2μnW(R_o³-R_i³)/3(R_o²-R_i² )

For constant wear, T = (μNw(r_o+ r_i))/2

n = number of pairs of contact surfaces.

Q8. A short vertical column consists of a hollow steel tube of 48 mm outside diameter and 40 mm inside diameter with a solid brass rod of 34 mm diameter within it. The steel tube is 380 mm long and the brass rod is 1 mm shorter. The brass rod is supported on a raised boss so that the top of the tube and the top of the rod are level.

Calculate the maximum load that can be applied to the column so that the compressive stress in the brass rod does not exceed 50 MN/m².

Note: For steel, Modulus of Elasticity = 210 GN/m²

For brass, Modulus of Elasticity = 80 GN/m²

Q5. A hollow square section beam of external dimension 100 mm and thickness 5 mm is loaded as shown in Fig Q7. Calculate EACH of the following:

(a) The maximum stress due to shear in the beam;

(b) The position of the point of contra flexure from the left-hand side of the beam.

Q2. A hollow square section beam of external dimension 200 mm, and thickness 10 mm, is loaded as shown in Fig Q6. Calculate EACH of the following:

(a) The maximum stress due to shear in the beam;

(b) The point of contraflexure