Q7. The stepped steel shaft shown in Fig Q4 is to transmit a torque. The larger section of the shaft is to have a hole drilled in it to a depth of 80 mm. Calculate EACH of the following:
(a) the diameter of the drilled hole ‘d’ that would make the maximum stress in the hollow part of the shaft equal to that in the 30 mm diameter section;
(b) the length of the 30 mm section if the total angle of twist for the shaft is to be 0.02 radians when a torque of 360 Nm is applied.
Note: Modulus of Rigidity for shaft material = 80 GN/m2
Q2. When a mass is suspended vertically from a helical spring, the length of the spring is found to increase by 60 mm. The mass is pulled down 40 mm below its position of rest and then released. The arrangement can be assumed to move with Simple Harmonic Motion.
Calculate EACH of the following:
(a) the time taken for one complete oscillation of the mass;
(b) the acceleration of the mass when it is 12 mm from its highest point;
(c) the velocity of the mass when it is 12 mm from its highest point.
Q1. A 5 m long ladder of uniform cross-section with a mass of 25 kg is placed with its base on the ground and resting against a pipe 1.8 m from the top of the ladder as shown in Fig Q6. The ladder makes an angle of 60° to the horizontal and the coefficient of friction is 0.3 at all surfaces. A person of mass 70 kg is to ascend the ladder.
(a) Redraw the arrangement showing all of the forces.
(b) Calculate the highest point up the ladder that the person of mass 70 kg can ascend without the ladder slipping.
Q1. An engine runs at 720 rev/min and has two connecting rods attached to a single crank-pin A as shown in Fig Q8. The longitudinal axis of each cylinder is inclined at 30° to the vertical and the stroke for each piston is 480 mm. The connecting rod length is 600 mm. The crank-pin is 60° before its top position and moving clockwise. Determine EACH of the following:
(a) the instantaneous linear velocity of piston X;
(b) the instantaneous linear velocity of piston Y.
Q3. A conical friction clutch has a semi-apex angle of 20° and transmits torque at an effective diameter of 200 mm. An axial force of 300 N is applied to the clutch and the coefficient of friction at the contact surfaces is 0.7.
The clutch is used to connect an electric motor running at 720 rev/min to a flywheel of mass 14 kg and radius of gyration 140 mm. Calculate EACH of the following:
(a) The maximum power which can be delivered through the clutch;
(b) The time taken to accelerate the flywheel from rest to full speed;
(c) The angular impulse given to the flywheel during the period of acceleration.
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