Q1. TWO blocks, weighing 36 N and 8 N respectively, are tethered together by a cord that is inclined at an angle of 10o above the horizontal plane when they are initially at rest as shown in Fig Q1.
A force of 18 N is applied to the 36 N block parallel to the horizontal plane, and the coefficient of friction at the 8 N block and 36 N block is 0.5 and 0.25 respectively.
Calculate the tension in the cord. (16)
Q2. A 1.0 diameter circular plate of uniform thickness has a square hole and a triangular hole cut into it as shown in Fig Q2.
The square hole has sides of length 0.2 m and the triangular hole is right-angled with a base length of 0.3 m and a height of 0.7 m.
Calculate the co-ordinates of the centroid of the plate from the reference point labelled ‘0’. (16)
Q3. A dual slider mechanism is driven anti-clockwise by a crank rotating at a constant angular speed of 1200 rpm as shown in Fig Q3. Crank OA is 300 mm in length, connecting rod AB is 500 mm in length and connecting rod AC is 515 mm in length.
Determine the relative angular velocities of connecting rods AB and AC. (16)
Q4. A screw-jack has a square thread with a mean diameter of 60 mm and a pitch of 8 mm. The lifting cap has an outer diameter of 90 mm and an inner diameter of 60 mm. The coefficient of friction at all contact surfaces is a constant 0.15 when a load of 5600 N is lifted or lowered using a bar that is 1.5 m in length.
Calculate the difference in the applied force required to lift and lower the load. (16)
Q5. A truck with an overall mass of 3.5 tonnes has FOUR 610 mm diameter wheels, EACH with a mass of 85 kg and a 430 mm radius of gyration. The truck travels 100 m from rest down a slope inclined 2o above the horizontal and is brought to rest by a set of buffers.
Each of the FOUR identical buffer springs, arranged in parallel, has a stiffness of 475 N/mm.
Calculate EACH of the following:
(a) the velocity of the truck on impact; (10)
(b) the spring compression. (6)
Q6. Block A has a mass of 100 kg and is connected to block B by a cable running over a 1.2 m diameter drum supported in frictionless bearings as shown in Fig Q6.
The coefficient of friction between block A and the plane is 0.25, whilst the 250 kg drum has a radius of gyration of 840 mm.
Calculate the mass of the block B that causes the blocks to accelerate from rest to a velocity of 4 m/s in SIX seconds. (16)
Q7. A box section cantilever beam has an overall depth of 160 mm, an overall width of 120 mm and is fabricated so that it is uniform over its entire 2 m span. The top and bottom plates are 20 mm thick whilst the side plates are 10 mm thick. The maximum bending stress is restricted to 40 MN/m2.
Calculate the maximum concentrated mass that can be supported on the free end of the beam. (16)
Note:
Density for steel= 7860 kg/m3.
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