F192023 Pages:3

PARTB
Answer any three full questions, each carries 10 marks.
A shaft carries four masses A, B , C and D of magnitude 250kg, 350kg,

480kg and 250kg respectively and revolving at radii 64mm, 60mm, 50mm,
and 64mm in planes measured from A at 300mm, 400mm, and 700mm.
The angles between the cranks measured anticlockwise are A to B 45°, B
to C 70°, C to D 120°. The balancing masses are placed in planes P and Q.
The distance between the planes A and P is 100mm, between P and Q is
400mm and between Q and D is 200mm. If the balancing mass Q revolve
at a radius of 100 mm, and balance mass P revolve at a radius of 150mm,
find their magnitudes and angular positions.

A single cylinder engine is producing 25hP at 4000rpm with 2000 explosions per
minute. The fluctuation of speed not to exceed 1% on either side. Find the
dimensions of a solid flywheel so that the hoop stress does not exceed 101/01,
Assume that the work done during the power stroke is 1.4 times work done
during the cycle. Density of flywheel material is 7200kg/m* :

The turbine rotor of a ship has a mass of 3500 kg. It has a radius of gyration of
0.45m and a speed of 3000 r.p.m. clockwise when looking from stern. Determine
the gyroscopic couple and its effect upon the ship: 1. when the ship is steering to
the left on a curve of 100 m radius at a speed of 36 km/h. 2. when the ship is
pitching in a simple harmonic motion, the bow falling with its maximum
velocity. The period of pitching is 40 seconds and the total angular displacement
between the two extreme positions of pitching is 12 degrees.

A racing car weighs 20KN. It has a wheel base of 2m, track width 1൩ and height
of C.G. 300 mm above the ground level and lies midway between the front and
rear axle. The engine flywheel rotates at 3000 r.p.m. clockwise when viewed
from the front. The moment of inertia of the flywheel is 4 kgm? and moment of
inertia of each wheel is 3 kgm?. Find the reactions between the wheels and the
ground when the car takes a curve of 60m radius towards right at 60km/h, taking
into consideration the gyroscopic and the centrifugal effects. Each wheel radius

is 300mm.

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