Subject : Rigid Body Dynamics
M.M :30
Time :90 minutes
Note: All questions are compulsory. Q1 is of 10 marks and Q2,Q3,Q4 and Q5
are of 5 marks each.
Q1a)A string is wrapped round a pulley of 60 cm diameter. One end is tied to
the pulley and the weight is attached to the other end of the string. The
weight travels a distance of 8 m within four seconds after attaching the
weight. Find out:
a)Angular acceleration of the pulley
b)Final angular velocity of the pulley
c)Total distance travelled by the weight when pulley rotates at 300 rpm. (3)
b)At the instant shown in figure below the rod AB is rotating clockwise at
2.5 rad/s .If end C of the rod BC is free to move on a horizontal
surface, make calculations for the angular velocity of rod BC and velocity
of its end point C .
(3)
c)A 400 –kg motor supported by four springs ,each of stiffness 150 kN /m, is
constrained to move vertically. Knowing that the unbalance of the rotor is
equivalent to a 23-g mass located at a distance of 100 mm from the axis of
rotation ,determine for a speed of 800 rpm i) the amplitude of the
fluctuating force transmitted to the foundation ii)the amplitude of the
vertical motion of the motor.
(4)
Q2)A cord is wrapped around the outer surface of the 8- kg disk. If a force of
F=(1/4θ2) N, where θ is in radians, is applied to the cord, determine the
disk’s angular velocity when it has turned 5 revolutions. The disk has
an initial angular velocity of ωo = 1 rad/s.
(5)
Q3)The flywheel of a punching machine has a mass of 300 kg and radius of
gyration of 600 mm. Each punching operation requires 2500 J of work.
i)Knowing that the speed of the flywheel is 300 rpm just before punching,
determine the speed immediately after the punching.
ii)If a constant 25 N.m couple moment is applied to the shaft of the flywheel,
determine the number of revolutions executed before the speed is again
300 rpm.
(5)
Q4)Derive the relation for coefficient of restitution in eccentric impact.
(5)
Q5)The 40 kg roll of paper rests along the wall where the coefficient of kinetic
friction is µk = 0.2.If a vertical force of P = 40 N is applied to the
paper ,determine the angular velocity of the roll when t = 6 seconds starting
from rest. Neglect the mass of the unraveled paper and take radius of
gyration of spool about the axle O to be Ko = 80 mm.
(5)