Please solve problems 6/140 and 6/127 only. Refer attachment for fig.

Problem 6/140 : The sheave of 400 mm radius has a mass of 50 kg and a radius of gyration of 300 mm. The sheave and its 100 kg load are suspended by the cable and the spring which has a stiffness of 1.5 kN/m. If the system is released from rest with the spring initially stretched 100 mm, determine the velocity of O after it has dropped 50 mm.

Problem 6/127 : The drum of 375 mm radius and its shaft have a mass of 41 kg and a radius of gyration of 300 mm about its axis of rotation. A total of 18m of flexible steel cablewith a mass of 3.08 kg per m of length is wrapped around the drum with one end secured to the surface of the drum. The free end of the cable has an initial overhang x = 0.6m as the drum is released from rest. Determine the angular velocity of the drum for the instant when x = 6m. Assume that centre of mass of the portion of cable remaining on the drum lies on the shaft axis when x = 6m. Neglect friction.

** Please see the attachment for the complete problem description **
A rigidbody is spinning with an angular speed of 60pie radians per second (1800 rpm). The axis of rotation lies in the direction of the vector 2i + 2j -k. A small particle on the spinning body with mass of one kilogram passes through the point P with positi

Problem 1 : To determine moment of inertia about different axes of rotation of a circular disc of given radius of gyration.
Problem 2 : A two pulley system. To determine acceleration, tension in the cable etc.

1. The vector expression of an acceleration can be obtained by:
a. Differentiation position vector once
b. Differentiation velocity vector once
c. Differentiation position vector three times
d. Differentiation velocity vector twice
2. The work of forces acting on a rigidbody can be expressed as:
a. the dot product

The earth maybe considered as a rigid axisymmetric body with a small quadrupole deformation. (There are two problems (a) and (b))
(a) If the exterior gravitational potential is written as:
V(r)=-M_e*G*1/r*[1-J(R_e/r)^2* P_2(costheta)]
Here, M_e is the mass of the earth, R_e is the equatorial radius and theta the colatit

Please do probs 6/148 and 6/136 only. Refer attachment for fig.
Problem 6/148 : The fig. shows cross section of a garage door which is a uniform rectangular panel 8 x 8 ft ans weighing 200 lb. The door carries two spring assemblies, one on each side of the door, like the one shown. Each spring has a stiffness of 50 lb/ft, and

A bead slides on a smooth rigid wire bent into the form of a circular loop of radius b. If the plane of the loop is vertical and if the bead starts from rest at a point that is level with the center of the loop, find the speed of the bead at the bottom and the reaction of the wire on the bead at that point.

(Please refer attachment for detailed problem description)
Problem 1 : The 40 kg disc is released from rest with the spring compressed. At the instant shown (see attachment) it has a speed of 4 m/s and the spring is unstretched. From this poinr determine the distance d that the disc moves down the 30 degree ramp before moment

The figure is attached as file.
A rigidbody in the shape of a thumbtack formed from a thin disk of mass M and radius a and a mass-less stem is placed on an inclined plane that makes an angle α with the horizontal. The point of the tack remains stationary at the point α, and the head rolls along a circle of radius b.
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