Two solid spheres of radius 3 in., weighing 2 lb each, are mounted at a and b on the horizontal rod a’b’, which rotates freely about the vertical with a counterclockwise angular velocity of 6 rad/s.

the spheres are held in position by a cord which is suddenly cut. knowing that the centroidal moment of inertia of the rod and pivot is iy = 0.25 lb-ft-s2, determine (a) the velocity of the spheres after they have moved to positions a’ and b’, (b) the energy lost due to the plastic impact of the spheres and the stops at a’ and b’.

calculate (a) by treating the spheres as points with the same mass while neglecting the mass of the rod and pivot.

An electrical motor raises a 50kg load at a construct velencity .calculate the power of the motor, if it takes 40sec to raise the load through a height of 24m(take g =9.8n/g)

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

The flow rate of air through a through a pipe is 0.02 m5/s. a pitot static tube is placed in the flow. the radius of the pitot static tube is 1 mm. assuming the flow to be steady and the air to be at 300k, calculate the difference in total and static pressure if the diameter of the pipe is: (a) d 0.1 m d 0.05 m (c) d 0.01 m