The spool consists of a uniform cylinder 6 in diameter betwe

The spool consists of a uniform cylinder, 6 in diameter, between two cylindrical disks, 18 in diameter. The spool weights 16 lbs. A spring having k=24 lb/ft is attached to cords wrapped around the disks. A second cord is wrapped around the center of the spool, passes over a small pulley and is attached to a 30 lb crate A. If die crate has a speed of 4 ft/s downward when the spring is stretched 4 in and the spool rolls without slipping, determine: The maximum distance that the crate will drop. The speed of vc and the speed vA of the crate when the stretch in the spring is zero. The radius of gyration about axel going through the center of gravity is 4.743 in.

Solution

Compute the line integral of v = (r cos2 ?) r – (r cos ? sin ?) ? + 3r ? around the path shown in Fig. 1.50 (the points are labeled by their Cartesian coordinates). Do it either in cylindrical or in spherical coordinates. Check your answer, using Stokes\' theorem.