The spool consists of a uniform cylinder, 6 in diameter, between two cylindrical

Question

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 the 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 v_c and the speed v_A 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.

Explanation / Answer

select the lightest W-shape (using A992 Grade 50 material) that will provide

a factor of safety against tensile yielding equal to 1.67,

a factor of safety against shear yielding equal to 1.50, and

a maximum transverse deflection that does not exceed L/480.

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