The 20-kg roll of paper has a radius of gyration ka = 120 mm about an axis passing through point a. it is pin supported at both ends by two brackets ab. the roll rests on the floor, for which the coefficient of kinetic friction is μk = 0.2. if a horizontal force f = 60 n is applied to the end of the paper, determine the initial angular acceleration of the roll as the paper unrolls.

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.