A 1—ft cable weighing 5 lb / ft supports a safe weighing 500 lb. Find the work done in winding 80 ft of the cable on a drum.
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
1. A 1—ft cable weighing 5 lb / ft supports a safe weighing 500 lb. Find the work done in
winding 80 ft of the cable on a drum.
2. A right circular cylindrical tank of radius 2 ft and height 8 ft is full of water. Find the workdone in pumping the water to the top of the tank. Assume that the water weighs 62.5 lb/ft3
3. A conical vessel is 12 ft across the top and 15 ft tall. If it contains a liquid weighing ?
??/??3 to a depth of 10 ft, find the work done in pumping the liquid to a height 3 ft above the top of the vessel.
4. A force is of 3 pounds is needed to stretch a spring to 12 inches from its natural length of 10 inches. Determine the spring constant and find the work done in stretching the spring from its natural length to 16 inches.
5. A horizontal cylindrical tank 4 ft in diameter and 10 ft long is full of water. Find the work done by pumping all the water upward through an outlet 10 ft above the axis of the tank.
note: need illustrations for each solution
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