Math 152 Week in Review Sections 7.3, 7.4

7.3 Find the volume of the solid formed if the region bounded by f(x) and the given lines or interval is rotated about the given axis.

7.4 6. A force measures Newtons at x meters from the origin. How much work is done if the force is applied from x=0.5 to x=1 meter?

7. The force required to hold a spring 6 inches beyond its natural length is 4 pounds. How much work is done :

a) in stretching the spring 2 feet beyond its natural length?

b) in stretching the spring from 1 foot to 2 feet beyond its natural length?

8. Six Joules of work will stretch a spring from a length of 1 meter to a length of 1.5 meters. Ten Joules will stretch the spring from 1.5 meters to 2 meters. Find the natural length of the spring.

9. (#12, page 448 of Stewart) A uniform cable is 40 ft. long and weighs 60 lb. How much work is required to pull 10 ft. of cable to the top?

10. A tank in the shape of a trough is 4 meters wide at the top and 5 meters tall. (The face is an isosceles triangle.) The tank is 10 meters long.

a) If the tank is full of water, how much work is done in pumping all the water out a spout which is 1 meter above the top?

b) If the water l is only 3 meters deep, how much work is done in pumping the water out the spout?

11. A trough with semicircular ends is 6 meters wide at the top and 12 meters long. The tank is full of water. How much work is done in pumping the water out a spout 2 meters above the top of the tank?