9. a. A spring has constant k-5lb./in. Its natural length is 12 inches. What is the work required to compress it to 9 inches? b. A 100 ft. cable weighs 40 lbs. Find the work done in winding the c...
9. a. A spring has constant k-5lb./in. Its natural length is 12 inches. What is the work required to compress it to 9 inches? b. A 100 ft. cable weighs 40 lbs. Find the work done in winding the cable onto a winch, if the cable is hanging vertically c. An unknown positive charge q is placed at the origin. The force F (in Newtons) with which this charge repels a unit positive charge is given by F-kq/r, where k is a constant and r is the distance in meters between the two charges. Suppose the force is 1 Newton when the unit charge is at (1,0). Find the work done in bringing the unit charge from+oo to (1,0) along the x-axis. (Try substituting a very large number for + oo in your integral.) d.* A milk truck has a cylindrical tank (with the long axis horizontal) measuring 15 feet in length and 6 ft. in diameter. It is half full, and the valve on the bottom is jammed. How much work is required to pump the milk over the top? Assume the density of milk is that of water, about 62.4 lb./cubic foot.
9. a. A spring has constant k-5lb./in. Its natural length is 12 inches. What is the work required to compress it to 9 inches? b. A 100 ft. cable weighs 40 lbs. Find the work done in winding the cable onto a winch, if the cable is hanging vertically c. An unknown positive charge q is placed at the origin. The force F (in Newtons) with which this charge repels a unit positive charge is given by F-kq/r, where k is a constant and r is the distance in meters between the two charges. Suppose the force is 1 Newton when the unit charge is at (1,0). Find the work done in bringing the unit charge from+oo to (1,0) along the x-axis. (Try substituting a very large number for + oo in your integral.) d.* A milk truck has a cylindrical tank (with the long axis horizontal) measuring 15 feet in length and 6 ft. in diameter. It is half full, and the valve on the bottom is jammed. How much work is required to pump the milk over the top? Assume the density of milk is that of water, about 62.4 lb./cubic foot.