Math 150B/155A Worksheet for 6.4

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<LI>A spring, whose unstretched length is 1 meter, stretches to a length of 3 meters when a force of 3 newtons is applied. Find the work needed to stretch the spring to a length of 2 meters from its natural length.</LI>
<LI>How much work is required to stretch the spring in Problem 1 to a length of 4 meters?</LI>
<LI>A spring, whose unstretched length is 2 meters, is compressed to a length of 1/2 
    meter when a force of 10 newtons is applied. Find the work required to 
      compress the spring to a length of 1 meter.</LI>
<LI>How much work is required to compress the spring in Problem 3 to a length of 1.5 meters?</LI>
<LI>A spring, whose unstretched length is 4 feet, stretches to a length of 8 feet when a force of 2 pounds is applied. If 9 foot-pounds of work is expended to stretch this spring from an unstretched position, what is its total length?</LI>
<LI>If 8 foot-pounds of work is expended on the spring in Problem 5, how far is it stretched?</LI>
<LI>How much work is required to pump all the water over the top of a full cylindrical tank that is 4 meters in diameter and 6 meters high?</LI>
<LI>How much work is required to pump half the water over the top of the tank in Problem 7?</LI>
<LI>A full tank in the shape of an inverted right circular cone is 8 meters across the
top and 4 meters high. How much work is required to pump all the water over the top of the tank?</LI>
<LI> If the surface of the water in the tank of Problem 9 is 2 meters below the top of
the tank, how much work is required to pump all the water over the top of the
tank?</LI>
<LI>A water tank in the shape of a hemispherical bowl of radius 4 meters is filled with water to a depth of 2 meters. How much work is required to pump all the water over the top of the tank?</LI>
<LI>If the water tank in Problem 11 is completely filled with water, how much work is required to pump all the water to a height 2 meters above the tank?</LI>
<LI> A swimming pool is in the shape of a rectangular parallelepiped 6 feet deep, 30
feet long, and 20 feet wide. It is filled with water to a depth of 5 feet. How much work is required to pump all the water over the top?</LI></OL>