Paul's Online Notes
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Home / Calculus I / Applications of Integrals / Work
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May 6, 2021

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Section 6-6 : Work

  1. A force of \(F\left( x \right) = {x^2} - \cos \left( {3x} \right) + 2\), \(x\) is in meters, acts on an object. What is the work required to move the object from \(x = 3\) to \(x = 7\)? Solution
  2. A spring has a natural length of 18 inches and a force of 20 lbs is required to stretch and hold the spring to a length of 24 inches. What is the work required to stretch the spring from a length of 21 inches to a length of 26 inches? Solution
  3. A cable with mass ½ kg/meter is lifting a load of 150 kg that is initially at the bottom of a 50 meter shaft. How much work is required to lift the load ¼ of the way up the shaft? Solution
  4. A tank of water is 15 feet long and has a cross section in the shape of an equilateral triangle with sides 2 feet long (point of the triangle points directly down). The tank is filled with water to a depth of 9 inches. Determine the amount of work needed to pump all of the water to the top of the tank. Assume that the weight of the water is 62 lb/ft3. Solution