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Math Help - work,volume problem

  1. #1
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    work,volume problem

    Consider the region bounded by y=x^3 +24x^2 + 192x 0<=x<=2 on the left, by x axis along the bottom, by the line y=488 along the top, and by the line x=4 along the right. Suppose the region is revolved around the line x=8 to produce a solid of revolution. Find the network done in turning this solid upside down. Assume that the solid is made of a metal alloy whose density is 9200 kg/m^3 and units are meters. Express answer in Joules.

    My first question is what od they mean by turning it upside down. FLipping it so it's underneath the x-axis? Where do I go from there?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sheridan View Post
    Consider the region bounded by y=x^3 +24x^2 + 192x 0<=x<=2 on the left, by x axis along the bottom, by the line y=488 along the top, and by the line x=4 along the right. Suppose the region is revolved around the line x=8 to produce a solid of revolution. Find the network done in turning this solid upside down. Assume that the solid is made of a metal alloy whose density is 9200 kg/m^3 and units are meters. Express answer in Joules.

    My first question is what od they mean by turning it upside down. FLipping it so it's underneath the x-axis? Where do I go from there?
    (no not flipping it so its under the x-axis but flipping it then moving it back up so that its lower edge is on the x axis)

    Calculate the center of mass c=(x_c,y_c) , and the mass m of the solid.

    Then the work done in flipping it upside down is the change in potential energy when a mass m is moved from (x_c, y_c) to (x_c,488-y_c).


    Which is mg(488-2y_c)

    RonL
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