PARAGRAPH A tool moving in $$x-y$$ plane under a quality control process under the action of various forces. One force is F→$$=$$− α x $$y2j^$$ , a force in the negative $$y-direction$$ whose magnitude depends on the position of the tool. The constant α is $$2.50$$ $$N/m3$$. Consider the displacement of the tool from the origin to the point x $$=$$ $$3.00$$ m, y $$=$$ $$3.00$$ m.Q. Calculate the work done on the tool by the force F→ if this displacement is along the straight line y $$=$$ x that connects these two points

Question

PARAGRAPH  A  tool moving in $$x-y$$ plane under a quality control process under the action of  various forces.  One force is F→$$=$$− α x $$y2j^$$     , a force in the negative $$y-direction$$ whose magnitude  depends on the position of the tool.   The constant α      is $$2.50$$ $$N/m3$$.  Consider the displacement of the tool from  the origin to the point  x $$=$$ $$3.00$$ m, y  $$=$$ $$3.00$$ m.Q. Calculate  the work done on the tool by the force F→      if this displacement  is along the straight line y $$=$$ x that connects these two points

Infinity Learn · Accepted Answer

$$w=$$∫F→ (dxi^+dyj^)          $$w=$$−∫$$03$$α $$y3dy$$                                  $$($$∴      x $$=$$ $$y)$$       $$=$$ −$$2.5(y44)03=$$−$$2.54$$.(81)                   $$w=$$−$$50.6$$ J

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