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Q.

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

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a

– 50.6 joule

b

– 67.5 joule

c

– 77.5 joule

d

– 60.5 joule

answer is A.

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Detailed Solution

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