A mysterious object is accelerated in a straight line across the table by a myst

Question

A mysterious object is accelerated in a straight line across the table by a mysterious force. The force is not constant, but varies depending on the position of the object. The graph and equations below give the magnitude of the force F on the object as a function of the position x of the object. Find the work W_o done by the force on the object as it travels from x = 3.00 mm to x = 8.00 mm. F (x) = {20 N/2 mm x + 60 N, 0 mm lessthanorequalto x lessthanorequalto 2 mm 110 N - 60 N/4 mm x, 2 mm lessthanorequalto x lessthanorequalto 6 mm 40 N/4 mm x - 40 N, 6 mm lessthanorequalto x lessthanorequalto 10 mm

Explanation / Answer

as we know that

dw = F. dx

so the work done from x = 3 mm = 0.003 m to x = 8 mm = 0.008 m

W = integration [ ( 110 - 60x / 4 ) x 4 ]63 + integration [ ( 40x / 4 - 40 ) x 4 ]86

= integration [ 440 - 60x ]63 + integration [ 40x - 160 ]86

= [ 440x - 30x2 ]63 + [ 20x2 - 160x ]86

= ( 1080 -810 ) + ( 560 - 320 )

= 510 J Ans

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