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_0 done by the force on the object as it travels from x = 4.00 mm to x = 10.00 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 6 mm lessthanorequalto x lessthanorequalto 10 mm W_0 =

Explanation / Answer

formula for wqork done is

W = integral Fx dx

the workdone by the force on object from x= 4 mm to 10 mm

W= integral 4 mm to 6 mm ( 110 N- 60 N/4 mm* x) dx + integral 6 mm to 10 mm ( 40 N/4mm* x- 40 N) dx

= ( 110 x- 60/4 * x^2/2) 4 mm to 6 mm + ( 40/4 * ( x^2/2) - 40 x) 6 mm to 10 mm

= ( 110(6-4) - 60/8 ( 6^2 - 4^2) ) + ( 40/8 ( 10^2- 6^2 ) - 40 ( 10-6))

=(70 + 160) N mm

= 230 * 10^-3 m N

=230 * 10^-3 J

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