The force applied against a moving object travelling on a linear path is given by #F(x)= cosx + 2 #. How much work would it take to move the object over #x in [ 0, (13 pi) / 8 ] #?

1 Answer
Yonas Yohannes
Mar 30, 2016

#W=(4sin(13/8pi)+13pi)/4 ~~ 2.286#

Explanation:

Given: Force, #F(x)=cos(x)+2#
Required: Work done over #x in [0,(13pi)/8]#
Solution Strategy: Use the Work/ Force formula:
#dW = vecF*vecdr; W= F_x*dx + F_y*dy+F_z*dz= |F_x|*dx#
Since #vecF = F_x# only then we integrate in #dx# only:
#W = int_0^(13/8pi) F_x*dx=int_0^(13/8pi) (cosx +2)*dx#
#W=(4sin(13/8pi)+13pi)/4 ~~ 2.286#

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