The force applied against a moving object travelling on a linear path is given by #F(x)= sinx + 2 #. How much work would it take to move the object over #x in [ 0, (3 pi) / 8 ] #?

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Answer 1 · 2016-01-14T21:05:10

#2.9735J#

From precise definition of work,

#W=int_CvecF.dvecr#

So in this particular case we may reduce it to

#W=int_0^((3pi)/8)(sinx+2)dx#

#=[-cosx+2x]_0^((3pi)/8)#

#=(-0.3827+(6pi)/8)-(-1+0)#

#=2.9735J#.