The force applied against a moving object travelling on a linear path is given by #F(x)= sinx + 1 #. How much work would it take to move the object over #x in [ 0,pi/8 ] #?

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Answer 1 · 2017-06-22T09:00:25

The work is #=0.469J#

We need

#intsinxdx=-cosx#

The work done is

#W=F*d#

The force is #F=1+sinx#

The work done is

#W=int_0^(1/8pi)(1+sinx)dx#

#=[x-cosx]_(0)^(1/8pi)#

#=(1/8pi-cos(pi/8))-(0-cos0)#

#=(1/8pi-0.92+1)#

#=(1/8pi+0.08)#

#=0.469J#