An object with a mass of #6 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 2+sinx #. How much work would it take to move the object over #x in [2, 5], where x is in meters?

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Answer 1 · 2017-07-19T14:35:57

The work is #=311.7J#

We need

#intsinxdx=-cosx+C#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

The normal force is #N=mg#

The mass is #m=6kg#

#F_r=mu_k*mg#

#=6(2+sinx)g#

The work done is

#W=6gint_(2)^(5)(2+sinx)dx#

#=6g*[2x-cosx]_(2)^(5)#

#=6g((10-cos5)-(4-cos2))#

#=6g(6-cos5+cos2)#

#=6g(*5.3)#

#=311.7J#