An object with a mass of #8 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 2x^2-x+7 #. 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 · 2017-06-09T05:57:23

The work is #=6938.4J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

The normal force is #N=mg#

#F_r=mu_k*mg#

#=8(2x^2-x+7))g#

The work done is

#W=8gint_(2)^(5)(2x^2-x+7)dx#

#=8g*[2/3x^3-1/2x^2+7x]_(2)^(5)#

#=8g((250/3-25/2+35)-(16/3-2+14))#

#=8g(234/3-25/2+23)#

#=8g(177/2)#

#=6938.4J#