An object with a mass of #1 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= e^x-1 #. How much work would it take to move the object over #x in [1, 2], where x is in meters?

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Answer 1 · 2017-05-02T06:25:09

The work is #=35.97J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

#N=mg#

#F_r=mu_k*mg#

#=1(e^x-1)g#

The work done is

#W=int_(1)^(2)(e^x-1)gdx#

#=gint_(1)^(2)(e^x-1)dx#

#=g*[e^x-x]_(1)^(2)#

#=g(e^2-2)-(e-1))#

#=g(5.39-1.72)#

#=g*3.67#

#=35.97J#