An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= e^x+x #. How much work would it take to move the object over #x in [1, 4], where x is in meters?

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Answer 1 · 2017-05-26T06:55:09

The work is #=2909.6J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

#N=mg#

#F_r=mu_k*mg#

#=5(e^x+x)g#

The work done is

#W=5gint_(1)^(4)(e^x+x)dx#

#=5g*[e^x+1/2x^2]_(1)^(4)#

#=5g((e^4+8)-(e+1/2))#

#=5g(e^4-e+8-1/2)#

#=2909.6J#