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, 3], where x is in meters?

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Answer 1 · 2018-05-22T12:14:03

The work is #=150.63J#

#"Reminder : "#

#inte^xdx=e^x+C#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

The coefficient of kinetic friction is #mu_k=(e^x-1)#

The normal force is #N=mg#

The mass of the object is #m=1kg#

#F_r=mu_k*mg#

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

The work done is

#W=1gint_1^3(e^x-1)dx#

#=1g*[e^x-x]_1^3#

#=1g(e^3-3)-(e-1)#

#=1g(15.37)#

#=150.63J#