An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= xe^x-x #. How much work would it take to move the object over #x in [1, 2], where x is in meters?

1 Answer
Aug 23, 2017

Answer:

The work is #=288.6J#

Explanation:

We need

#intxe^xdx=xe^x-e^x+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=5kg#

#F_r=mu_k*mg#

#=5*(xe^x-x)g#

The work done is

#W=5gint_(1)^(2)(xe^x-x)dx#

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

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

#=5g(e^2-2+1/2)=5g(e^2-3/2)#

#=288.6J#