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
Nov 7, 2017

Answer:

The work is #=435.6J#

Explanation:

We need

#intxe^xdx=e^x(x-1)+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+3/2)#

#=435.6J#