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

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