Question

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?

Answer 1

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`