Question

An object with a mass of `5 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= e^x+x`. How much work would it take to move the object over #x in [3, 4], where x is in meters?

Answer 1

The work done is `=1862.5J`

Explanation:

`"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+x)`

The normal force is `N=mg`

The mass of the object is `m=5kg`

`F_r=mu_k*mg`

`=5*(e^x+x)g`

The work done is

`W=5gint_(3)^(4)(e^x+x)dx`

`=5g*[e^x+x^2/2]_(3)^(4)`

`=5g((e^4+8)-(e^3+9/2))`

`=5g(38.01)`

`=1862.5J`