Question

An object with a mass of `1 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= e^x-x+3`. How much work would it take to move the object over #x in [1, 4], where x is in meters?

Answer 1

The work is `=523.1J`

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+3)`

The normal force is `N=mg`

The mass of the object is `m=1kg`

`F_r=mu_k*mg`

`=1*(e^x-x+3)g`

The work done is

`W=1gint_(1)^(4)(e^x-x+3)dx`

`=1g*[e^x-x^2/2+3x]_(1)^(4)`

`=1g((e^4-8+12)-(e^1-1/2+3))`

`=1g(e^4-e+3/2)`

`=523.1J`