Question

An object with a mass of `3 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= e^x-2x+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 `=1348.9J`

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-2x+3)`

The normal force is `N=mg`

The mass of the object is `m=3kg`

`F_r=mu_k*mg`

`=3*(e^x-2x+3)g`

The work done is

`W=3gint_(1)^(4)(e^x-2x+3)dx`

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

`=3g((e^4-16+12)-(e-1+3))`

`=3xx9.8xx45.88`

`=1348.9J`