Question

An object with a mass of `8 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= x^2+3x`. How much work would it take to move the object over #x in [2, 3], where x is in meters?

Answer 1

The work is `=1084.5J`

Explanation:

We need

`intx^ndx=x^(n+1)/(n+1)+C (n!=-1)`

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=8kg`

`F_r=mu_k*mg`

`=8*(x^2+3x)g`

The work done is

`W=8gint_(2)^(3)(x^2+3x)dx`

`=8g*[x^3/3+3x^2/2]_(2)^(3)`

`=8g((9+27/2)-(8/3+6))`

`=8g(3+65/6)`

`=1084.5J`