Question

An object with a mass of `8 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 2x^2-x+7`. 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 `=1009.4J`

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(2x^2-x+7)g`

The work done is

`W=8gint_(2)^(3)(2x^2-x+7)dx`

`=8g*[2/3x^3-1/2x^2+7x]_(2)^(3)`

`=8g((18-9/2+21)-(16/3-2+14))`

`=8g(27-59/6)`

`=6g(103/6)`

`=1009.4J`