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`. 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 `=797.1J`

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)g`

The acceleration due to gravity is `g=9.8ms^-2`

The work done is

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

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

`=8g(2/3*3^3-9/2))-(2/3*8-2)`

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

`=8g(20-59/6)`

`=797.1J`