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, 6], where x is in meters?

Answer 1

The work is `=9199J`

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)^(6)(x^2+3x)dx`

`=8g*[1/3x^3+3/2x^2]_(2)^(6)`

`=8g((1/3*6^3+3/2*6^2)-(1/3*2^3+3/2*2^2))`

`=8g(72+54-8/3-6)`

`=8g*352/3`

`=9199J`