# An object with a mass of 3 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= x^2-3x+6 . How much work would it take to move the object over x in [1, 3], where x is in meters?

##### 1 Answer
Jul 12, 2016

We know that the work done against variable frictional force is

$w = {\int}_{1}^{3} {\mu}_{k} \left(x\right) m g \mathrm{dx}$

$= m g {\int}_{1}^{3} \left({x}^{2} - 3 x + 6\right) \mathrm{dx}$

$= m g {\left[\frac{1}{3} \cdot {x}^{3} - \frac{3}{2} \cdot {x}^{2} + 6 x\right]}_{1}^{3}$

=3*9.8[(1/3*3^3-3/2*3^2+6*3)-(1/3*1^3-3/2*1^2+6*1)#
$= 29.4 \cdot \left(13.5 - 4.8\right) = 255.78 J$