# An object with a mass of 5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= x+2 . How much work would it take to move the object over x in [2, 3], where x is in meters?

Jun 1, 2017

The work is $= 220.5 J$

#### Explanation:

The work done is

$W = F \cdot d$

The frictional force is

${F}_{r} = {\mu}_{k} \cdot N$

$N = m g$

${F}_{r} = {\mu}_{k} \cdot m g$

=5(x+2))g

The work done is

$W = 5 g {\int}_{2}^{3} \left(x + 2\right) \mathrm{dx}$

$= 5 g \cdot {\left[{x}^{2} / 2 + 2 x\right]}_{2}^{3}$

=5g((9/2+6)-(4/2+4)#

$= 5 g \left(\frac{21}{2} - 6\right)$

$= 5 g \left(\frac{9}{2}\right)$

$= \frac{45}{2} g J$

$= 220.5 J$