An object with a mass of 5kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=xexx. How much work would it take to move the object over #x in [1, 2], where x is in meters?

1 Answer
Aug 23, 2017

The work is =288.6J

Explanation:

We need

xexdx=xexex+C

The work done is

W=Fd

The frictional force is

Fr=μkN

The normal force is N=mg

The mass is m=5kg

Fr=μkmg

=5(xexx)g

The work done is

W=5g21(xexx)dx

=5g[xexexx22]21

=5g((2e2e22)(ee12))

=5g(e22+12)=5g(e232)

=288.6J