Question

An object with a mass of `7 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 4+secx`. How much work would it take to move the object over #x in [(pi)/8, (pi)/4], where x is in meters?

Answer 1

The work is `=140.6J`

Explanation:

We need

`intsecxdx=ln(tanx+secx)+C`

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=7kg`

`F_r=mu_k*mg`

`=7*(4+secx)g`

The work done is

`W=7gint_(1/8pi)^(1/4pi)(4+secx)dx`

`=7g*[4x+ln(tanx+secx)]_(1/8pi)^(1/4pi)`

`=7g(pi+ln(tan(pi/4)+sec(pi/4))-(1/2pi+ln(tan(1/8pi)+sec(1/8pi))`

`=7g(2.05)`

`=140.6J`