Question

An object with a mass of `7 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 3+2sin(x)`. How much work would it take to move the object over #x in [pi, 4pi], where x is in meters?

Answer 1

The work is `=1665J`

Explanation:

We need

`intsinxdx=-cosx+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*(3+2sinx)g`

The work done is

`W=7gint_(pi)^(4pi)(3+2sinx)dx`

`=7g*[3x-2cosx]_(pi)^(4pi)`

`=7g(12pi-2cos(4pi))-(3pi-2cospi)`

`=7g(9pi-2-2)`

`=7g(9pi-4)`

`=1665J`

The value of `g=9.8ms^-2`