Question

An object with a mass of `7 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 1-cos(x/6)`. How much work would it take to move the object over #x in [0, 8pi], where x is in meters?

Answer 1

The work is `=2078.6J`

Explanation:

`"Reminder : "`

`intcosaxdx=1/asinax+C`

The work done is

`W=F*d`

The frictional force is

`F_r=mu_k*N`

The coefficient of kinetic friction is `mu_k=(1-cos(x/6))`

The normal force is `N=mg`

The mass of the object is `m=7kg`

`F_r=mu_k*mg`

`=7*(1-cos(x/6))g`

The work done is

`W=7gint_(0)^(8pi)(1-cos(x/6))dx`

`=7g*[x-6sin(1/6x)]_(0)^(8pi)`

`=7g(8pi-6sin(4/3pi)-(0))`

`=7g(30.3)`

`=2078.6J`