Question

An object with a mass of `6 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 1+cotx`. How much work would it take to move the object over #x in [(pi)/12, (5pi)/8], where x is in meters?

Answer 1

The work is `=174.64J`

Explanation:

`"Reminder : "`

`intcotxdx=ln|(sin(x))|+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+cot(x))`

The normal force is `N=mg`

The mass of the object is `m=6kg`

`F_r=mu_k*mg`

`=6*(1+cot(x))g`

The work done is

`W=6gint_(1/12pi)^(5/8pi)(1+cot(x))dx`

`=6g*[x+ln|(sin(x))|]_(1/12pi)^(5/8pi)`

`=6g((5/8pi+ln(sin(5/8pi))-1/12pi-ln(sin(1/12pi)))`

`=6g(2.97)`

`=174.64J`