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+5cotx`. How much work would it take to move the object over `x in [(pi)/12, (3pi)/8]`, where `x` is in meters?

Answer 1

The work is `=428.1J`

Explanation:

`"Reminder : "`

`intcotxdx=ln(|sinx|)+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+5cotx)`

The normal force is `N=mg`

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

`F_r=mu_k*mg`

`=6*(1+5cotx)g`

The work done is

`W=6gint_(1/12pi)^(3/8pi)(1+5cot)dx`

`=6g*[x+5ln(sin(x) ] _(1/12pi)^(3/8pi)`

`=6g((3/8pi+5ln(sin(3/8pi))-(1/12pi+5ln(sin(1/12pi))`

`=6xx9.8xx7.28`

`=428.1J`