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+3cotx`. 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 `=128.8J`

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+3cotx)`

The normal force is `N=mg`

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

`F_r=mu_k*mg`

`=6*(1+3cotx)g`

The work done is

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

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

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

`=6*9.8*2.19`

`=128.8J`