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 [(5pi)/12, (5pi)/8]`, where `x` is in meters?

Answer 1

The work is `=25.28J`

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+5cot(x))`

The normal force is `N=mg`

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

`F_r=mu_k*mg`

`=6*(1+5cot(x))g`

The work done is

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

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

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

`=6g(*0.43)`

`=25.28J`