Question

An object with a mass of `4 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 5+tanx`. How much work would it take to move the object over `x in [(-pi)/12, (pi)/4]`, where `x` is in meters?

Answer 1

The work is `=217.6J`

Explanation:

We need

`inttanxdx=-ln(|cosx|)+C`

The work done is

`W=F*d`

The frictional force is

`F_r=mu_k*N`

The normal force is `N=mg`

The mass is `m=4kg`

`F_r=mu_k*mg`

`=4*(5+tanx)g`

The acceleration due to gravity is `g=9.8ms^-2`

The work done is

`W=4gint_(-1/12pi)^(1/4pi)(5+tanx)dx`

`=4g*[5x-ln|cosx|]_(-1/12pi)^(1/4pi)`

`=4g(5/4pi-ln|cos(1/4pi)|))-(-5/12pi-ln|cos(-1/12pi)|)`

`=4g(5.55))`

`=217.6J`