Question

An object with a mass of `5 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 1-cos(x/2)`. How much work would it take to move the object over #x in [0, 8pi], where x is in meters?

Answer 1

The work is `=1231.4J`

Explanation:

`"Reminder : "`

`intcosxdx=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-cos(x/2))`

The normal force is `N=mg`

The mass of the object is `m=5kg`

`F_r=mu_k*mg`

`=5*(1-cos(x/2))g`

The work done is

`W=5gint_(0)^(8pi)(1-cos(x/2))dx`

`=5g*[x-2sin(x/2)]_(0)^(8pi)`

`=5g((8pi-2*0)-(0-2*0))`

`=5g(8pi)`

`=1231.4J`