Question

Question #87f21

Answer 1

`K =[Fcostheta-mu(mg-Fsintheta)]d`

Explanation:

Use work-energy principle:

`W_"net" = DeltaK`

`vecF_"net"*vecd =K-0`

`K = vecF_"net"*vecd`

Because the sheeps is pulled a distance horizontally, meaning the net force is in the direction only, as components in the vertical (y) direction canceled out.

`K = vecF_"net"*vecd = F_"net"d`

The net force is the difference between the horizontal component of F and the friction counting the motion:

`F_"net"=F_x-f_k = Fcostheta-mu_kN`

Note: `N !=mg` because both the normal force and the vertical component of F are lifting the sheep such that

`Fsintheta+N=mg rArr N= mg-Fsintheta`

`therefore K =[Fcostheta-mu(mg-Fsintheta)]d`