Question #87f21

1 Answer
Feb 13, 2018

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