TM No. 377 



- A r*w * 



represents the net force per unit area acting in the horizontal direction on 

 the slab. 



If the slab is moving in the X direction at a velocity u, then 



£||f *v <£* 



(v-31) 



represents the work done on the slab per unit area per unit time. 

 It follows that 





f itW 



(V-32) 



is the time rate of work on a unit slab by stresses per unit horizontal area. 

 For a finite volume 



ft 



CAftt'oM* 



s, 



(v-33) 



represents the rate of work done on the slab of thickness 2q_ "bounded on the 

 top by the free surface (« = 0) and on the bottom by the plane Eq_ (a constant), 

 Integral (V-33) may be written as: 





/-o 



~uf>Mclt + 



d£ 



J 





h 



(V-3*0 



Integrating the first term directly gives: 



136 



