98 



STATICS OF EIGID BODIES 



ILLUSTRATIVE EXAMPLE 



Forces P, Q, B act on a rigid body, all the forces being in one plane,_and their 

 lines of action forming a right-angled isosceles triangle of sides a, a, Vj? a. Find 

 their resultant, 



Let ABC be the triangle, the forces P, Q, E acting along BC, CA, AB 

 respectively. Take C for origin and CB, CA for axes of x, y. Let the resultant 

 have components X, Y. Then, resolving along Cx, we obtain 



V2 



and similarly resolving along Cy, 



Thus the resultant is of magnitude R given by 



> Q' 



R 2 = X* + F 2 = ( - 



V2/ 

 = P 2 + Q 2 + E 2 - V2 (P + Q) . 



The angle which it makes with Cx is given by 



y 



P B 



FIG. 52 



x 



To find the line of action, we express that the moment of R about C must be 

 to the sum of the moments of P, Q, and R. If p is the perpendicular 

 from C on to the line of action of the resultant R, this gives 



a 



Rp = E 



VI' 



so that 



E a 



and this determines the line of action of R. 



EXAMPLES 



(All forces are supposed to be acting on rigid bodies) 



1. ABCD is a square, and along the sides AB, BC, CD there act forces of 

 1, 2, 3 pounds respectively. Determine the magnitude and line of action of the 

 resultant. 



2. ABCD is a square and forces P, Q, E, S act along the sides A B, BC, CD, 

 DA respectively. What is the condition that their resultant shall pass through 

 the center of the square ? 



3. In question 2, what is the condition 



(a) that the resultant shall pass through A ? 



(b) that it shall pass through B ? 



(c) that the four forces shall be in equilibrium ? 



