THE POLYGON OF FORCES 41 
Exercises IV. 
It is intended that all the following exercises should be worked graphically, but 
addition the student will find it advantageous to also calculate the reset: : =a 
1. Determine the resultant of the forces shown at Ex. 1, Fig. 39, (1) by means 
of the parallelogram of forces; (2) by means of the polygon of forces, taking 
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Fia. 39. 
In reproducing the above diagrams the sides of the small 
Squares are to be taken equal to half an inch. 
the forces in the order given ; and (3) by means of the polygon of forces, taking 
the forces alternately, instead of in the order given. 
2. By means of the polygon of forces determine the resultant of the forces 
shown at Ex. 2, Fig. 39. Also, find the magnitudes of two forces, one acting 
horizontally and the other vertically, which will balance the given forces. 
= 3 he eae polygon, determine the resultant of the forces shown 
at Ex, 3, . 39, 
4. Using a funicular polygon, determine the resultant of the forces shown 
at Ex. 4, Fig. 39. 
- 5. Find the resultant of the forces shown at Ex. 5, Fig. 39. 
6. Find the resultant ofthe forces shown at Ex. 6, Fig. 39. 
7. The forces shown at Ex. 7, Fig. 39, are in equilibrium. Find the mag- 
nitudes of P and Q. 
8. A beam, loaded as shown at Ex. 8, Fig. 39, rests on supports at its ends. 
Determihe the magnitudes of the reactions R, and Rg at the supports. 
9. Determine the resultant of the forces shown at Ex. 9, Fig. 39. 
10. The forces shown at Ex. 10, Fig. 39, are balanced by parallel forces acting 
at Aand B. Determine the forces at A and B. 
11. Find the resultant of the forces shown at Ex. 11, Fig. 39. 
12. The forces shown at Ex. 12, Fig. 39, are balanced by two forces, one of 
_ which (P) acts along the vertical line through A, and the other (Q) acts in a 
horizontal direction. Determine the forces P and Q. 
