Book Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 edition. Excerpt: ... angle of 80 between them. With any convenient scale, say 10 pounds to the inch, measure off A B: 60 +10 = 6 inches, and A C: 90 + 10: 9 inches. Through B, draw B D parallel to A C, and through C, draw C D parallel to A B, intersecting at D. Then draw A D, and A D will be the resultant; its direction is towards the point D, as shown by the arrow. Measuring A D, we find that its length: 11.7 inches. Hence, 11.7 X 1(_): 117 pounds. Ans. Caution.---In solving problems by the graphical method, use as large a scale as possible. More accurate results are then obtained. 87 7. The above example might also have been solved by the method called the triangle of forces, which is as follows: In Fig. 114, suppose that the two forces acted separately, first from A to B, and then from B to D, in the direction of the arrows. Draw A D; then A D is the resultant of the forces A B and A C, since BD= A C; but AD is a side of the triangle A B D. It will A also be noticed that the direction of A D is opposed to that of A B and B D; hence, to find the resultant of two forces acting upon a body at a common point, by the method of triangle of forces: Rule II.--Draw the lines of action of the two forces as if each force acted separately, the lengths of the lines being proportional to the magnitude of the forces. foin the extremities of the two lines by a straight line, and it will be the resultant; its direction will be opposite to that of the two forces. No'1E.--When we speak of the resultant being opposed in direction to the other forces around the polygon, we mean that, starting from the point where we began to draw the polygon, and tracing each line in succession, the pencil will have the same general direction around the polygon, as if passing around a circle, ...