(^72) A Textbook of Engineering Mechanics
- Select some suitable point p and draw a vertical line pq equal to 15 N to some suitable
scale representing weight (PQ) of the electric fixture. - Through p draw a line pr parallel to PR and through q, draw a line qr parallel to QR. Let
these two lines meet at r and close the triangle pqr, which means that joint C is in
equilibrium. - By measurement, we find that the forces in strings AC (TAC) and BC (TPC) is equal to
1.0 N and 7.8 N respectively. Ans.
Example 5.12. Five strings are tied at a point and are pulled in all directions, equally
spaced from one another. If the magnitude of the pulls on three consecutive strings is 50 N, 70 N and
60 N respectively, find graphically the magnitude of the pulls on two other strings.
Solution. Given : Pulls = 50 N ; 70 N and 60 N and angle between the forces =
360
72
5=°.
Let P 1 and P 2 = Pulls in the two strings.
First of all, let us draw the space diagram for the given system of forces and name them
according to Bow’s notations as shown in Fig 5.29 (a).
Fig. 5.29.
Now draw the vector diagram for the given forces as shown in Fig. 5.29 (b) and as discussed below :
- Select some suitable point a and draw a horizontal line ab equal to 50 N to some suitable
scale representing the force AB. - Through b draw a line bc equal to 70 N to the scale and parallel to BC.
- Similarly through c, draw cd equal to 60 N to the scale and parallel to CD.
- Through d draw a line parallel to the force P 1 of the space diagram.
- Similarly through a draw a line parallel to the force P 2 meeting the first line at e, thus
closing the polygon abcde, which means that the point is in equilibrium. - By measurement, we find that the forces P 1 = 57.5 N and P 2 = 72.5 N respectively. Ans.
5.9. CONDITIONS OF EQUILIBRIUM
Consider a body acted upon by a number of coplaner non-concurrent forces. A little consider-
ation will show, that as a result of these forces, the body may have any one of the following states:
- The body may move in any one direction.
- The body may rotate about itself without moving.
- The body may move in any one direction and at the same time it may also rotate about
itself. - The body may be completely at rest.