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Reduction of a number of forces (ex. 1). 4 times that representing E. e. approximately 2\\° from the direction of C. (b) The number of forces may first be reduced by combining those directly opposite each other. Thus in Fig. 5 N . Then these are shown with Β in the polygon of Fig. 5, which gives the same resultant as in (a), Fig. 3. 6 shows another six-sided polygon equivalent to Fig. 3 but taking the five original forces in a different order, namely C, Β, A, E, D. COMBINATIONS O F FORCES FIG. 5.

Calculate (a) the coefficient of 38 VOL. I. 24. WORKED EXAMPLE A horizontal pivot passes through the centre of gravity of a horizontal beam weighing 20 N . 0 cm from the pivot. Determine the angle θ for equilibrium and the two values of reaction at the pivot, assuming the direction of the applied force to be (a) as in Fig. 20, and (b) as in Fig. 22. Solution (a) The horizontal component of Fa in Fig. 20 has no turning moment since it passes through the pivot, but the vertical compo2 nent 50 sin θ has a clockwise turning moment 50 sin 0 X 8 .

Here Ff% is equal to the maximum value calculated for (a) but in the reverse direction. 8 = 14 N . COMBINATIONS OF FORCES FIG. 18. Inclined position (ex. 19(a)). 37 FIG. 19. Inclined position (ex. 19(b)). 20. A metal block rests on a board 45 cm long. T o what height may one end of the board be raised before the block slips? 60. 21. 0 kg rests on a horizontal surface. A force of 30 Ν in a cord applied at 35° upward from the horizontal just moves the casting. Calculate the maximum friction force.

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