. A text book of elementary mechanics, for the use of colleges and schools. ese general equa-tions take a special form applicable to the particular case. (a) The power act* along the plane (Fig. 178). Hereft = 0, and cos ft = 1; hence, from the general value _ IF sin # , , . P = --—, we obtain cosp P = If sin or, (3) and, from the general value of i? = —771——, we obtain cosp J? = If cos a. (4) 238 STATICS. (b) The power acts horizontally (Pig. 179).fi = — ol, cos (— a) = cos a. Hence, for Here p __ W sin a . , -r—, is obtained cos/3 P = JTsin <^ cos or W tan or, (5) and, for R = TTcos(ar+/?
. A text book of elementary mechanics, for the use of colleges and schools. ese general equa-tions take a special form applicable to the particular case. (a) The power act* along the plane (Fig. 178). Hereft = 0, and cos ft = 1; hence, from the general value _ IF sin # , , . P = --—, we obtain cosp P = If sin or, (3) and, from the general value of i? = —771——, we obtain cosp J? = If cos a. (4) 238 STATICS. (b) The power acts horizontally (Pig. 179).fi = — ol, cos (— a) = cos a. Hence, for Here p __ W sin a . , -r—, is obtained cos/3 P = JTsin <^ cos or W tan or, (5) and, for R = TTcos(ar+/?) . , \ ^—jt9 is obtained cos/? • R Wcos or = W sec or. (6) From (5), it a - 90°, P = oo ; that is, no finite forcecan support a body against a vertical surface if the sur-faces in contact are perfectly smooth and there is noadhesion. This is only a special case of the generalprinciple that the action of a force does not affect themotion of a body in a direction at right angles to that inwhich it acts. 230. The results in (a) and (b) of the preceding. article can also be obtained independently by anothermethod. (a) The power acts along the plane. Let the linesP, P, W represent the three forces holding the body at 230.] IKCLIKED PLANE. 239 A in equilibrium. From P draw BC parallel to thedirection of W\ then the triangle ABC has its threesides respectively parallel to the three forces, and hence(132, Cor.) these sides are proportional to them. Again,the triangles AB C and KHL are mutually equiangularand similar, hence P: W:R = AB:BC: AC, or and = HK: HL: LK; p w = HKHL = Sm a> RW = LK -^yy = cos a. (1) (2) The result in (1) is sometimes stated in this form:Wlien the Potver acts along the plane, the Poiver is to theWeight as the height of the plane is to the length. (i) The power acts horizontally. Let (Fig. 179) the
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectmechanics, bookyear18
