122

STATICS.

body, the magnitude and direction of an unknown pressure,and so on, we may frequently set aside some of the equationsas having n*o reference to the particular point of enquiry.Thus in Art. 121 . the object is to find T, the tension of thetie-beam. Upon examining the four equations we see imme-diately that (2) may be set aside, because it contains an un-known quantity R, which does not enter any of the otherequations, and therefore (2) is of use solely to determine R,a quantity which it is not the immediate object of the problemto discover. Equation (l) gives T when P and 9 are known,and these are found from ( 3 ) and ( 4 ). Again, Art. 122 . givesa good illustration of an indeterminate problem. For (l) (2)(3) are the only mechanical equations that can possibly exist,and these contain only one unknown geometrical quantity a.’,and consequently a fourth equation does not exist, or theproblem is indeterminate: as we might easily have foreseenfrom the nature of the case. It does not follow that everyunknown quantity in the equations is indeterminate, as we seein this instance.

146. We shall now add a few Problems.

Prob. 1. A given weight W is held at rest on a knowncurve AP lying in a vertical plane by means of a given weightQ acting over the pully B : required the position of rest:fig. 60.

The vertical BM through B is the axis of w, B the origin,BM = <v, MP = y, P being the position of the weight; angleB = 6- Now the weight is held in equilibrium by Q actingin PB, W in PW, and the reaction of the curve, or R, actingin GR a normal to the curve at P: hence, resolving theseforces vertically and horizontally, Art. 23 . gives

W - Q cos 9 - R cos PGB = 0,

Q sin 9 — R sin PGB = 0;

or, since tan PGB = — ,

dy

W- Qcos9 -R^ = 0

as

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