An Elementary Treatise On Theoretical Mechanics

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'' C ' or A B C 215. To show the application of the conditions of equilibrium, let us consider the simple machine called the wheel and axle. It consists of a horizontal shaft (Fig. 71) resting with its ends on the supports or bear- ings A, B, and is intended to raise a weight W, suspended vertically by means of a rope wound' around the shaft. The driving force F is applied •b a a, a fR^lTr ^ ■■W Fig. 71.
on the circumference of the "wheel," «>. in a vertical plane at right angles to the axis of
... the shaft. It is required to find the relation between F and W for equilibrium, and the pressures on the bearings A,B.
I30 STATICS. [216.
Let r be the radius of the shaft, R that of the wheel, i.e. the lever- arm of the force F, and let F be inclined to the vertical at an angle Q ; then, with the co-ordinates and notations of the figure, the conditions %X=o, 2F=o, 2Z=o, give A,-\-B^=Q, Ay-\-By—W—F coi,6 = o, A,+£,+FsinO:=o, where A^, Ay, A^ are the components of the unknown reaction at A ■, B„ By, B„ those at B.


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