By Arthur Stanley Ramsey
A. S. Ramsey (1867-1954) used to be a uncommon Cambridge mathematician and President of Magdalene collage. He wrote a number of textbooks 'for using greater divisions in faculties and for first yr scholars at university'. This e-book on statics, released in 1934, was once meant as a better half quantity to his Dynamics of 1929 and prefer the latter used to be established upon his lectures to scholars of the mathematical tripos, however it assumes no earlier wisdom of the topic, presents an advent and provides extra that a hundred instance issues of their strategies. issues comprise vectors, forces performing at some extent, moments, friction, centres of gravity, paintings and effort, and elasticity.
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Additional info for Statics: A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities
4*5. Centre of Parallel Forces. Let n parallel forces Ply P2, ... Pn act at points Ax, A2, ... An. Then, whether the forces are all in the same sense or not, if we compound them together step by step, the resultant of P1 and P 2 is P1 + P2 acting at a point Bx on AXA2 such that P x . A1B1 = P 2 . B2AS and so on. But this process is that defined in 2*6 as finding the centroid of the points Ax, A2,... An for multiples P1,P2,... Pn, and as proved in 2*61 it leads to a unique point 0 through 4-4-4-51] CENTRE OF PARALLEL FORCES 37 which the resultant of the parallel forces P 1 ; P 2 , ...
If we denote the tensions in BC, CA, AB by 3-5-3-7] CONSTBAINTS 23 Tlt T2, T3, then, considering each particle separately, and A is in equilibrium under the forces P, T2, T3, B is in equilibrium under the forces Q, T3, Tx, C is in equilibrium under the forces R, Tx, Ta. And the system of three particles A, B, C is in equilibrium under the action of the three forces P, Q, R, because when we add together the nine forces previously named they include three pairs of equal and opposite forces which cancel out.
So far we have only considered the case of forces acting 'at a point' or on a single particle. It is a simple step further to the case of two or more particles in equilibrium under the action of given forces and the interactions of the particles upon one another. Q For example, let A, B, C be three particles connected by light threads which are kept taut by applying forces P, Q, B to the particles A, B, C respectively. The interaction between each pair of particles is then a tension in the string joining them, which acts in opposite directions on the two particles.