The Elementary Principles of Mechanics; Kinetics. 1895 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1895 Excerpt: ...particle and curve or surface, or the reaction on the particle must always be away from the curve or surface. We have then for the friction, when there is any, F = Mn, where M is the coefficient of kinetic friction. The direction of the friction is always opposite to the direction of the motion. The resultant tangential force is then T--F= T--mn, or T--F at Wt COS fa + Fy cos fa + Fz cos fa--Mn... (8) The resultant reaction R (figure, page 118) lies in the plane of Tand Tand makes the angle of friction P with N, so that 'B = VN1 + M'n' = NVT+P = (9) cos p If T--F = 0, we have equilibrium. If there is no equilibrium, T--F must be greater or less than zero, and hence For a smooth curve or surface fi = 0, F = 0. For a straight line or plane p = oo and = 0. p Reaction--External Forces Zero.--If there are no external forces we have Fx = 0, Fy= 0, Fz = 0. Hence from (3) Nn = 0, and from (4) and (5) N = Np and vp--0, Vn = 90, or the normal reaction lies in the radius of curvature. We have then from (2)' Np=+--, always acting towards the centre of curvature. There can only be friction when there is pressure between the curve or surface and particle, that is, when Np is away from the curve, or the particle is on the concave side. Reaction--All Forces Co-planar.--If all the forces are co-planar, H' (figure, page 118) must lie in the plane of p and T, and hence Nn = 0 and N = Np, or the normal reaction lies in the radius of curvature. Reaction--Plane Curve in General.--For a plane curve in general we may take the plane of the curve that of IF; we have then 9z = 90, = 90, e = 90, e = 90, e = Q... (1);OS Vx = COS Vp COS 9a;, COS Vy = COS Vp COS 6y, COS Vz--COS Vn. (6) In order that there may be friction there must be pressure between the curve and particle ...