By Brian H. Chirgwin
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Extra resources for A Course of Mathematics for Engineers and Scientists. Volume 3: Theoretical Mechanics
The plane containing the axes of the cylinders makes an angle a + /3 with the horizontal, p is the coefficient of friction between the cylinders and piis the coefficient of friction bet ween each cylinder and the plane. If the cylinders are in equilibrium, show that: (i) the frictional force is the same at all contacts, (ii) for equilibrium to be maintained at the line of contact of the cylinders /1 „>- cot/3 , (iii) for the upper cylinder not to slip on the plane tan a a 1 + p, sec/3 PLANE STATICS AND VIRTUAL WORK 43 5.
The rod therefore departs slightly from the strict linear shape, the deflection at a point depending on the stresses there and the elastic properties. We discuss this type of problem in Chap. III. Miscellaneous Exercises II 1. Three smooth circular cylinders, of equal radii a and equal weights W, are held together in contact along generators by a light elastic band of natural length 2na and modulus nn W. Two of the cylinders rest on a horizontal table with the third above them. Show that the reaction of the upper cylinder on either of the 1 lower cylinders is W and the reaction between the lower cylinders is (3n1/3, either zero or W (3n, 2 according as n < or > 1/ 3 18 1 ) 2.
LOB, is frequently useful in finding equivalent sets of forces. Examples. (i) A system of coplanar forces acting on a rigid body is equivalent to forces X, Y along rectangular axes Ox, Oy together with a couple of moment G. Prove that the system is equivalent to a single force in the line Xy — Yx G 0. The moments of a system of coplanar forces about the points (2, 1), ( 3, 4) and (1, — 3) are 11, — 15 and 15 units respectively. Find the magnitude and the equation of the line of action of the force acting at the point (3, 2) which, together with the given system, constitute a couple.
A Course of Mathematics for Engineers and Scientists. Volume 3: Theoretical Mechanics by Brian H. Chirgwin