Read e-book online A Course of Mathematics for Engineers and Scientists. PDF

By Brian H. Chirgwin, Charles Plumpton

ISBN-10: 0080093760

ISBN-13: 9780080093765

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Sample text

A third cylinder, of radius a and weight 2 W, rests symmetrically on the first two. Show that for equilibrium the angle of friction for the cylinders in contact must not be less than π/8. Show also that the coefficient of friction between the cylinders and the ground must not be less than -J tan(:rc/8). 4. Two uniform circular cylinders, of equal weight but unequal radii, are placed in contact with their axes horizontal on a rough plane inclined at an angle a to the horizontal, the lower cylinder having the smaller radius.

The rod therefore d e p a r t s slightly from the strict linear shape, the deflection a t a point depending on the stresses there and the elastic properties. We discuss this t y p e of problem in Chap. I I I . 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 2πα and modulus nnW. 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 lower cylinders is W I 3n -f —^-1 and the reaction between the lower cylinders is / 1 \ |3 either zero or W 13 n — I, according as n < or > -— .

A heavy uniform chain of length I is attached at one end to a point A at height h < I above a rough horizontal table. The point A is moved parallel to the table with constant velocity. Show that the length s of the chain which remains free of the table is the positive root of s2+ 2μΚ8 = Ä2 + 2μΜ, where μ is the coefficient of friction between the chain and the table. 13. A perfectly flexible uniform heavy chain has one end fixed at a point A and the other end at a point B, which is higher than A.

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A Course of Mathematics for Engineers and Scientists. Theoretical Mechanics by Brian H. Chirgwin, Charles Plumpton


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