By Andrew M. Gleason
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Additional resources for The William Lovell Putnam Mathematical Competition. Problems and solutions 1938-1964
P. Canale. Numerical Methods for Engineers, 4th edition, McGraw-Hill, New York (2002). REFERENCES 33 Elmqvist, H. and M. Otter. Methods for Tearing Systems of Equations in Object-Oriented Modeling. Proceedings of the European Simulation Multiconference, Barcelona (1994). Faucett, L. Numerical Methods Using Mathcad, Prentice Hall, Upper Saddle River, NJ (2002). Hamming, R. W. Introduction to Applied Numerical Analysis, McGraw-Hill, New York (1971). Heath, T. L. Diophantus of Alexandria: A Study in the History of Greek Algebra, 2nd edition, Dover Publications, New York (1964).
8 mi north of the intended point. ground exerts a force on the bottom end of the beam indicated by F2. We recognize that under the equilibrium condition, the summation of forces in the horizontal (x-) direction must be zero. Similarly, the summation of forces acting in the vertical (y-) direction must also be zero; therefore, F2 cos(θ ) − F1 = 0 and F2 sin(θ ) − W = 0. 33) For us to solve these equations, we must determine the angle, θ: We do this by using two right triangles and the first of these is formed using the lower half of the beam such that the hypotenuse is 15 ft; the vertical leg is the distance from the midpoint of the beam to the ground.
1. We will interpret this shear stress, τyx, as a force acting on the y-plane (the fixed surface is located at y = 0) due to fluid motion in the x-direction. Since we have three principal directions, it is clear that each of the two indices on τ can assume one of three values, corresponding to x, y, and z in Applied Mathematics for Science and Engineering, First Edition. Larry A. Glasgow. © 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 1. Shear stress created by fluid motion past a solid surface.
The William Lovell Putnam Mathematical Competition. Problems and solutions 1938-1964 by Andrew M. Gleason