By S.Cahn, B.Nadgorny
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Extra info for A Guide to Physics Problems. part 12 Mechanics, Relativity, and Electrodynamics
You may assume that the flow of the water is irrotational that the amplitude of the waves is small (in practice, this means that where is the MECHANICS 29 height of the waves), that surface tension effects are not important, and that water is incompressible. 48 Suspension Bridge (Stony Brook) A flexible massless cable in a suspension bridge is subject to uniform loading along the The weight of the load per unit length of the cable is and the tension in the cable at the center of the bridge (at is (see Figure P.
29b). Write down the Lagrangian in terms of the generalized PROBLEMS 18 coordinates and Identify two conserved quantities and express them as functions of and Which way does the cylinder spin? 30 Six Uniform Rods (Stony Brook) Six equal uniform rods, fastened at their ends by frictionless pivots, form a regular hexagon and lie on a frictionless surface. 31 19 Period as Function of Energy (MIT) A particle of mass moves in a one-dimensional potential where A is a constant. 32 Rotating Pendulum (Princeton, Moscow PhysTech) The bearing of a rigid pendulum of mass is forced to rotate uniformly with angular velocity (see Figure P.
10 Thru-Earth Train (Stony Brook, Boston (a), Wisconsin-Madison (a)) A straight tunnel is dug from New York to San Francisco, a distance of 5000 kilometers measured along the surface. A car rolling on steel rails is released from rest at New York, and rolls through the tunnel to San Francisco (see Figure P. 10). MECHANICS 9 a) Neglecting friction and also the rotation of the Earth, how long does it take to get there? Take the gravitational acceleration and the radius of the Earth R = 6400 km. b) Suppose there is now friction proportional to the square of the velocity (but still ignoring the rotation of the Earth).