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A Guide to Physics Problems. part 12 Mechanics, Relativity, by S.Cahn, B.Nadgorny

By S.Cahn, B.Nadgorny

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See Figure P. 47). a) Find an expression for the velocity of the water b) Find the corresponding dispersion relation. 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.

C) For what is the stable equilibrium value of d) What is the frequency of small oscillations about this point? 33. Two balls, each of mass are attached by means of four hinged arms, each of length to sleeves on a vertical rod. The upper sleeve is fastened to the rod; the lower sleeve has mass M and is free to slide up and down the rod as the balls move out from or in toward the rod. The rod-and-ball system rotates with constant angular velocity 20 PROBLEMS a) Set up the equation of motion, neglecting the weight of the arms and rod.

Estimate the magnitude of the centrifugal and Coriolis forces relative to the gravitational force (ignore friction). Take New York and San Francisco to be of equal latitude (approximately 40° North). 11 String Oscillations (Moscow Phys-Tech) The frequency of oscillation of a string depends on its length L, the force applied to its ends T, and the linear mass density Using dimensional analysis, find this dependence. 12 Hovering Helicopter (Moscow Phys-Tech) A helicopter needs a minimum of a 100 hp engine to hover (1 hp = 746 W).

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