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Problem 2.3-14 A bar ABC revolves in a horizontal plane about a vertical axis at the midpoint C (see figure). The bar, which has length 2 L and cross-sectional area A , revolves at constant angular speed . Each half of the bar ( AC and BC ) has weight W 1 and supports a weight W 2 at its end. Derive the following formula for the elongation of one-half of the bar (that is, the elongation of either AC or BC ): 3 L g 2 EA 2 ( W 1 3 W 2 ) in which E is the modulus of elasticity of the material of the bar and g is the acceleration of gravity. Solution 2.3-14 Rotating bar SECTION 2.3 Changes in Lengths under Nonuniform Conditions 85 A C B L L W 2 W 1 W 1 W 2 C B L W 1 W 2 x F(x) dx d angular speed A cross-sectional area E modulus of elasticity g acceleration of gravity F ( x ) axial force in bar at distance x from point C Consider an element of length dx at distance x from point C . To find the force F ( x ) acting on this element, we must find the inertia force of the part of the bar from
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