University Physics with Modern Physics with Mastering Physics (11th Edition)

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5.58: The hooks exert forces on the ends of the rope. At each hook, the force that the hook exerts and the force due to the tension in the rope are an action-reaction pair. The vertical forces that the hooks exert must balance the weight of the rope, so each hook exerts an upward vertical force of 2 w on the rope. Therefore, the downward force that the rope exerts at each end is 2 sin end w θ T = , so ). sin 2 ( ) sin 2 ( end θ Mg θ w T = = b) Each half of the rope is itself in equilibrium, so the tension in the middle must balance
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Unformatted text preview: the horizontal force that each hook exerts, which is the same as the horizontal component of the force due to the tension at the end; , cos middle end T θ T = so . ) tan 2 ( ) sin 2 ( cos middle θ Mg θ θ Mg T = = (c) Mathematically speaking, θ ≠ because this would cause a division by zero in the equation for end T or middle T . Physically speaking, we would need an infinite tension to keep a non-massless rope perfectly straight....
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This document was uploaded on 02/04/2008.

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