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University Physics with Modern Physics

You are a construction engineer working on the interior design of a retail store in a mall. A 2.00-m-long uniform bar of mass 8.50 kg is to be attached at one end to a wall, by means of a hinge that allows the bar to rotate freely with very little friction. The bar will be held in a horizontal position by a light cable from a point on the bar (a distance $x$ from the hinge) to a point on the wall above the hinge. The cable makes an angle $\theta$ with the bar. The architect has proposed four possible ways to connect the cable and asked you to assess them: (a) There is concern about the strength of the cable that will be required. Which set of $x$ and $\theta$ values in the table produces the smallest tension in the cable? The greatest? (b) There is concern about the breaking strength of the sheetrock wall where the hinge will be attached. Which set of $x$ and $\theta$ values produces the smallest horizontal component of the force the bar exerts on the hinge? The largest? (c) There is also concern about the required strength of the hinge and the strength of its attachment to the wall. Which set of $x$ and $\theta$ values produces the smallest magnitude of the vertical component of the force the bar exerts on the hinge? The largest? ($Hint:$ Does the direction of the vertical component of the force the hinge exerts on the bar depend on where along the bar the cable is attached?) (d) Is one of the alternatives given in the table preferable? Should any of the alternatives be avoided Discuss.