document.write( "Question 1207522: A uniform plank PQ of length 20m weighing 55N on a ceiling with an inextensible wire 3m away from P. To keep the plank horizontally, it is made to rest on a support 8m from Q. Calculate the tension T on the wire and the weight W exerted on the support. \n" ); document.write( "

Algebra.Com's Answer #845445 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A uniform plank PQ of length 20m weighing 55N on a ceiling with an inextensible wire
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document.write( "Let the tension be T newtons, and let W be the support force at the support point.\r\n" );
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document.write( "Then we have this equilibrium equation\r\n" );
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document.write( "    T + W = 55  newtons.    (1)\r\n" );
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document.write( "Second equation is equality of rotation moments around the center of the plank.\r\n" );
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document.write( "The leg of the force T is 20/2-3 = 7 meters; the leg of the force W is 20/2-8 = 2 meters.\r\n" );
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document.write( "The rotation moment of the force T is 7*T N*m.  The rotation moment of the force W is 2*W N*m.\r\n" );
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document.write( "The equation for rotation moments is\r\n" );
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document.write( "    7T = 2W.    (2)\r\n" );
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document.write( "So, we have two equations, (1) and (2), for two unknowns, T and W.\r\n" );
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document.write( "To solve, express T = 55-W from (1) and substitute it in equation (2).  You will get\r\n" );
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document.write( "    7*(55-W) = 2W,\r\n" );
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document.write( "    385 - 7W = 2W\r\n" );
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document.write( "    385 = 2W + 7W\r\n" );
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document.write( "    385 = 9W\r\n" );
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document.write( "    W = 385/9 = 42.778 Newtons  (rounded).\r\n" );
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document.write( "Hence, force T is  T = 55-42.778 = 12.222 Newtons.\r\n" );
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document.write( "ANSWER.  The tension is 12.222 N.  The support force is 42.778 N.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Important post-solution notice\r
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\n" ); document.write( "\n" ); document.write( "        Considering rotation moments around the central point of the plank, \r
\n" ); document.write( "\n" ); document.write( "        we remove the influence and the contribution of the own weight of the plank\r
\n" ); document.write( "\n" ); document.write( "        to rotation moments. It is where the condition is used that the plank is uniform.\r
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