document.write( "Question 1145964: Please help me to solve this problem,,\r
\n" ); document.write( "\n" ); document.write( "A uniform beam 15 feet long weight 3 poundy pee linear foot. at what point should it be supported by a fulcrum if a weight of 25 pounds on end is balanced by a weight of 65 pounds on the other end? \n" ); document.write( "

Algebra.Com's Answer #767247 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " I will assume that your level of knowledge and intuition in Physics does correspond to the complexity level of the problem\r
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document.write( "Let x be the distance from the end point loaded by the weight of 25 pounds to the fulcrum.\r\n" );
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document.write( "Then the distance from the other end to the fulcrum is  (15-x) feet.\r\n" );
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document.write( "The moment of the force (which is weight) at the (x)-th part of the beam is  25x + .                     (1)\r\n" );
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document.write( "The moment of the force (which is weight) at the (15-x)-th part of the beam is  65*(15-x) + .    (2)\r\n" );
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document.write( "The condition of equilibrium is equality of these two moments of force\r\n" );
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document.write( "    25x +  = 65*(15-x) + .\r\n" );
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document.write( "To solve this equation, multiply both sides by 2\r\n" );
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document.write( "    50x + 3x^2 = 130*15 - 130x + 3*(15-x)^2,\r\n" );
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document.write( "    50x + 3x^2 = 130*15 - 130x + 3*(15-x)^2.\r\n" );
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document.write( "Simplify this quadratic equation to its standard form and solve using the quadratic formula.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice. In formulas (1) and (2), the fraction parts represent the moments of force created by \r
\n" ); document.write( "\n" ); document.write( "uniformly distributed weight along the parts of the beam.\r
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\n" ); document.write( "\n" ); document.write( "In such problems, when calculating moments, uniformly distributed force (weight, in this case)\r
\n" ); document.write( "\n" ); document.write( "is replaced by the equal concentrated force, applied at the middle of the corresponding arm/shoulder of the leverage.\r
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