SOLUTION: Please help me to solve this problem,,
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
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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
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Question 1145964: Please help me to solve this problem,,
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? Answer by ikleyn(52798) (Show Source):
I will assume that your level of knowledge and intuition in Physics does correspond to the complexity level of the problem
to such extent that you understand elementary facts without my explanations.
Let x be the distance from the end point loaded by the weight of 25 pounds to the fulcrum.
Then the distance from the other end to the fulcrum is (15-x) feet.
The moment of the force (which is weight) at the (x)-th part of the beam is 25x + . (1)
The moment of the force (which is weight) at the (15-x)-th part of the beam is 65*(15-x) + . (2)
The condition of equilibrium is equality of these two moments of force
25x + = 65*(15-x) + .
To solve this equation, multiply both sides by 2
50x + 3x^2 = 130*15 - 130x + 3*(15-x)^2,
50x + 3x^2 = 130*15 - 130x + 3*(15-x)^2.
Simplify this quadratic equation to its standard form and solve using the quadratic formula.
Notice. In formulas (1) and (2), the fraction parts represent the moments of force created by
uniformly distributed weight along the parts of the beam.
In such problems, when calculating moments, uniformly distributed force (weight, in this case)
is replaced by the equal concentrated force, applied at the middle of the corresponding arm/shoulder of the leverage.
