This in fact is the principle of the balance A balance has two pans of equal

# This in fact is the principle of the balance a

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This, in fact, is the principle of the "balance." A balance has two pans of equal weight suspended from the ends of a horizontal rod that pivots about a central fulcrum. If an object of unknown weight is placed in one pan, combinations of known weights can be put on the other till the two pans balance. We then know that the unknown weight is equal to the sum of the known weights in the other pan. (As explained this actually serves to measure mass as well as weight.) Because of its use in the balance, a lever subjected to equal and opposite torques is said to be in equilibrium (from Latin words meaning "equal weights"), and this expression has come to be applied to any system under the stress of forces that produce effects that cancel out and leave the overall condition unchanged. For a lever to be in equilibrium it must-be subjected to equal and opposite torques, and this may be true even it the forces applied are unequal. Consider a downward force (f) applied on one side of a lever at a given distance (r) from the fulcrum. The torque would be fr. Next consider a downward force twice as large (2f) applied to the other side of the fulcrum but at a distance only half that of the first (-r/2). (The distance is here given a negative sign, because it is in the opposite direction from that fulcrum, as compared with the first). This second torque is (2f)(-r/2), or -fr. The two torques are equal and opposite, and the lever mains in equilibrium. If the forces are produced by unequal weights resting on the ends of the lever, it is easy to see that the center of gravity of the system must shift toward the end with the greater weight. To maintain equilibrium, the fulcrum must be directly under the new position of-the center of gravity. When this is done, it will be found that its position is such that the product of
one weight and its distance from the fulcrum will be equal to the product of the other and its distance from the fulcrum. Thus if two children of roughly equal weight are on a seesaw, they are right to sit at the ends. If one child is markedly heavier than the other, he should sit closer to the fulcrum. The two should so distribute themselves, in fact, that their own center of gravity plus that of the seesaw remains directly above the fulcrum. (it is also possible, in the case of some seesaws, to shift the board and adjust the position of the fulcrum.) Because of the fact that torques rather than forces must be equal in order to produce equilibrium, a lever can be put to good use. Suppose a 250-kilogram weight (equivalent to a force of about 2450 newtons) is placed 1 meter from the fulcrum. Next suppose that 10 meters from the fulcrum on the other side of the lever a man applies a downward force of 245 newtons (the equivalent of a 25-kilogram weight). The torque associated with the force (25 X 10) is equal and opposite to that of the torque produced by the weight on the other side of the lever (250 X 1). The lever is then placed in equilibrium and the heavy weight is supported by the light force. If the man applies a somewhat greater force (one that is

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