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Explain the construction and working of an ideal lever and also explain the principle of moment of force. |
Answer» Solution :An ideal lever is a light ROD of negligible mass pivoted at the point along its length. This point is CALLED the fulcrum. The lever is a system in mechanical equilibrium.  Two forces `vec(F_(1)) and vec(F_(2))` parallel to each other and usually perpendicular to the lever, as shown here, act on the lever at distances `d_(1)andd_(2)` respectively from the fulcrum as shown in fig. Let `vecR` be the reaction of the support at the fulcrum. `vecR` is directed opposite to the forces `vec(F_(1))` and `vec(F_(2))`. The forces in upward direction are considered positive and the forces in downward direction are considered negative. For translational equilibrium `R-F_(1)-F_(2)=0....(1)` `therefore R=F_(1)+F_(2)` The lever force `F_(1)` is some weight to be LIFTED. It is called the load and its distance from the fulcrum `d_(1)` is called the load arm. Force `F_(2)` is the effort applied to lift the load, distance `d_(2)` of the effort from the fulcrum is the effort arm. For rotational equilibrium, sum of torque about a effort point should be ZERO and moment of force `tau=d xxF[because theta=90^(@), therefore sin90^(@)=1]` `therefore d_(1)F_(1)-d_(2)F_(2)=0` Here, the anticlockwise moment is considered as positive and the clockwise moment is considered as negative. So `d_(2)F_(2)` taken with negative. `therefore d_(1)F_(1)=d_(2)F_(2)` Means load arm `xx` load = effort arm `xx` effort The above equation expresses the principle of moment for a lever. The ratio `(F_(1))/(F_(2))` is called the mechanical advantage [M.A.] `therefore M.A.=(F_(1))/(F_(2))=(d_(2))/(d_(1)) [because d_(1)F_(1)=d_(2)F_(2)]` If the effort arm `d_(2)` is larger than the load arm, `[d_(2)gtd_(1)]` the mechanical advantage is greater than one. Means that a small effort can be used to lift a large load. The principle of moment holds even when the parallel force `vec(F_(1))andvec(F_(2))` are not perpendicular but act at some angle to the lever. |
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