To understand how to double the mechanical advantage of a lever, we need to consider how the position of the fulcrum affects the distances from the fulcrum to the points where the forces are applied.
Initially, with the fulcrum at the center of a 12-meter lever, it is located 6 meters from both ends. The mechanical advantage (MA) of a lever can be calculated using the formula:
\[ MA = \frac{d_{effort}}{d_{load}} \]
where \( d_{effort} \) is the distance from the fulcrum to the point where the effort (or input force) is applied, and \( d_{load} \) is the distance from the fulcrum to the load (or output force).
In the initial configuration, if we assume that force is applied on one side and the load is at the other side of the fulcrum, we have:
- \( d_{effort} = 6 \) meters (the distance from the fulcrum to where the force is applied)
- \( d_{load} = 6 \) meters (the distance from the fulcrum to where the load is located)
Thus, the initial mechanical advantage is:
\[ MA = \frac{6}{6} = 1 \]
To double the mechanical advantage to 2, we want the relationship:
\[ MA = 2 = \frac{d_{effort}}{d_{load}} \]
To achieve this and double the mechanical advantage, we can either increase the distance \( d_{effort} \) (move the force application point away from the fulcrum) or decrease the distance \( d_{load} \) (move the load point closer to the fulcrum).
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Moving the fulcrum 2 meters away from the side on which the force is applied: This increases \( d_{load} \) but does not help achieve a double mechanical advantage.
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Moving the fulcrum 2 meters toward the side on which the force is applied: This would not provide a doubling of the mechanical advantage because \( d_{effort} \) is decreased, while \( d_{load} \) stays the same.
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Moving the fulcrum 4 meters away from the side on which the force is applied: This increases \( d_{load} \) and does not help achieve a double mechanical advantage.
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Moving the fulcrum 4 meters toward the side on which the force is applied: Initially, \( d_{effort} \) is 6 meters and \( d_{load} \) is also 6 meters. Moving the fulcrum 4 meters toward the load results in:
- New \( d_{effort} = 6 + 4 = 10 \) meters
- New \( d_{load} = 6 - 4 = 2 \) meters
Now, we can recalculate:
\[ MA = \frac{10}{2} = 5 \]
Though this configuration increases the mechanical advantage substantially, the goal is not just to have a higher MA, but to specifically target doubling the original MA.
Thus, the best way to double the mechanical advantage, which started at 1, would be to increase the distance to the effort or reduce the distance to the load.
So the best choice to double the mechanical advantage is to move the fulcrum 4 meters toward the side on which the force is applied.
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