A construction worker needs to lift a heavy metal beam using a lever but has a limited length of plank. Which adjustment would allow the worker to lift the beam with the least effort if the position of the fulcrum can be changed but the plank length remains constant?
Move the fulcrum closer to the beam
To solve this problem, it is essential to understand the concept of levers, which is a simple machine used to amplify force. The lever operates around a fulcrum and helps lift heavy loads using an applied force. The lever principle is explained by the formula:
F_1 \times d_1 = F_2 \times d_2
where:
- F_1 is the force applied by the worker.
- d_1 is the distance from the fulcrum to the point where the force is applied.
- F_2 is the force exerted on the load (beam).
- d_2 is the distance from the fulcrum to the load.
To lift the beam with the least effort, the worker needs to maximize the mechanical advantage, which depends on the ratio of these distances. By moving the fulcrum closer to the beam, d_2 becomes shorter, and d_1 becomes longer. This means that for the same effort, a larger load can be lifted because the mechanical advantage is increased.
Now, let's analyze the options:
- Keeping the fulcrum fixed at any point does not take advantage of the lever principle since no adjustment is made to increase mechanical advantage.
- Moving the fulcrum closer to the worker decreases d_1, making it harder to lift the beam.
- Moving the fulcrum closer to the beam increases d_1, which increases the mechanical advantage and allows the worker to lift the beam with less effort.
- Placing the fulcrum at the center of the plank is not optimal as it does not take full advantage of the potential mechanical advantage.
Thus, the correct choice is to move the fulcrum closer to the beam, which will maximize the lifting capability with minimal effort.
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