To analyze the situation, we can use the concepts of work, force, and distance. In a system with a compound pulley, the advantage is often in the mechanical advantage it provides.
Work is calculated as:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
In this case, Alan is lifting the crate a vertical distance of 3.5 meters by pulling on the rope for a distance of 10.5 meters. The relationship between the work done with the pulley and the force exerted can be understood as follows:
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Mechanical Advantage: A compound pulley allows Alan to exert a smaller force over a longer distance. The mechanical advantage can be calculated based on the distances involved. If Alan pulls 10.5 meters of rope to lift the crate 3.5 meters, this indicates a mechanical advantage of:
\[ \text{Mechanical Advantage} = \frac{\text{Distance pulled}}{\text{Distance lifted}} = \frac{10.5 \text{ m}}{3.5 \text{ m}} = 3 \]
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Force Exertion: If he has a mechanical advantage of 3, that means he can lift the crate with one-third the force he would need to lift it directly without the pulley. This inverted relationship is due to the fact that the input effort is spread over a greater distance.
From the options given, the correct statement is:
Alan uses one-third the force he would have needed without the compound pulley.
Thus, the correct response is: "Alan uses one-third the force he would have needed without the compound pulley."
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