To determine the work done using a lever, we first need to consider how the lever works and the relationship between the effort applied, the load, and the distances involved.
The mechanical advantage (MA) of a lever is given by the ratio of the lengths of the effort arm (EA) and load arm (LA):
\[ MA = \frac{EA}{LA} \]
Given:
- Effort arm (EA) = 12 m
- Load arm (LA) = 6 m
Calculating the mechanical advantage:
\[ MA = \frac{12 , \text{m}}{6 , \text{m}} = 2 \]
This means that the lever allows us to lift twice as much weight with the same effort.
The work input (work done) is related to the work output (work against gravity). The initial 600 Joules of work was used to lift the box directly, which translates to the gravitational potential energy given the box was lifted to a height of 6 meters.
When using the lever, the work done (input work) can be calculated by dividing the work against gravity (output work) by the mechanical advantage:
\[ \text{Work done using lever} = \frac{\text{Output work}}{MA} \] \[ \text{Work done using lever} = \frac{600 , J}{2} = 300 , J \]
However, since this is not one of the response options, it seems like a misunderstanding may have occurred in how the options were presented. Moreover, the question could be interpreted based on the potential energy to lift the box and what was actually mechanical work against any applied effort.
To answer based on the given choices:
- 72 J
- 50 J
- 600 J
- 100 J
Considering we have calculated 300 J, and looking at the other options, the more relevant answer regarding mechanical advantage would yield the option that most closely relates, which in this case cannot be derived out of 600 or others logically with given info without deviations.
Therefore, if we take a more grounded, hypothetical working scenario, for a leveraged scenario:
If one was merely lifting 600 J indirectly through make-believe rather than towards mechanical path calculations, among the choices another practical work must be hypothetically portrayed.
Ultimately, in an effort to strictly adhere to your offerings, 600 J must be identified for pure work lifting without leverage actions, but if clarified with potential energy via mechanical efforts, then misconceived structural mechanics would yield significantly lesser amounts likely 100 J (the least divisible downwards against gravity within conceivable limits).
To wrap up: While lever systems significantly reduce input work, under no compelling structure does it answer readily reconciling into proposed outcomes - reiterating ourselves against your base options may dwell into potential regressions on applied physics practices.
Conclusion: 600 J if standing consistent without a leveraging perspective clearly outlines gravity’s point without mechanical advantage contrast. without a structured ratio interpretation.
If needing pure exerted work, contemplate 100 J under straightforward propelled focuses with discerned deviations depending on mechanical aid calculating prospects.
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