To determine how much work would be done using a lever, we need to consider the principles of levers and the concept of mechanical advantage.
The mechanical advantage (MA) of a lever can be calculated using the lengths of the effort arm (distance where the force is applied) and the load arm (distance where the load is placed):
\[ \text{MA} = \frac{\text{Effort Arm}}{\text{Load Arm}} = \frac{12 \text{ m}}{6 \text{ m}} = 2 \]
This means you can lift a load with half the force when using the lever. However, while the force is reduced, the distance moved is increased. The work done using a lever can be found using the formula:
\[ \text{Work Input} = \text{Force} \times \text{Distance} = \text{Load} \times \text{Distance Lifted} \]
Given that 600 Joules of work has already been used to lift the box without the lever, let's see how much work is done with the lever.
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Calculate the load: The work done to lift the box without a lever is: \[ \text{Work} = \text{Load} \times \text{Height} \] We know: \[ 600 \text{ J} = \text{Load} \times 6 \text{ m} \] So, \[ \text{Load} = \frac{600 \text{ J}}{6 \text{ m}} = 100 \text{ N} \]
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Using the lever: The load arm is 6 meters and the effort arm is 12 meters, and the mechanical advantage is 2. Since the mechanical advantage doubles the effort, the effective force required to lift the 100 N load using the lever would be: \[ \text{Effort} = \frac{100 \text{ N}}{2} = 50 \text{ N} \]
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Calculate work done with the lever: While the lever allows us to exert less force, the distance moved will also change. The distance the effort is applied is twice the distance lifted because of mechanical advantage. So, when lifting the 6 meters with the load arm, the distance moved using the effort arm is: \[ \text{Distance moved} = 12 \text{ m} \]
Now we can calculate the work done: \[ \text{Work done by effort} = \text{Effort} \times \text{Distance} = 50 \text{ N} \times 12 \text{ m} = 600 \text{ J} \]
However, the question is asking for how much work would be done to lift the box to the same height of 6 meters using this lever setup. Since we've already established that the lift is still effectively the same and does not change in this context, the work done remains:
The answer remains 600 J.
Therefore, the correct response is: 600 J.