To find the work done using a lever, we first need to understand that the lever reduces the amount of force applied while allowing the work to remain the same. The work done by the lever can still be calculated using the formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
In this case, the work done in lifting the box using a lever will be the same as the work done without the lever to lift the box, which is 600 Joules.
However, we can find the effort force applied when using the lever. The mechanics of levers can be described by the formula which relates the lengths of the effort arm (EA) and load arm (LA) and the forces applied:
\[ \frac{\text{Effort}}{\text{Load}} = \frac{LA}{EA} \]
In this case:
- Load = Weight of the box = \( \text{mass} \times \text{gravity} \)
- Load arm (LA) = 6 meters
- Effort arm (EA) = 12 meters
The load can be calculated based on the work done (600 J) and the height (6 m):
\[ \text{Load} = \frac{\text{Work}}{\text{height}} = \frac{600 , \text{J}}{6 , \text{m}} = 100 , \text{N} \]
Now that we know the load is 100 N, we can use the lever formula:
\[ \text{Effort} = \text{Load} \times \frac{LA}{EA} \]
Substituting the values we have:
\[ \text{Effort} = 100 , \text{N} \times \frac{6 , \text{m}}{12 , \text{m}} = 100 , \text{N} \times 0.5 = 50 , \text{N} \]
The crucial point is that the work done on the lever is still equal to the work done lifting the box, which was 600 J.
Since the question seems to be about how much work would have been done “if a lever had been used,” indicating the nature of applying effort using a lever rather than directly lifting it, the work done remains the same. Therefore, the answer is:
600 J
This is the work done regardless of how it is achieved with or without the lever.