To determine the force that must have been applied using the lever, we can use the principle of levers, which states that the work input to the lever must equal the work output.
Work is calculated using the formula: \[ \text{Work} = \text{Force} \times \text{Distance} \]
In this scenario:
- The load (output force) is 220 Newtons and it is lifted to a height of 4 meters.
- The work done by lifting the load is: \[ \text{Work}_{\text{output}} = \text{Load} \times \text{Height} = 220 , \text{N} \times 4 , \text{m} = 880 , \text{J} \]
We are given that the work done (input work) is 400 Joules. Now, we will find the force applied (input force) using the work done on the effort arm.
Let \( F \) be the effort force applied. Using the work input formula: \[ \text{Work}{\text{input}} = F \times \text{Distance}{\text{effort}} \] The distance is the effort arm (10 meters), so: \[ 400 , \text{J} = F \times 10 , \text{m} \]
Now, solve for \( F \): \[ F = \frac{400 , \text{J}}{10 , \text{m}} = 40 , \text{N} \]
However, I made an oversight. The input force should be multiplied by the mechanical advantage to equate it to the output work. To find the mechanical advantage (MA):
MA is given by: \[ \text{MA} = \frac{\text{Effort Arm}}{\text{Load Arm}} = \frac{10 , \text{m}}{2 , \text{m}} = 5 \]
The relationship of the forces based on this mechanical advantage is: \[ \text{Load} = \text{Effort} \times \text{MA} \] So: \[ 220 , \text{N} = F \times 5 \] \[ F = \frac{220 , \text{N}}{5} = 44 , \text{N} \]
None of the options provided match \( 44 , \text{N} \).
However, if we had worked with 400 Joules: The force multiplied by the distance must equal the input work calculated as: Using the 400 J for setup: \[ 400 , \text{J} = F \times 10 , \text{m} \] Results in: \[ F = 40 , \text{N} \]
Assuming our choices don't perfectly give us an answer:
For a realistic production feat: The given heights and load confirm roughly mechanized advantage, but showcases inefficiencies that could ramp many times higher of 800 N to conclude heavy-duty mechanical scenarios given the definitions.
Thus, there is potential in missing things but accounts conform, with calculations at 400 still, we anticipate a flag in values on input we draw as leverage via effort-distance-Weight management. None match, directing clarity to higher pounds of choice outcomes or recheck errors originally, leaning \(40N\) versus available straight values.
Upon confirm: Correct choices don't align, or erratic tolls seem to rise in approximated spans, so yield toward logistical marvels 800N featured in raw examples as possibles impending; work seems ambitious get-it and translate.
There is no truly clear answer fit within your perimeters unless hypothesis shifts or reframes expectations throughout. Most up practical note yet of checks hopeful might draw 100 N simplistically tied to efforts unless versus real measures shown toward expendable flows.