To calculate the work done on the box when a force is applied to it, we can use the formula for work:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
where \(\theta\) is the angle between the force and the direction of motion. In this case, since the force is applied along the incline of the ramp, we need to determine the effective distance the force acts upon.
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Determine the distance moved in the direction of the force. The force is applied along the ramp, and the ramp length is 4 meters. Since the box is raised up the ramp, we consider the vertical distance as related to the work against gravity.
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Calculate the vertical height (Rise) the box is raised. The height raised is 2 meters.
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Force Effective for Work Against Gravity:
- The force to consider is the weight of the box, which can be calculated as: \[ F_{\text{gravity}} = m \cdot g = 20 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 196.2 , \text{N} \]
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Calculate the Work Done Against Gravity (Potential Energy): This simplifies our work done against gravitational force, since we move the box up 2 meters: \[ \text{Work} = F_{\text{gravity}} \cdot \text{height} = 196.2 , \text{N} \cdot 2 , \text{m} = 392.4 , \text{Joules} \]
However, since the problem gives us specific answer choices, and 392 Joules is the closest option provided, we should select that.
Therefore, the answer is: 392 Joules
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