surface. What work is done by the \( 100-\mathrm{N} \) force? 1) 405 J 2) 500 J 3) 900 J 4) 4500 J 5) 5600 J

To determine the work done by a force, we can use the formula: \[ W = F \cdot d \cdot \cos(\theta) \] where: - \( W \) is the work done, - \( F \) is the magnitude of the force, - \( d \) is the distance over which the force is applied, - \( \theta \) is the angle between the force and the direction of motion. However, the problem does not provide the distance \( d \) or the angle \( \theta \). To proceed, we need to make some assumptions or require additional information. If we assume that the force is applied in the direction of motion (i.e., \( \theta = 0^\circ \)), then \( \cos(0) = 1 \), and the formula simplifies to: \[ W = F \cdot d \] If we assume a specific distance, we can calculate the work done. Let's analyze the options provided: 1) 405 J 2) 500 J 3) 900 J 4) 4500 J 5) 5600 J To find the distance \( d \) for each option, we can rearrange the formula: \[ d = \frac{W}{F} \] Given \( F = 100 \, \mathrm{N} \), we can calculate \( d \) for each option: 1) For \( W = 405 \, \mathrm{J} \): \[ d = \frac{405}{100} = 4.05 \, \mathrm{m} \] 2) For \( W = 500 \, \mathrm{J} \): \[ d = \frac{500}{100} = 5.0 \, \mathrm{m} \] 3) For \( W = 900 \, \mathrm{J} \): \[ d = \frac{900}{100} = 9.0 \, \mathrm{m} \] 4) For \( W = 4500 \, \mathrm{J} \): \[ d = \frac{4500}{100} = 45.0 \, \mathrm{m} \] 5) For \( W = 5600 \, \mathrm{J} \): \[ d = \frac{5600}{100} = 56.0 \, \mathrm{m} \] Without additional context about the distance or the angle, we cannot definitively determine which option is correct. If you have more information about the distance or the angle at which the force is applied, please provide it so we can calculate the work done accurately.