Final answer:
Charlie and Lauren both elevate boxes to the same height, but assuming no friction and only addressing vertical displacement, Charlie does 600 J of work, while Lauren would do more due to the 5 m displacement along the ramp, resulting in 2500 J if the full force is applied over the entire distance.
Step-by-step explanation:
The student is asking about the concept of work in physics, which is calculated as the product of force and displacement in the direction of the force. In this scenario, both Charlie and Lauren are performing work to elevate boxes to the same height, but the question is which person did more work. The key concept is that work is force times the displacement in the direction of the force. So, for Charlie, who lifts the box directly upward for a displacement of 1.2 m with a force of 500 N, the work done can be calculated by the formula:
W = F × d = 500 N × 1.2 m = 600 J (joules)
Lauren's situation is slightly more complex because she is pushing the box up a ramp. Nevertheless, if we assume no friction and only account for the vertical displacement, which is the same height that Charlie lifted the box, the work done by both would be the same because they displaced the box the same vertical distance against gravity. However, if we consider the actual distance moved along the ramp and the force applied, Lauren would exert the force over a longer displacement of 5 m:
W = F × d = 500 N × 5 m = 2500 J
Therefore, assuming that Lauren applies the force through the entire length of the ramp, she would indeed do more work due to the longer displacement even though the vertical change in both situations is the same. This indicates that not all of the 500 N force from Lauren is directed towards raising the height of the box; some of it is directed along the ramp to overcome gravity and any potential friction.