Final answer:
Work needed by workers to move a crate at constant velocity is calculated using the friction force and distance traveled, where the force is the mass times gravitational acceleration times the coefficient of friction. Different coefficients of friction for each floor need to be used for accurate calculations, and the work done by the elevator is not considered.
Step-by-step explanation:
To find the work needed by the workers to move a crate in different scenarios, we must consider the formula for work done against friction: Work = Friction Force × Distance. The friction force is calculated as the product of the mass of the object, gravitational acceleration (9.81 m/s2), and the coefficient of kinetic friction. Because the crate has a mass of 200 kg and there are different coefficients of friction on the ground floor and the third floor:
- On the ground floor, with a coefficient of friction of 0.100, the friction force is 200 kg × 9.81 m/s2 × 0.100.
- On the third floor, with a coefficient of friction of 0.300, the friction force is 200 kg × 9.81 m/s2 × 0.300.
For each path, the total work is the sum of the work done on each floor. Since the question specifies that the work done by the elevator is not to be included, only the work on the two surfaces (ground and third floor) should be computed. The distance components would be taken from the specifics of paths A to E as described.