Final answer:
The work done by the workers to move the crate from A to E can be calculated by multiplying the frictional force on each floor by the distance moved. The frictional force is found using the coefficient of kinetic friction and the mass of the crate. The total work is the sum of the work done on the ground and third floors for each path.
Step-by-step explanation:
To calculate the work needed by the workers for each path shown from A to E, given that the elevator does not contribute to the work against gravity, we need to consider the forces involved in sliding the crate and apply the formula work (W) = force (F) × distance (d).
The coefficient of kinetic friction (μk) on the ground floor is 0.100, and on the third floor, it is 0.300. The normal force (N) on each floor is equal to the weight of the crate, which is the mass (m) of the crate times the acceleration due to gravity (g), i.e., N = m × g.
For the ground floor, with a coefficient of kinetic friction of 0.100, the frictional force (Ff) is Ff = μk × N = 0.100 × m × g. For the third floor, Ff = 0.300 × m × g. To slide the crate at constant velocity, the workers must apply a force equal to the frictional force over the distance the crate is moved.
Therefore, to find the work done by the workers over each path, we multiply the frictional force for each floor by the respective distance the crate is moved on that floor. The total work is the sum of work done on the ground floor and on the third floor for each path.