Final answer:
To calculate the work needed for moving a crate via elevator or by sliding across different floors, we use the formula for work, accounting for the differing coefficients of kinetic friction on each surface and multiplying by the relevant distances.
Step-by-step explanation:
The calculation of the work needed to move the crate both using the elevator and by sliding it on different floor surfaces involves the concept of frictional forces and work in physics. To find the work done, we use the formula Work = force × distance, where the force is the frictional force, which is given by Frictional force = coefficient of kinetic friction × normal force. Since the crate is being moved at a constant velocity, the normal force is equal to the gravitational force on the crate, which is mass × acceleration due to gravity (g). We calculate the work done for each section of the path by multiplying the frictional force by the distance traveled on each surface.
To find the work done on the ground floor, we use the coefficient of kinetic friction of 0.100, the mass of the crate (200 kg), and the acceleration due to gravity (9.8 m/s²). The normal force is 200 kg × 9.8 m/s², and we multiply this by the coefficient of kinetic friction and the distance covered on the ground floor. For the third floor, we do a similar calculation with the higher coefficient of friction of 0.300. By comparing the total work done on each path, we determine which requires less effort by the workers, not including the work done by the elevator against gravity.