What is the total work done on the crate?

Steps to Solve

1. Identify the forces acting on the crate The main forces acting on the crate are the applied force (due to the worker pushing the crate) and the frictional force opposing the motion.

2. Calculate the weight of the crate The weight ($W$) can be calculated using the formula: $$ W = m \cdot g $$ where $m = 28.9 , \text{kg}$ (mass of the crate) and $g = 9.81 , \text{m/s}^2$ (acceleration due to gravity).

3. Calculate the normal force Since the crate is on a level floor, the normal force ($F_n$) is equal to the weight: $$ F_n = W $$

4. Calculate the frictional force The frictional force ($F_f$) can be found using the formula: $$ F_f = \mu \cdot F_n $$ where $\mu = 0.26$ (coefficient of kinetic friction). Substitute in the normal force from the previous step.

5. Calculate the total work done Since the crate is moving at a constant velocity, the work done ($W_d$) against friction is given by: $$ W_d = F_f \cdot d $$ where $d = 4.85 , \text{m}$ (distance).

6. Final calculation Insert the values from the previous steps into the formula for work done to find the total work.