Final answer:
To determine if the box will slide down the inclined conveyor, we compare the force of gravity to the maximum static friction. If the force of friction is less than the maximum static friction, the box will slide down.
Step-by-step explanation:
To determine if the box will slide down the inclined conveyor, we need to compare the force of gravity pulling the box downward to the maximum force of static friction keeping the box in place. The formula used to calculate this is:
Force of friction < μ_s × Normal force
where μ_s is the static coefficient of friction and the Normal force is given by:
Normal force = mass × gravitational acceleration × cos(theta)
If the force of friction is less than the maximum static friction, the box will slide down the incline. If the force of friction is greater than or equal to the maximum static friction, the box will not slide.