Final answer:
Box A on level ground has a normal force equal to its weight, while box B on an incline has a smaller normal force due to the angle of inclination. The normal force on box A is larger than that on box B, and this is true even if the angle of inclination is 10°.
Step-by-step explanation:
To rank the boxes based on the magnitude of the normal force, we need to consider the scenarios. For box A at rest on a horizontal surface, the normal force (ℓ) is equal in magnitude to the weight (w) of the box and acts in the opposite direction. This can be expressed as ℓ = mg, where m is the mass of the box, and g is the acceleration due to gravity.
For box B resting on an incline, the normal force is less than the full weight of the box because only a component of the weight acts perpendicular to the incline. The expression for the normal force on the incline is ℓ = mg cos(θ), where θ is the angle of the incline. Therefore, the magnitude of the normal force acting on box B will be smaller than that on box A, assuming equal masses.
If the angle of incline is 10°, you'd plug in that value into the cosine function to calculate the normal force for box B, which will still be less than the normal force on box A on level ground.