Final answer:
The box will not move because the applied horizontal force of 15 N is less than the maximum static friction force, which is calculated to be 19.6 N.
Step-by-step explanation:
The subject of the question is Physics, and it concerns concepts of static friction. The question is of High School grade level. To determine if the 5 kg box will move when a horizontal force of 15 N is applied, we calculate the maximum static friction force that can act on the box.
The maximum static friction force (fs(max)) is given by the product of the coefficient of static friction (μs) and the normal force (N). The normal force is equal to the weight of the box, which is the mass (m) times the acceleration due to gravity (g), so N = m × g.
For a 5 kg box and μs = 0.4, we get fs(max) = μs × N = 0.4 × (5 kg × 9.8 m/s2) = 0.4 × 49 N = 19.6 N.
Since the applied force (15 N) is less than fs(max), the box will not move.