Final answer:
Yes, the box will move.
Step-by-step explanation:
In this question, we have a 5 kg box at rest on the floor with a coefficient of static friction of 0.4. A horizontal force of 50 N is applied to the box. To determine if the box will move, we need to compare the applied force to the maximum static friction force.
The maximum static friction force can be calculated using the formula maximum static friction force = coefficient of static friction * normal force. Since the box is at rest, the normal force is equal to the weight of the box, which is normal force = mass * acceleration due to gravity = 5 kg * 9.8 m/s^2 = 49 N. Therefore, the maximum static friction force is maximum static friction force = 0.4 * 49 N = 19.6 N.
Since the applied force of 50 N is greater than the maximum static friction force of 19.6 N, the box will move.