inal answer:
The coefficient of kinetic friction between the box and the floor is determined by the ratio of the force needed to overcome static friction (100N) to the normal force (500N), resulting in a coefficient of 0.2.
Step-by-step explanation:
When a person pushes against a box weighing 500N and it starts moving when a 100N force is applied, this situation is related to the concept of static and kinetic friction. Since the box starts moving with a force of 100N, this is the force that overcomes the static friction.
The coefficient of kinetic friction (μ) can be calculated using the equation f_k = μk N, where f_k is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force. The normal force is equal to the weight of the box (since it is at rest on a horizontal surface), which is 500N in this case.
Therefore, the coefficient of kinetic friction is calculated as:
μk = f_k / N = 100N / 500N = 0.2
Thus, the coefficient of friction is 0.2, which aligns with option (a).