To determine the maximum static friction force that can act on a 5 kg box resting on a horizontal surface with a coefficient of static friction of 0.4, we can use the formula for static friction: ### Step 1: Understand the Formula The maximum static friction force (\(F_{s, \text{max}}\)) can be calculated using the formula: \[ F_{s, \text{max}} = \mu_s \cdot F_N \] Where: - \(F_{s, \text{max}}\) is the maximum static friction force. - \(\mu_s\) is the coefficient of static friction. - \(F_N\) is the normal force acting on the box. ### Step 2: Calculate the Normal Force For an object resting on a horizontal surface, the normal force (\(F_N\)) is equal to the weight of the object. The weight can be calculated using the formula: \[ F_N = m \cdot g \] Where: - \(m\) is the mass of the box (5 kg). - \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)). Calculating the normal force: \[ F_N = 5 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 49.05 \, \text{N} \] ### Step 3: Calculate the Maximum Static Friction Force Now, we can substitute the values into the static friction formula: \[ F_{s, \text{max}} = \mu_s \cdot F_N = 0.4 \cdot 49.05 \, \text{N} \] Calculating this gives: \[ F_{s, \text{max}} = 0.4 \cdot 49.05 \approx 19.62 \, \text{N} \] ### Step 4: Rounding and Selecting the Correct Option Since the options provided are whole numbers, we can round \(19.62 \, \text{N}\) to \(20 \, \text{N}\). Therefore, the maximum static friction force that can act on the box before it starts to move is: **Correct Option: B. 20 N** ### Step 5: Explanation of Other Options - **Option A (10 N)**: This value is too low. It does not take into account the mass of the box and the gravitational force acting on it. - **Option C (25 N)**: This value is higher than the calculated maximum static friction force. It suggests a higher coefficient of friction or a greater normal force than what is present in this scenario. - **Option D (50 N)**: This value is also too high. It would imply a coefficient of static friction of 1.02, which is unrealistic for most materials in contact. ### Common Pitfalls - **Ignoring the Normal Force**: Always remember that the normal force is crucial in calculating friction. It is not always equal to the weight, especially on inclined surfaces. - **Misunderstanding Coefficients**: The coefficient of static friction is a ratio and should be multiplied by the normal force to find the maximum static friction force. - **Rounding Errors**: Be careful with rounding; always keep significant figures in mind until the final answer. ### Revision Summary - The maximum static friction force is calculated using \(F_{s, \text{max}} = \mu_s \cdot F_N\). - The normal force for a horizontal surface is equal to the weight of the object. - For a 5 kg box with \(\mu_s = 0.4\), the maximum static friction force is approximately 20 N. - Always check the reasonableness of your answer against the options provided.