Multiple Cholce Question The figure shows a \( 50-\mathrm{lb} \) uniform thin panel placed in a truck with end \( A \) resting on a rough horizontal surface and end \( B \) supported by a smooth vertical surface. Determine the minimum required coefficient of static friction at end \( A \) if the frictional force \( F=6 \mathrm{lb} \). 1.863 0.12 0.1023 0.5

To determine the minimum required coefficient of static friction at end \( A \), we can use the following steps: 1. **Identify the forces acting on the panel:** - The weight of the panel \( W = 50 \, \text{lb} \) acts downward at the center of gravity. - The frictional force \( F = 6 \, \text{lb} \) acts at end \( A \) to prevent sliding. - The normal force \( N \) at end \( A \) acts upward. 2. **Set up the equilibrium equations:** - Since the panel is in static equilibrium, the sum of vertical forces must equal zero: \[ N - W = 0 \implies N = W = 50 \, \text{lb} \] 3. **Relate the frictional force to the normal force:** - The frictional force can be expressed in terms of the coefficient of static friction \( \mu_s \): \[ F = \mu_s N \] - Substituting the known values: \[ 6 \, \text{lb} = \mu_s (50 \, \text{lb}) \] 4. **Solve for the coefficient of static friction \( \mu_s \):** \[ \mu_s = \frac{F}{N} = \frac{6 \, \text{lb}}{50 \, \text{lb}} = 0.12 \] Thus, the minimum required coefficient of static friction at end \( A \) is \( 0.12 \). The correct answer is **0.12**.