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

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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**.
The minimum required coefficient of static friction at end $$ A $$ is **0.12**.

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