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Let us solve a fun physics problem! Suppose a wooden block is resting on a wooden plank. You slowly lift one end of the plank. When the plank makes an angle of $30^{\circ}$ with the ground, the wooden block just barely starts to slide down. Find the coefficient of static friction ($\mu_s$) between the block and the plank. Step 1: Identify what is given in the problem. The angle at which the block just starts sliding is the angle of repose, which is $\alpha = 30^{\circ}$. Step 2: Remember the magic rule connecting the angle of repose and friction. The formula is $\mu_s = \tan(\alpha)$. Step 3: Substitute the given number into the formula. We get $\mu_s = \tan(30^{\circ})$. Step 4: Look up or calculate the value of $\tan(30^{\circ})$, which is approximately $0.577$. Step 5: Write down the final answer with units. The coefficient of static friction ($\mu_s$) is $0.577$ (it has no units because it is a ratio of two forces).