Sure! Here’s a **step-by-step solution** for finding the **coefficient of static friction (\(\mu_s\))** using Newton's 2nd Law and a typical physics lab setup (such as a block on an inclined plane, which is a very common scenario for these questions). Since you referenced using a video, I'll generalize the steps so you can match them to your observations. --- ## **Step 1: Start with Newton’s 2nd Law** Newton’s 2nd Law states: \[ F = ma \] For an object at rest (just about to slide), \(a = 0\), so the **net force is zero**. --- ## **Step 2: Draw the Free-Body Diagram (FBD)** For a block on an inclined plane at angle \(\theta\): - **Gravity** (\(mg\)) acts downward. - **Normal force** (\(N\)) acts perpendicular to the surface. - **Friction force** (\(f_s\)) acts up the incline, opposing motion. --- ## **Step 3: Resolve Forces** - **Parallel to the incline:** \(mg \sin\theta\) (down the incline) - **Perpendicular to the incline:** \(mg \cos\theta\) (into the plane) **At the verge of sliding:** \[ f_{s,\text{max}} = \mu_s N \] But also: \[ f_{s,\text{max}} = mg \sin\theta \] and \[ N = mg \cos\theta \] --- ## **Step 4: Set Up the Equilibrium Equation** At the threshold of motion (static friction at maximum): \[ f_{s,\text{max}} = mg \sin\theta \] \[ \mu_s N = mg \sin\theta \] But \(N = mg \cos\theta\): \[ \mu_s (mg \cos\theta) = mg \sin\theta \] --- ## **Step 5: Solve for the Coefficient of Static Friction (\(\mu_s\))** Divide both sides by \(mg \cos\theta\): \[ \mu_s = \frac{mg \sin\theta}{mg \cos\theta} \] \[ \mu_s = \frac{\sin\theta}{\cos\theta} \] \[ \mu_s = \tan\theta \] --- ## **Step 6: Use a Measurement from the Video** From the video, **measure the angle \(\theta\) at which the object just starts to slide**. Let’s say the angle measured is \(28^\circ\) (replace this with your actual measurement). \[ \mu_s = \tan(28^\circ) \approx 0.53 \] --- ## **Final Answer with Explanation** **Equation Used:** \[ F = ma \implies \text{Set net force to 0 at threshold of motion, resolve forces, and solve for } \mu_s \] **Key Step:** \[ \mu_s = \tan\theta \] **Example Calculation:** If \(\theta = 28^\circ\): \[ \mu_s = \tan(28^\circ) \approx 0.53 \] --- ## **Summary Table** | Step | Equation / Principle | Explanation | |------|---------------------|-------------| | 1 | \(F = ma\) | Start with Newton's 2nd Law | | 2 | FBD | Draw and resolve forces | | 3 | \(mg \sin\theta, mg \cos\theta\) | Resolve into components | | 4 | \(\mu_s N = mg \sin\theta\) | Set friction equal to downslope force | | 5 | \(\mu_s = \tan\theta\) | Rearranged to solve for coefficient | | 6 | Measurement | Substitute measured angle | --- ### **Upload a Picture (Optional)** If you can, draw and upload a Free-Body Diagram (FBD) showing the forces on the block. --- ### **In Summary:** **To find the coefficient of static friction from the video:** 1. Measure the angle \(\theta\) where the object starts to slide. 2. Use the equation: \[ \mu_s = \tan\theta \] **Show all steps, starting with \(F=ma\), and include your FBD for full credit!**