Subjects physics

Inclined Plane Bb3F7A

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1. **Problem statement:** A body weighing 10 N is placed on a rough inclined plane at angle $\theta$ and is about to move under its own weight. 2. **Understanding the problem:** The body is on the verge of motion, meaning the component of its weight down the slope equals the maximum static friction force. 3. **Formula and forces:** Weight component down the slope: $$W \sin \theta$$ Maximum static friction force: $$f_{max} = \mu_s W \cos \theta$$ Since the body is about to move, these forces are equal: $$W \sin \theta = \mu_s W \cos \theta$$ 4. **Simplify to find coefficient of friction $\mu_s$:** $$\mu_s = \tan \theta$$ 5. **For the second body weighing 20 N:** Weight component down slope: $$20 \sin \theta$$ Maximum static friction: $$\mu_s \times 20 \cos \theta = 20 \tan \theta \cos \theta = 20 \sin \theta$$ 6. **Interpretation:** The forces scale proportionally with weight, so the second body will also be on the verge of motion. 7. **Answer:** The second body will be about to move down. **Final answer:** (a) be about to move down.