A monkey is relaxing on a tree branch inclined at an angle with the ground. Which of the Free Body Diagrams below is correct? (Be careful; the relative lengths of the vectors matters!) (actually an ape) A с F i 122 B P Re B D FN 13 W Fx W 100 √₂ To 10

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Understanding Free Body Diagrams: Monkey on an Inclined Tree Branch

In this educational resource, we analyze the forces acting on a monkey (actually an ape) relaxing on a tree branch inclined at an angle \(\theta\) with the ground. The objective is to determine which of the Free Body Diagrams (FBDs) provided correctly represent the forces at play. The relative lengths of the vectors in these diagrams are crucial.

#### Diagram Description
- **Inclined Plane:** A tree branch is depicted inclined at an angle \(\theta\) from the horizontal ground. 
- **Ape:** An ape is positioned reclining on the tree branch, creating a scenario where we need to analyze the forces involved.

#### Force Components
The forces to consider in Free Body Diagrams for this scenario are:
- **Gravitational Force (\(w\)):** Always acts downwards towards the center of the Earth.
- **Normal Force (\(F_N\)):** Perpendicular to the surface of contact (the branch).
- **Frictional Force (\(F_s\)):** Parallel to the surface and opposing the motion, if any.

#### Free Body Diagrams (A, B, C, D)

**Option A:**
- The normal force (\(F_N\)) is correctly perpendicular to the branch.
- Gravitational force (\(w\)) acts downward.
- The frictional force (\(F_s\)) is parallel to the branch.
- However, this depiction does not clearly show the relative magnitudes and directions reflecting the balance of forces accurately.

**Option B:**
- The normal force (\(F_N\)) is perpendicular to the branch.
- Gravitational force (\(w\)) acts downward.
- Frictional force (\(F_s\)) is shown parallel and pointing up the incline.
- Angle \(\theta\) is delineated, but the relative magnitudes of forces might not accurately represent physical balance.

**Option C:**
- The normal force (\(F_N\)) is correctly drawn perpendicular to the branch.
- Gravitational force (\(w\)) acts downward.
- Frictional force (\(F_s\)) appears correctly balanced within the context of friction acting parallel to the surface and opposing the motion.

**Option D:**
- The normal force (\(F_N\)) is perpendicular to the branch.
- Gravitational force (\(w\)) acts downward.
-
Transcribed Image Text:### Understanding Free Body Diagrams: Monkey on an Inclined Tree Branch In this educational resource, we analyze the forces acting on a monkey (actually an ape) relaxing on a tree branch inclined at an angle \(\theta\) with the ground. The objective is to determine which of the Free Body Diagrams (FBDs) provided correctly represent the forces at play. The relative lengths of the vectors in these diagrams are crucial. #### Diagram Description - **Inclined Plane:** A tree branch is depicted inclined at an angle \(\theta\) from the horizontal ground. - **Ape:** An ape is positioned reclining on the tree branch, creating a scenario where we need to analyze the forces involved. #### Force Components The forces to consider in Free Body Diagrams for this scenario are: - **Gravitational Force (\(w\)):** Always acts downwards towards the center of the Earth. - **Normal Force (\(F_N\)):** Perpendicular to the surface of contact (the branch). - **Frictional Force (\(F_s\)):** Parallel to the surface and opposing the motion, if any. #### Free Body Diagrams (A, B, C, D) **Option A:** - The normal force (\(F_N\)) is correctly perpendicular to the branch. - Gravitational force (\(w\)) acts downward. - The frictional force (\(F_s\)) is parallel to the branch. - However, this depiction does not clearly show the relative magnitudes and directions reflecting the balance of forces accurately. **Option B:** - The normal force (\(F_N\)) is perpendicular to the branch. - Gravitational force (\(w\)) acts downward. - Frictional force (\(F_s\)) is shown parallel and pointing up the incline. - Angle \(\theta\) is delineated, but the relative magnitudes of forces might not accurately represent physical balance. **Option C:** - The normal force (\(F_N\)) is correctly drawn perpendicular to the branch. - Gravitational force (\(w\)) acts downward. - Frictional force (\(F_s\)) appears correctly balanced within the context of friction acting parallel to the surface and opposing the motion. **Option D:** - The normal force (\(F_N\)) is perpendicular to the branch. - Gravitational force (\(w\)) acts downward. -
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