Figure 5.11 The forces on an object on an i (a) Analyzing forces on an incline The normal force always points perpendicular to the surface.. When we rotate the x-axis to match the surface, the angle between w and the negative y-axis is the same as the angle of the slope. 15 X The weight force always points straight down. w can into x- Wy is in th

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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**Question:**

Based on Figure 5.11, what is the y-component of the weight force \( w \) in the y-direction? (The axis is tilted.)

**Options:**

- ( ) \(-w \cos \theta\)
- ( ) \(-w\)
- ( ) \(w \cos \theta\)
- ( ) \(-w \sin \theta\)
- ( ) 0
- ( ) \(w\)
- ( ) \(w \sin \theta\)

*Note:* Figure 5.11 likely includes a diagram involving a tilted coordinate system in which a weight \( w \) is acting, showing how forces are resolved into their components.
Transcribed Image Text:**Question:** Based on Figure 5.11, what is the y-component of the weight force \( w \) in the y-direction? (The axis is tilted.) **Options:** - ( ) \(-w \cos \theta\) - ( ) \(-w\) - ( ) \(w \cos \theta\) - ( ) \(-w \sin \theta\) - ( ) 0 - ( ) \(w\) - ( ) \(w \sin \theta\) *Note:* Figure 5.11 likely includes a diagram involving a tilted coordinate system in which a weight \( w \) is acting, showing how forces are resolved into their components.
**Figure 5.11 The forces on an object on an incline.**

**(a) Analyzing forces on an incline**

- **Diagram Explanation:**
  - The figure is divided into two parts, both illustrating an object on an inclined plane.

**Left Diagram:**
- The normal force (\(\vec{n}\)) is shown pointing perpendicular to the surface of the incline.
- The weight force (\(\vec{w}\)) is depicted pointing straight down.
- The angle \(\theta\) is labeled between the incline plane and the horizontal.
- Annotations explain:
  - "The normal force always points perpendicular to the surface."
  - "The weight force always points straight down."
  - "When we rotate the x-axis to match the surface, the angle between \(\vec{w}\) and the negative y-axis is the same as the angle \(\theta\) of the slope."

**Right Diagram:**
- The weight force (\(\vec{w}\)) is decomposed into its components along the x and y axes.
- The components are labeled:
  - \(w_x = w \sin \theta\) along the incline
  - \(w_y = -w \cos \theta\) perpendicular and opposite to the normal force
- Additional annotations detail:
  - "\(\vec{w}\) can be decomposed into x- and y-components."
  - "\(w_y\) is negative because \(\vec{w}\) points in the negative y-direction."
Transcribed Image Text:**Figure 5.11 The forces on an object on an incline.** **(a) Analyzing forces on an incline** - **Diagram Explanation:** - The figure is divided into two parts, both illustrating an object on an inclined plane. **Left Diagram:** - The normal force (\(\vec{n}\)) is shown pointing perpendicular to the surface of the incline. - The weight force (\(\vec{w}\)) is depicted pointing straight down. - The angle \(\theta\) is labeled between the incline plane and the horizontal. - Annotations explain: - "The normal force always points perpendicular to the surface." - "The weight force always points straight down." - "When we rotate the x-axis to match the surface, the angle between \(\vec{w}\) and the negative y-axis is the same as the angle \(\theta\) of the slope." **Right Diagram:** - The weight force (\(\vec{w}\)) is decomposed into its components along the x and y axes. - The components are labeled: - \(w_x = w \sin \theta\) along the incline - \(w_y = -w \cos \theta\) perpendicular and opposite to the normal force - Additional annotations detail: - "\(\vec{w}\) can be decomposed into x- and y-components." - "\(w_y\) is negative because \(\vec{w}\) points in the negative y-direction."
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