You are holding a fridge of width, b, and length, d, at an angle so that it does not topple over by exerting a force, Fyf, at a height, h, as indicated in the diagram below. For simplicity, assume that fridge is a uniform object so that the weight from the Earth on the fridge acts through its center. You can also assume that ground is so slick that there is negligible friction between the fridge and the ground.

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a. Draw an Extended Free Body Diagram (FBD) of the fridge.

b. Solve for the contact force from the ground on the fridge, \( \vec{F}_{gf} \), in terms of the geometric parameters shown in the diagram, the mass of the fridge (\( m \)), and \( g \).

c. Solve for the contact force from you on the fridge, \( \vec{F}_{yf} \), in terms of the geometric parameters shown in the diagram, the mass of the fridge (\( m \)), and \( g \). Your answer can also have \( \vec{F}_{gf} \) in it if you solved for it in part b in terms of the known quantities as then \( \vec{F}_{gf} \) becomes a known quantity.
Transcribed Image Text:a. Draw an Extended Free Body Diagram (FBD) of the fridge. b. Solve for the contact force from the ground on the fridge, \( \vec{F}_{gf} \), in terms of the geometric parameters shown in the diagram, the mass of the fridge (\( m \)), and \( g \). c. Solve for the contact force from you on the fridge, \( \vec{F}_{yf} \), in terms of the geometric parameters shown in the diagram, the mass of the fridge (\( m \)), and \( g \). Your answer can also have \( \vec{F}_{gf} \) in it if you solved for it in part b in terms of the known quantities as then \( \vec{F}_{gf} \) becomes a known quantity.
**Transcription for Educational Website:**

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**Problem Description:**

You are holding a fridge of width, \( b \), and length, \( d \), at an angle so that it does not topple over by exerting a force, \( \vec{F}_{yf} \), at a height, \( h \), as indicated in the diagram below. For simplicity, assume that the fridge is a uniform object so that the weight from the Earth on the fridge acts through its center. You can also assume that the ground is so slick that there is negligible friction between the fridge and the ground.

**Diagram Explanation:**

- **Fridge Dimensions:**
  - Width (\( b \))
  - Length (\( d \))

- **Visual Elements:**
  - The fridge is depicted as a rectangle tilted at an angle \( \theta \) with respect to the ground.
  - The center of the fridge is marked.
  - Dotted lines indicate half of the width (\( b/2 \)) and half of the length (\( d/2 \)) from the center to the edges.
  - A right triangle is formed within the fridge to represent the trigonometric relationships, featuring the angle \( \theta \).

- **Force Exertion:**
  - The force \( \vec{F}_{yf} \) is exerted at a point on the fridge at height \( h \) from the ground.
  
- **Cartesian Basis:**
  - Shown at the top-right corner of the diagram with the unit vectors: 
    - \( \hat{i} \) (horizontal axis)
    - \( \hat{j} \) (vertical axis)
    - \( \hat{k} \) (perpendicular to the page, not used in 2D analysis)

**Additional Notes:**

- This setup is used to analyze the balance and stability conditions under applied forces, considering negligible friction.

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Transcribed Image Text:**Transcription for Educational Website:** --- **Problem Description:** You are holding a fridge of width, \( b \), and length, \( d \), at an angle so that it does not topple over by exerting a force, \( \vec{F}_{yf} \), at a height, \( h \), as indicated in the diagram below. For simplicity, assume that the fridge is a uniform object so that the weight from the Earth on the fridge acts through its center. You can also assume that the ground is so slick that there is negligible friction between the fridge and the ground. **Diagram Explanation:** - **Fridge Dimensions:** - Width (\( b \)) - Length (\( d \)) - **Visual Elements:** - The fridge is depicted as a rectangle tilted at an angle \( \theta \) with respect to the ground. - The center of the fridge is marked. - Dotted lines indicate half of the width (\( b/2 \)) and half of the length (\( d/2 \)) from the center to the edges. - A right triangle is formed within the fridge to represent the trigonometric relationships, featuring the angle \( \theta \). - **Force Exertion:** - The force \( \vec{F}_{yf} \) is exerted at a point on the fridge at height \( h \) from the ground. - **Cartesian Basis:** - Shown at the top-right corner of the diagram with the unit vectors: - \( \hat{i} \) (horizontal axis) - \( \hat{j} \) (vertical axis) - \( \hat{k} \) (perpendicular to the page, not used in 2D analysis) **Additional Notes:** - This setup is used to analyze the balance and stability conditions under applied forces, considering negligible friction. ---
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