Learning Goal: To make the connection between intuitive understanding of a seesaw and the standard formalism for torque. This problem deals with the concept of torque, the "twist" that an off-center force applies to a body that tends to make it rotate. (Figure 1) Figure Lend La Fx ما 3 of 3 Review Constants Gilles has an identical twin, Jean, also of weight w. The two twins now sit on the same side of the seesaw, with Gilles at distance L2 from the pivot and Jean at distance L3. (Figure 2) Part D Where should Marcel position Jacques to balance the seesaw? Express your answer in terms of L2, L3, W, and w. View Available Hint(s) w(L3+L₂) Submit Previous Answers ✓ Correct Part E Bad news! When Marcel finds the distance L from the previous part, it turns out to be greater than Lend, the distance from the pivot to the end of the seesaw. Hence, even with Jacques at the very end of the seesaw, the twins Gilles and Jean exert more torque than Jacques does. Marcel now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is at height h above the pivot. (Figure 3) With what force in the rightward direction, F₂, should Marcel push? If your expression would give a negative result (using actual values) that just means the force should be toward the left. Express your answer in terms of W, Lend, w, L2, L3, and h. View Available Hint(s) --| ΑΣΦΑ 6 A Ĉ Pa 2

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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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I just need help with part E please! Thank you!

### Educational Website Content

#### Problem Scenario

**Context:**  
Marcel encounters a problem when he finds that the distance \( L \) from a previous analysis is greater than \( L_{\text{end}} \), which is the distance from the pivot to the end of the seesaw. Although Jacques is positioned at the very end of the seesaw, the twins Gilles and Jean produce more torque than Jacques. To resolve this, Marcel decides to push sideways on an ornament shown in red that is positioned at a height \( h \) above the pivot.

**Objective:**  
Determine the force \( F_x \) that Marcel needs to apply in the rightward direction to balance the seesaw. If the result of your expression is negative, it indicates that the force should be applied toward the left.

**Instructions:**  
Express your answer in terms of the following variables:
- \( W \) (weight),
- \( L_{\text{end}} \),
- \( L_2 \),
- \( L_3 \), and
- \( h \).

**Interactive Component:**  
A formula box is provided for users to input their calculations for \( F_x \). After performing the necessary calculations, click "Submit" to verify your answer.

**Available Hints:**  
Users can access additional hints by clicking "View Available Hint(s)."

#### Diagram Explanation

**Figure Description:**  
The diagram illustrates a seesaw with four people involved. The components are labeled as follows:

- **Person on the Left:** The individual is seated on the left end of the seesaw. The distance from this person to the pivot is represented as \( L_{\text{end}} \).

- **Central Pivot:** The pivot point is the central fulcrum on which the seesaw balances. There is a red arrow labeled \( F_x \) indicating the direction of Marcel's force on an ornament at a height \( h_1 \) above the pivot.

- **Persons on the Right:** Two individuals are positioned on the right side of the seesaw. The distances from the pivot to these individuals are marked as \( L_2 \) and \( L_3 \), respectively.

This illustration provides a visual aid to understand the distribution of forces and torques acting on the seesaw.
Transcribed Image Text:### Educational Website Content #### Problem Scenario **Context:** Marcel encounters a problem when he finds that the distance \( L \) from a previous analysis is greater than \( L_{\text{end}} \), which is the distance from the pivot to the end of the seesaw. Although Jacques is positioned at the very end of the seesaw, the twins Gilles and Jean produce more torque than Jacques. To resolve this, Marcel decides to push sideways on an ornament shown in red that is positioned at a height \( h \) above the pivot. **Objective:** Determine the force \( F_x \) that Marcel needs to apply in the rightward direction to balance the seesaw. If the result of your expression is negative, it indicates that the force should be applied toward the left. **Instructions:** Express your answer in terms of the following variables: - \( W \) (weight), - \( L_{\text{end}} \), - \( L_2 \), - \( L_3 \), and - \( h \). **Interactive Component:** A formula box is provided for users to input their calculations for \( F_x \). After performing the necessary calculations, click "Submit" to verify your answer. **Available Hints:** Users can access additional hints by clicking "View Available Hint(s)." #### Diagram Explanation **Figure Description:** The diagram illustrates a seesaw with four people involved. The components are labeled as follows: - **Person on the Left:** The individual is seated on the left end of the seesaw. The distance from this person to the pivot is represented as \( L_{\text{end}} \). - **Central Pivot:** The pivot point is the central fulcrum on which the seesaw balances. There is a red arrow labeled \( F_x \) indicating the direction of Marcel's force on an ornament at a height \( h_1 \) above the pivot. - **Persons on the Right:** Two individuals are positioned on the right side of the seesaw. The distances from the pivot to these individuals are marked as \( L_2 \) and \( L_3 \), respectively. This illustration provides a visual aid to understand the distribution of forces and torques acting on the seesaw.
**Learning Goal:**
To make the connection between intuitive understanding of a seesaw and the standard formalism for torque.

This problem deals with the concept of torque, the "twist" that an off-center force applies to a body that tends to make it rotate.

**Part D**

Where should Marcel position Jacques to balance the seesaw?

_Express your answer in terms of \(L_2\), \(L_3\), \(W\), and \(w\)._

**Available Hint(s):**

\[ L = \frac{w(L_3 + L_2)}{W} \]

**Correct**

---

**Bad news!** When Marcel finds the distance \(L\) from the previous part, it turns out to be greater than \(L_{end}\), the distance from the pivot to the end of the seesaw. Hence, even with Jacques at the very end of the seesaw, the twins Gilles and Jean exert more torque than Jacques does. Marcel now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is at height \(h\) above the pivot.

**Part E**

With what force in the rightward direction, \(F_x\), should Marcel push? If your expression would give a negative result (using actual values) that just means the force should be toward the left.

_Express your answer in terms of \(W\), \(L_{end}\), \(w\), \(L_2\), \(L_3\), and \(h\)._

**Available Hint(s):**

[Space for entering or submitting expressions]

---

**Figure Explanation:**

- **Diagram of the Seesaw:**
  - A seesaw is shown with a pivot in the middle.
  - Two individuals, Gilles and Jean, are sitting on the right side, each at a distance \(L_3\) from the pivot.
  - Another individual, Jacques, is shown on the left side, positioned at \(L_2\) from the pivot.
  - An ornamental object is present, on which Marcel applies a force \(F_x\), situated at a height \(h\) above the pivot.
  - The distance from the pivot to the end of the seesaw is labeled \(L_{end}\).
Transcribed Image Text:**Learning Goal:** To make the connection between intuitive understanding of a seesaw and the standard formalism for torque. This problem deals with the concept of torque, the "twist" that an off-center force applies to a body that tends to make it rotate. **Part D** Where should Marcel position Jacques to balance the seesaw? _Express your answer in terms of \(L_2\), \(L_3\), \(W\), and \(w\)._ **Available Hint(s):** \[ L = \frac{w(L_3 + L_2)}{W} \] **Correct** --- **Bad news!** When Marcel finds the distance \(L\) from the previous part, it turns out to be greater than \(L_{end}\), the distance from the pivot to the end of the seesaw. Hence, even with Jacques at the very end of the seesaw, the twins Gilles and Jean exert more torque than Jacques does. Marcel now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is at height \(h\) above the pivot. **Part E** With what force in the rightward direction, \(F_x\), should Marcel push? If your expression would give a negative result (using actual values) that just means the force should be toward the left. _Express your answer in terms of \(W\), \(L_{end}\), \(w\), \(L_2\), \(L_3\), and \(h\)._ **Available Hint(s):** [Space for entering or submitting expressions] --- **Figure Explanation:** - **Diagram of the Seesaw:** - A seesaw is shown with a pivot in the middle. - Two individuals, Gilles and Jean, are sitting on the right side, each at a distance \(L_3\) from the pivot. - Another individual, Jacques, is shown on the left side, positioned at \(L_2\) from the pivot. - An ornamental object is present, on which Marcel applies a force \(F_x\), situated at a height \(h\) above the pivot. - The distance from the pivot to the end of the seesaw is labeled \(L_{end}\).
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