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) gure → 4 <1 of 3 > more comfortable with torques. Part A Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is W, is sitting at distance L to the left of the pivot, at what distance L₁ should Marcel place Gilles, whose weight is w, to the right of the pivot to balance the seesaw? Express your answer in terms of L, W, and w. View Available Hint(s) Π| ΑΣΦ L₁= LWw Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity.) The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm. Part B Find the torque about the pivot due to the weight w of Gilles on the seesaw. Express your answer in terms of L₁ and w. T= -WL₁

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Chapter1: Units, Trigonometry. And Vectors
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I need help with parts A & D please!

**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 Description:**

The figure shows two children on a seesaw. The child on the left, Jacques, is at a distance \( L \) from the pivot, and the child on the right, Gilles, is at a distance \( L_1 \). The seesaw is balanced on a triangular pivot.

**Part A**

Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is \( W \), is sitting at distance \( L \) to the left of the pivot, at what distance \( L_1 \) should Marcel place Gilles, whose weight is \( w \), to the right of the pivot to balance the seesaw?

**Express your answer in terms of \( L, W, \) and \( w \).**

(Interactive box for inputting the equation)  
\( L_1 = \frac{LW}{w} \)

Submit  
Previous Answers  
Request Answer  

**Incorrect; Try Again; 4 attempts remaining**

Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity). The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm.

**Part B**

Find the torque \( \tau \) about the pivot due to the weight \( w \) of Gilles on the seesaw.

**Express your answer in terms of \( L_1 \) and \( w \).**

\( \tau = -wL_1 \)

(Checkmark indicating correct answer)
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. ([Figure 1]) **Figure Description:** The figure shows two children on a seesaw. The child on the left, Jacques, is at a distance \( L \) from the pivot, and the child on the right, Gilles, is at a distance \( L_1 \). The seesaw is balanced on a triangular pivot. **Part A** Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is \( W \), is sitting at distance \( L \) to the left of the pivot, at what distance \( L_1 \) should Marcel place Gilles, whose weight is \( w \), to the right of the pivot to balance the seesaw? **Express your answer in terms of \( L, W, \) and \( w \).** (Interactive box for inputting the equation) \( L_1 = \frac{LW}{w} \) Submit Previous Answers Request Answer **Incorrect; Try Again; 4 attempts remaining** Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity). The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm. **Part B** Find the torque \( \tau \) about the pivot due to the weight \( w \) of Gilles on the seesaw. **Express your answer in terms of \( L_1 \) and \( w \).** \( \tau = -wL_1 \) (Checkmark indicating correct answer)
**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:**

The diagram shows a seesaw with two children on it. One child is sitting on the left side at a distance \(L_3\) from the pivot, while two children sit on the right side at distances \(L_1\) and \(L_2\).

---

**Problem Statement:**

Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torques about the pivot must equal zero:

\[
\sum \tau = 0
\]

---

**Part C:**

Determine \(\sum \tau\), the sum of the torques on the seesaw. Consider only the torques exerted by the children.

**Express your answer in terms of \(W\), \(w\), \(L\), and \(L_1\).**

- **Hint View:**

\[
\sum \tau = 0 = LW - L_1w
\]

(correct)

---

**Explanation:**

If you did not solve for the distance \(L_1\) required to balance the seesaw in Part A, do so now.

The equation \(\sum \tau = 0\) applies to any body that is not rotationally accelerating. Combining this equation with \(\sum F = 0\) (which applies to any body that is not accelerating linearly) gives a pair of equations that are sufficient to form the basis of statics. The art of applying these equations to large or complicated structures constitutes a significant part of mechanical and civil engineering.

---

**Further Scenario:**

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 a distance \(L_2\) from the pivot and Jean at distance \(L_3\). (Figure 2)

---

**Part D:**

Where should Marcel position Jacques to balance the seesaw?

**Express your answer in terms of \(L_2\), \(L_3\), \(W\), and \(w\).
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. (Figure 1) --- **Figure:** The diagram shows a seesaw with two children on it. One child is sitting on the left side at a distance \(L_3\) from the pivot, while two children sit on the right side at distances \(L_1\) and \(L_2\). --- **Problem Statement:** Marcel wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. For the angular acceleration to be zero, the sum of the torques about the pivot must equal zero: \[ \sum \tau = 0 \] --- **Part C:** Determine \(\sum \tau\), the sum of the torques on the seesaw. Consider only the torques exerted by the children. **Express your answer in terms of \(W\), \(w\), \(L\), and \(L_1\).** - **Hint View:** \[ \sum \tau = 0 = LW - L_1w \] (correct) --- **Explanation:** If you did not solve for the distance \(L_1\) required to balance the seesaw in Part A, do so now. The equation \(\sum \tau = 0\) applies to any body that is not rotationally accelerating. Combining this equation with \(\sum F = 0\) (which applies to any body that is not accelerating linearly) gives a pair of equations that are sufficient to form the basis of statics. The art of applying these equations to large or complicated structures constitutes a significant part of mechanical and civil engineering. --- **Further Scenario:** 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 a distance \(L_2\) from the pivot and Jean at distance \(L_3\). (Figure 2) --- **Part D:** Where should Marcel position Jacques to balance the seesaw? **Express your answer in terms of \(L_2\), \(L_3\), \(W\), and \(w\).
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