### Problem StatementConsider a beam of length \( L = 11 \) feet with a fulcrum \( x \) feet from one end as shown in the figure below. Two objects weighing 36 pounds and 96 pounds are placed at opposite ends of the beam. Find \( x \) (the distance between the fulcrum and the object weighing 36 pounds) such that the system is in equilibrium.### Diagram ExplanationThe diagram illustrates a beam balanced on a fulcrum. The beam has a total length of 11 feet. There are two objects placed at each end of the beam:- **Object 1** (weighing 36 pounds) is placed on the left end.- **Object 2** (weighing 96 pounds) is placed on the right end.The fulcrum (pivot point) is located \( x \) feet from Object 1. The distance from the fulcrum to Object 2 is \( L - x \) feet.In equilibrium conditions, the moments around the fulcrum must balance out. The moments are calculated by multiplying the weight of the object by its distance from the fulcrum.### Multiple Choice Options\[ \begin{aligned}\text{9 feet} \\\text{10 feet} \\\text{7 feet} \\\text{8 feet} \\\text{6 feet}\end{aligned} \]### Equilibrium ConditionTo solve for \( x \):1. Use the formula for moments about the fulcrum.2. Set the anticlockwise moments equal to the clockwise moments:\[ 36 \cdot x = 96 \cdot (11 - x) \]3. Solve the equation for \( x \):\[ 36x = 96 \cdot (11 - x) \]\[ 36x = 1056 - 96x \]\[ 132x = 1056 \]\[ x = \frac{1056}{132} \]\[ x = 8 \]So, the correct answer is:\[ \boxed{8 \text{ feet}} \]

Consider the clockwise direction of the moment as negative and the counterclockwise direction of the…

Consider a beam of length L = 11 feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 96 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium. Object 1 9 feet O 10 feet O 7 feet 8 feet 6 feet XL-x- Ubject 2

Consider a beam of length L = 11 feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 96 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium. Object 1 9 feet O 10 feet O 7 feet 8 feet 6 feet XL-x- Ubject 2

College Physics

11th Edition

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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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

### Problem Statement

Consider a beam of length \( L = 11 \) feet with a fulcrum \( x \) feet from one end as shown in the figure below. Two objects weighing 36 pounds and 96 pounds are placed at opposite ends of the beam. Find \( x \) (the distance between the fulcrum and the object weighing 36 pounds) such that the system is in equilibrium.

### Diagram Explanation

The diagram illustrates a beam balanced on a fulcrum. The beam has a total length of 11 feet. There are two objects placed at each end of the beam:
- **Object 1** (weighing 36 pounds) is placed on the left end.
- **Object 2** (weighing 96 pounds) is placed on the right end.

The fulcrum (pivot point) is located \( x \) feet from Object 1. The distance from the fulcrum to Object 2 is \( L - x \) feet.

In equilibrium conditions, the moments around the fulcrum must balance out. The moments are calculated by multiplying the weight of the object by its distance from the fulcrum.

### Multiple Choice Options

\[ \begin{aligned}
\text{9 feet} \\
\text{10 feet} \\
\text{7 feet} \\
\text{8 feet} \\
\text{6 feet}
\end{aligned} \]

### Equilibrium Condition

To solve for \( x \):
1. Use the formula for moments about the fulcrum.
2. Set the anticlockwise moments equal to the clockwise moments:
\[ 36 \cdot x = 96 \cdot (11 - x) \]

3. Solve the equation for \( x \):
\[ 36x = 96 \cdot (11 - x) \]
\[ 36x = 1056 - 96x \]
\[ 132x = 1056 \]
\[ x = \frac{1056}{132} \]
\[ x = 8 \]

So, the correct answer is:
\[ \boxed{8 \text{ feet}} \]

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