Consider a beam of length L with a fulcrum x feet from one end (see figure). There are objects with weights W₁ and W₂ placed on opposite ends of the beam. In order to move a 600 pound rock, a person weighing 100 pounds wants to balance it on a beam that is 5 feet long. Find x such that the system is in equilibrium. W₂ W L-x Step 1 Assign the values. W₂ = 600 W₁ = 100✔ L = 5 ft Step 2 Assume that the person has to sit x feet away from the fulcrum in order to balance the system. Assume the fulcrum is located at the origin. Therefore, if x₂ = x, then X1 = L-X - X. Step 3 For equilibrium, the resultant moment should be 0 Therefore, Mo = 0 = W₁x1 + W₂x2 0 = 100 x x X = 600 X = 100 X (5-x) x= 30 x = 30 x= 30 X = X = 100 100 X (5-x) - 600 ✓ (5-x) Enter an exact number. 30
Consider a beam of length L with a fulcrum x feet from one end (see figure). There are objects with weights W₁ and W₂ placed on opposite ends of the beam. In order to move a 600 pound rock, a person weighing 100 pounds wants to balance it on a beam that is 5 feet long. Find x such that the system is in equilibrium. W₂ W L-x Step 1 Assign the values. W₂ = 600 W₁ = 100✔ L = 5 ft Step 2 Assume that the person has to sit x feet away from the fulcrum in order to balance the system. Assume the fulcrum is located at the origin. Therefore, if x₂ = x, then X1 = L-X - X. Step 3 For equilibrium, the resultant moment should be 0 Therefore, Mo = 0 = W₁x1 + W₂x2 0 = 100 x x X = 600 X = 100 X (5-x) x= 30 x = 30 x= 30 X = X = 100 100 X (5-x) - 600 ✓ (5-x) Enter an exact number. 30
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem: Balancing a Beam with Weights**
Consider a beam of length \( L \) with a fulcrum \( x \) feet from one end (see figure). There are objects with weights \( W_1 \) and \( W_2 \) placed on opposite ends of the beam.
In order to move a 600-pound rock, a person weighing 100 pounds wants to balance it on a beam that is 5 feet long. Find \( x \) such that the system is in equilibrium.
![Diagram Description]
The diagram consists of a beam balanced on a fulcrum. Weight \( W_1 \) (100 pounds) is placed on one end of the beam and weight \( W_2 \) (600 pounds) on the other end. The distances from the fulcrum are noted as \( x \) and \( L - x \) respectively.
### Step 1: Assign the Values
\[
W_2 = 600
\]
\[
W_1 = 100
\]
\[
L = 5 \text{ ft}
\]
### Step 2: Determine the Distance from the Fulcrum
Assume the person has to sit \( x \) feet away from the fulcrum in order to balance the system. Assume the fulcrum is located at the origin. Therefore, if \( x_2 = x \), then:
\[
x_1 = L - x
\]
\[
x_1 = 5 - x
\]
### Step 3: Ensure Equilibrium
For equilibrium, the resultant moment should be 0.
\[
M_0 = 0 = W_1 x_1 + W_2 x_2
\]
Therefore,
\[
0 = 100 (5 - x) - 600 x
\]
Simplify:
\[
100 (5 - x) = 600 x
\]
\[
500 - 100x = 600x
\]
\[
500 = 700x
\]
\[
x = \frac{500}{700}
\]
\[
x = \frac{5}{7} \text{ ft}
\]
Thus, the person must sit \( \frac{5}{7} \) feet away from the fulcrum to balance the system.
---
### Explanation of Diagram
The diagram shows a horizontal beam (5 feet in length) balanced on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fdef185-de8b-42f5-933e-8018dcf36541%2F2d4e76dd-8921-4c7f-814d-243a1ca76189%2F060692k_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Balancing a Beam with Weights**
Consider a beam of length \( L \) with a fulcrum \( x \) feet from one end (see figure). There are objects with weights \( W_1 \) and \( W_2 \) placed on opposite ends of the beam.
In order to move a 600-pound rock, a person weighing 100 pounds wants to balance it on a beam that is 5 feet long. Find \( x \) such that the system is in equilibrium.
![Diagram Description]
The diagram consists of a beam balanced on a fulcrum. Weight \( W_1 \) (100 pounds) is placed on one end of the beam and weight \( W_2 \) (600 pounds) on the other end. The distances from the fulcrum are noted as \( x \) and \( L - x \) respectively.
### Step 1: Assign the Values
\[
W_2 = 600
\]
\[
W_1 = 100
\]
\[
L = 5 \text{ ft}
\]
### Step 2: Determine the Distance from the Fulcrum
Assume the person has to sit \( x \) feet away from the fulcrum in order to balance the system. Assume the fulcrum is located at the origin. Therefore, if \( x_2 = x \), then:
\[
x_1 = L - x
\]
\[
x_1 = 5 - x
\]
### Step 3: Ensure Equilibrium
For equilibrium, the resultant moment should be 0.
\[
M_0 = 0 = W_1 x_1 + W_2 x_2
\]
Therefore,
\[
0 = 100 (5 - x) - 600 x
\]
Simplify:
\[
100 (5 - x) = 600 x
\]
\[
500 - 100x = 600x
\]
\[
500 = 700x
\]
\[
x = \frac{500}{700}
\]
\[
x = \frac{5}{7} \text{ ft}
\]
Thus, the person must sit \( \frac{5}{7} \) feet away from the fulcrum to balance the system.
---
### Explanation of Diagram
The diagram shows a horizontal beam (5 feet in length) balanced on
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