1) As a project, student's construct a mobile representing some of the major food groups. Their completed artwork is shown below. Find the masses m1, m2, m3that are required for a perfectly balanced mobile. Assume that strings and the horizontal rods have negligible mass 18 cm 31 cm 6.0 cm 24 cm 0.30 kg 12 cm 18 cm MILK
1) As a project, student's construct a mobile representing some of the major food groups. Their completed artwork is shown below. Find the masses m1, m2, m3that are required for a perfectly balanced mobile. Assume that strings and the horizontal rods have negligible mass 18 cm 31 cm 6.0 cm 24 cm 0.30 kg 12 cm 18 cm MILK
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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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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![### Transcription and Explanation
**Equation:**
\[ x_{cg} = \frac{x_1 m_1 + x_2 m_2}{m_1 + m_2} \]
---
**Problem:**
1) As a project, students construct a mobile representing some of the major food groups. Their completed artwork is shown below. Find the masses \(m_1, m_2, m_3\) that are required for a perfectly balanced mobile. Assume that strings and the horizontal rods have negligible mass.
**Diagram Description:**
- A mobile consists of several components suspended from rods.
- A mass of \(0.20 \, \text{kg}\) is located 18 cm from the fulcrum (center point of balance).
- Another mass of \(0.30 \, \text{kg}\) is located 24 cm from a different fulcrum.
- The mobile includes unknown masses \(m_1\), \(m_2\), and \(m_3\) at different points.
- The distances between the masses and their respective points of suspension are labeled: 12 cm, 18 cm, 6 cm, 31 cm.
**Strategy:**
We can find all three unknown masses by repeatedly applying the condition for balance:
\[ m_1 x_1 = m_2 x_2 \]
1. First, apply the balance condition to \(m_1\) and \(m_2\), with the distance \(x_1 = 12 \, \text{cm}\) and \(x_2 = 18 \, \text{cm}\). This provides a relationship between \(m_1\) and \(m_2\).
2. To establish a second relation between \(m_1\) and \(m_2\), apply the balance condition at the next level of the mobile. The mass \((m_1 + m_2)\) at the distance of 6 cm must balance with the mass \(0.30 \, \text{kg}\) located at 24 cm. These conditions help determine \(m_1\) and \(m_2\).
3. To find \(m_3\), apply the balance condition again, this time considering the mass:
\[ (m_1 + m_2 + 0.30 \, \text{kg} + 0.20 \, \text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7fd067d-2bd8-42c8-9cf1-a7f2351dbf76%2Fe97dce3f-3dfa-4a31-87d2-cfbacf29d2ec%2Fb8kb6oa_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription and Explanation
**Equation:**
\[ x_{cg} = \frac{x_1 m_1 + x_2 m_2}{m_1 + m_2} \]
---
**Problem:**
1) As a project, students construct a mobile representing some of the major food groups. Their completed artwork is shown below. Find the masses \(m_1, m_2, m_3\) that are required for a perfectly balanced mobile. Assume that strings and the horizontal rods have negligible mass.
**Diagram Description:**
- A mobile consists of several components suspended from rods.
- A mass of \(0.20 \, \text{kg}\) is located 18 cm from the fulcrum (center point of balance).
- Another mass of \(0.30 \, \text{kg}\) is located 24 cm from a different fulcrum.
- The mobile includes unknown masses \(m_1\), \(m_2\), and \(m_3\) at different points.
- The distances between the masses and their respective points of suspension are labeled: 12 cm, 18 cm, 6 cm, 31 cm.
**Strategy:**
We can find all three unknown masses by repeatedly applying the condition for balance:
\[ m_1 x_1 = m_2 x_2 \]
1. First, apply the balance condition to \(m_1\) and \(m_2\), with the distance \(x_1 = 12 \, \text{cm}\) and \(x_2 = 18 \, \text{cm}\). This provides a relationship between \(m_1\) and \(m_2\).
2. To establish a second relation between \(m_1\) and \(m_2\), apply the balance condition at the next level of the mobile. The mass \((m_1 + m_2)\) at the distance of 6 cm must balance with the mass \(0.30 \, \text{kg}\) located at 24 cm. These conditions help determine \(m_1\) and \(m_2\).
3. To find \(m_3\), apply the balance condition again, this time considering the mass:
\[ (m_1 + m_2 + 0.30 \, \text{kg} + 0.20 \, \text{
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