Find the x center of mass of the following masses at their respective coordinates: m1=1.5, x1=0.6,y1=-0.8 m2=4.0, x2=-0.8,y2=-2.8 m3=2.5, x3=-1.2,y3=-5.0 X_com=?
Find the x center of mass of the following masses at their respective coordinates: m1=1.5, x1=0.6,y1=-0.8 m2=4.0, x2=-0.8,y2=-2.8 m3=2.5, x3=-1.2,y3=-5.0 X_com=?
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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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![### Calculating the Center of Mass in the \(x\)-Direction
To find the \(x\) center of mass (\(x_{com}\)) of the given masses at their respective coordinates, follow these steps:
Given data:
- \(m_1 = 1.5\), \(x_1 = 0.6\), \(y_1 = -0.8\)
- \(m_2 = 4.0\), \(x_2 = -0.8\), \(y_2 = -2.8\)
- \(m_3 = 2.5\), \(x_3 = -1.2\), \(y_3 = -5.0\)
The formula to find the \(x\) center of mass ( \(x_{com}\) ) is:
\[
x_{com} = \frac{\sum (m_i \cdot x_i)}{\sum m_i}
\]
**Step-by-Step Calculation:**
1. Calculate the numerator of the \(x_{com}\):
\[
\sum (m_i \cdot x_i) = (m_1 \cdot x_1) + (m_2 \cdot x_2) + (m_3 \cdot x_3)
\]
\[
= (1.5 \cdot 0.6) + (4.0 \cdot -0.8) + (2.5 \cdot -1.2)
\]
\[
= 0.9 + (-3.2) + (-3.0)
\]
\[
= 0.9 - 3.2 - 3.0
\]
\[
= -5.3
\]
2. Calculate the denominator of the \(x_{com}\):
\[
\sum m_i = m_1 + m_2 + m_3
\]
\[
= 1.5 + 4.0 + 2.5 = 8.0
\]
3. Divide the numerator by the denominator to find the \(x_{com}\):
\[
x_{com} = \frac{-5.3}{8.0} \approx -0.6625
\]
Therefore, the \(x\) center of mass (\(x_{com}\)) of the given masses is approximately \(-0.6625\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0f85ff8-2ea0-4d43-a0c0-84de96cc63b8%2F99b1a0dd-2e54-4c71-a391-9c5b99a47b75%2Fiik9v0u_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating the Center of Mass in the \(x\)-Direction
To find the \(x\) center of mass (\(x_{com}\)) of the given masses at their respective coordinates, follow these steps:
Given data:
- \(m_1 = 1.5\), \(x_1 = 0.6\), \(y_1 = -0.8\)
- \(m_2 = 4.0\), \(x_2 = -0.8\), \(y_2 = -2.8\)
- \(m_3 = 2.5\), \(x_3 = -1.2\), \(y_3 = -5.0\)
The formula to find the \(x\) center of mass ( \(x_{com}\) ) is:
\[
x_{com} = \frac{\sum (m_i \cdot x_i)}{\sum m_i}
\]
**Step-by-Step Calculation:**
1. Calculate the numerator of the \(x_{com}\):
\[
\sum (m_i \cdot x_i) = (m_1 \cdot x_1) + (m_2 \cdot x_2) + (m_3 \cdot x_3)
\]
\[
= (1.5 \cdot 0.6) + (4.0 \cdot -0.8) + (2.5 \cdot -1.2)
\]
\[
= 0.9 + (-3.2) + (-3.0)
\]
\[
= 0.9 - 3.2 - 3.0
\]
\[
= -5.3
\]
2. Calculate the denominator of the \(x_{com}\):
\[
\sum m_i = m_1 + m_2 + m_3
\]
\[
= 1.5 + 4.0 + 2.5 = 8.0
\]
3. Divide the numerator by the denominator to find the \(x_{com}\):
\[
x_{com} = \frac{-5.3}{8.0} \approx -0.6625
\]
Therefore, the \(x\) center of mass (\(x_{com}\)) of the given masses is approximately \(-0.6625\).
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