### Calculating the Center of Mass in the \(x\)-DirectionTo 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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Description: ### Calculating the Center of Mass in the \(x\)-DirectionTo find the \(x\) center of mass (\(x_{com}\)) of the given masses at their respective coordinates, follow these steps:Given data:- \(m_1 = 1.5\), \(x_1 = 0.6\), \(y_1 = -0.8\)- \(m_2 = 4.0\),

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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=?

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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Find the x center of mass of the following masses at their respective coordinates: m1=2.5, x1=0.6,y1=-0.6 m2=3.5, x2=2.8,y2=3.8 m3=4.0, x3=-2.4,y3=-2.6 x_com=?
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