**Problem Statement:**5. A system consists of three particles as shown in the figure. Mass 1 is 8.10 kg and located at (0, 1.00) m. Mass 2 is 5.30 kg and located at (2.00, 1.00) m. Mass 3 is 1.00 kg and located at (2.00, 0) m. Calculate the center of mass of the system.**Diagram Explanation:**The diagram includes a 2D coordinate system with three masses:- $ m_1 $ at (0, 1.00) m- $ m_2 $ at (2.00, 1.00) m- $ m_3 $ at (2.00, 0)The vertical axis is labeled as $ y $ (m) and the horizontal axis as $ x $ (m).**Answer Choices:**a. $ (0.875\hat{\imath} + 1.00\hat{\jmath}) $ mb. $ (0.875\hat{\imath} + 0.931\hat{\jmath}) $ mc. $ (1.00\hat{\imath} + 2.00\hat{\jmath}) $ md. $ (2.00\hat{\imath} + 1.00\hat{\jmath}) $ me. $ (0.931\hat{\imath} + 0.875\hat{\jmath}) $ mTo solve for the center of mass ($ \vec{R}_{cm} $) of the system, use the formula:\[\vec{R}_{cm} = \frac{1}{M} \sum (m_i \cdot \vec{r}_i)\]Where:- $ M $ is the total mass of the system.- $ m_i $ are the individual masses.- $ \vec{r}_i $ are the position vectors of the masses.

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Description: **Problem Statement:**5. A system consists of three particles as shown in the figure. Mass 1 is 8.10 kg and located at (0, 1.00) m. Mass 2 is 5.30 kg and located at (2.00, 1.00) m. Mass 3 is 1.00 kg and located at (2.00, 0) m. Calculate the center o

Given: The mass of the first particle is 8.10 kg. The position of the first particle is (0,1.00). The mass of the second particle is 5.30 kg. The position of the second particle is (2.00, 1.00). The mass of the third particle is 1.00 kg. The position of the third particle is (2.00, 0).Calculation: Write the expression for the x-component of the center of mass. Cx=m1x1+m2x2+m3x3m1+m2+m3 Substitute the values. Cx=8.10 kg0+5.30 kg2.00+1.00 kg2.008.10 kg+5.30 kg+1.00 kg=0.875 Write the expression for the y-component of the center of mass. Cy=m1y1+m2y2+m3y3m1+m2+m3 Substitute the values. Cy=8.10 kg1.00+5.30 kg1.00+1.00 kg08.10 kg+5.30 kg+1.00 kg=0.93 The center of mass is 0.875i^+0.93j^ m. Thus, option b is correct.

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Physics

5. A system consists of three particles as shown in the figure. Mass 1 is 8.10 kg and located at (0, 1.00) m. Mass 2 is 5.30 kg and located at (2.00, 1.00) m. Mass 3 is 1.00 kg and located at (2.00, 0) m. Calculate the center of mass of the system. y (m) m, m2 m3 х (m) a. (0.875î + 1.003 ) m b. ( 0.875î + 0.931ĵ ) m c. ( 1.00î + 2.00ĵ ) m d. ( 200î + 1.00 ) m e. ( 0.931 î + 0.875ĵ ) m

5. A system consists of three particles as shown in the figure. Mass 1 is 8.10 kg and located at (0, 1.00) m. Mass 2 is 5.30 kg and located at (2.00, 1.00) m. Mass 3 is 1.00 kg and located at (2.00, 0) m. Calculate the center of mass of the system. y (m) m, m2 m3 х (m) a. (0.875î + 1.003 ) m b. ( 0.875î + 0.931ĵ ) m c. ( 1.00î + 2.00ĵ ) m d. ( 200î + 1.00 ) m e. ( 0.931 î + 0.875ĵ ) m

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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