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A system consists of three particles located as shown in the figure. Find the center of mass of the system. The masses are m, = m2 = 1.0 kg and m, = 2.0 kg. Two 1.0 kg particles are located on the x-axis,

A system consists of three particles located as shown in the figure. Find the center of mass of the system. The masses are m, = m2 = 1.0 kg and m, = 2.0 kg. Two 1.0 kg particles are located on the x-axis,

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The Center of Mass of Three Particles system consists of three particles located as shown in the figure. Find the center of mass of the system. The masses are m, = m, = 1.0 kg and m, = 2.0 kg. Two 1.0 kg particles are located on the x-axis, and a single 2.0 kg particle is located on the y-axis as shown. The vector indicates the location of the system's center of mass. у (m) x (m) 3. 1 SOLUTION Conceptualize The figure shows the three masses. Your intuition should tell you that the center of mass is located somewhere in the region between the blue particle and the pair of tan particles as shown in the figure. problem because we will be using the equations for the center of mass Categorize We categorize this example as --Select--- developed in this section. (For the next three answers, use the following as necessary: m,, m2, m3, Y1, Y2, Y3, X1, X2, and x3. Do not substitute numerical values; use variables only.) Use the defining equations for the coordinates of the center of mass and notice that zCM = 0: XCM = mx; m,x1 + m2x2 + m3×3 YCM = m,Y1 + m2Y2 + m, + m2 + m3 Write the position vector of the center of mass (Enter the components in meters.): rCM = XCMI + YCM) EXERCISE In the example, a fourth particle of mass k· m, (k > 0), is brought to the system at the origin such that the resulting ycM is at 0.90 m. Find k. Hint k = Need Help? Read It Submit Answer
Transcribed Image Text:The Center of Mass of Three Particles system consists of three particles located as shown in the figure. Find the center of mass of the system. The masses are m, = m, = 1.0 kg and m, = 2.0 kg. Two 1.0 kg particles are located on the x-axis, and a single 2.0 kg particle is located on the y-axis as shown. The vector indicates the location of the system's center of mass. у (m) x (m) 3. 1 SOLUTION Conceptualize The figure shows the three masses. Your intuition should tell you that the center of mass is located somewhere in the region between the blue particle and the pair of tan particles as shown in the figure. problem because we will be using the equations for the center of mass Categorize We categorize this example as --Select--- developed in this section. (For the next three answers, use the following as necessary: m,, m2, m3, Y1, Y2, Y3, X1, X2, and x3. Do not substitute numerical values; use variables only.) Use the defining equations for the coordinates of the center of mass and notice that zCM = 0: XCM = mx; m,x1 + m2x2 + m3×3 YCM = m,Y1 + m2Y2 + m, + m2 + m3 Write the position vector of the center of mass (Enter the components in meters.): rCM = XCMI + YCM) EXERCISE In the example, a fourth particle of mass k· m, (k > 0), is brought to the system at the origin such that the resulting ycM is at 0.90 m. Find k. Hint k = Need Help? Read It Submit Answer
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