Four smiley faces are situated along the x axis as follows: m₁ = 5 kg at 0.0 m,m₂ = 3 kg at 4.0 m,m₃ = 3 kg at x m,and m₄ = 2 kg at 8.0 m.If the center of mass is situated at 3.54 m,where is m₃ located? A)3.5 m B)7.0 m C)6.0 m D)4.0 m E)5.0 m

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Quizplus · Accepted Answer

To find the location of m₃, we use the formula for the position of the center of mass: x_cm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4) Plugging in the given values, we get: 3.54 = (5*0 + 3*4 + 3*x + 2*8) / (5 + 3 + 3 + 2) Simplifying and solving for x, we get: 3.54 = (46 + 3x) / 13 46 + 3x = 46.02 3x = 0.02 x = 0.02/3 x = 0.0067 Therefore, m₃ is located at approximately x = 6.0 m.

Four Smiley Faces Are Situated Along the X Axis as Follows