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

Question

Quizplus · Accepted Answer

To find the position of m₃, we can use the formula for the center of mass: x_cm = (m1x1 + m2x2 + m3x3 + m4x4)/(m1 + m2 + m3 + m4) where m is the mass and x is the position along the x-axis. Plugging in the given values, we get: 3.54 = (5*0 + 3*4 + 3*x + 2*8)/(5 + 3 + 3 + 2) Solving for x, we get: x = 6 Therefore, m₃ is located at 6 m on the x-axis, which corresponds to choice C.

Four Smiley Faces Are Situated Along the X Axis as Follows