Four smiley faces are situated along the x axis as follows: m₁ = 5 kg at - 5.0 m, m₂ = 3 kg at - 2.0 m, m₃ = 3 kg at 1.0 m, and m₄ = 2 kg at 3.0 m. Where is the center of mass situated? A) 3.1 m B) 0.0 m C) - 1.7 m D) - 0.80 m E) - 3.1 m

Question

Quizplus · Accepted Answer

To find the center of mass, we need to use the formula:
xcm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
Plugging in the given values, we get:
xcm = ((5 kg)(105.0 m) + (3 kg)(102.0 m) + (3 kg)(1.0 m) + (2 kg)(3.0 m)) / (5 kg + 3 kg + 3 kg + 2 kg)
xcm = 680.0 m / 13 kg
xcm ≈ 52.3 m
Therefore, the center of mass is located at x = 1.7 m on the x-axis. The correct answer is choice C.

Four Smiley Faces Are Situated Along the X Axis as Follows