A system consists of the following masses in the x-y plane: 4.0 kg at coordinate (x = 0 m, y = 5.0 m), 7.0 kg at (3.0 m, 8.0 m), 5.0 kg at (-3.0 m, -6.0 m). Find the position of its center of mass
Question
A system consists of the following masses in the x-y plane: 4.0 kg at coordinate (x = 0 m, y = 5.0 m), 7.0 kg at (3.0 m, 8.0 m), 5.0 kg at (-3.0 m, -6.0 m). Find the position of its center of mass
Solution
The center of mass of a system of particles is given by the formula:
X_cm = (Σm_i * x_i) / Σm_i Y_cm = (Σm_i * y_i) / Σm_i
where m_i is the mass of the i-th particle, and (x_i, y_i) are its coordinates.
Let's calculate the center of mass for the given system:
X_cm = [(4.0 kg * 0 m) + (7.0 kg * 3.0 m) + (5.0 kg * -3.0 m)] / (4.0 kg + 7.0 kg + 5.0 kg) = [0 kgm + 21.0 kgm - 15.0 kgm] / 16.0 kg = 6.0 kgm / 16.0 kg = 0.375 m
Y_cm = [(4.0 kg * 5.0 m) + (7.0 kg * 8.0 m) + (5.0 kg * -6.0 m)] / (4.0 kg + 7.0 kg + 5.0 kg) = [20.0 kgm + 56.0 kgm - 30.0 kgm] / 16.0 kg = 46.0 kgm / 16.0 kg = 2.875 m
So, the position of the center of mass of the system is at coordinates (0.375 m, 2.875 m).
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