A 3.00 kg mass is located at x = 2.0 cm and y = −4.0 cm. A 3.00 kg mass is located at x = −5.0 cm and y = 2.0 cm. A 4.00 kg mass is located at x = −3.0 cm and y = −3.0 cm. Where is the center of mass (x, y)?
Question
A 3.00 kg mass is located at x = 2.0 cm and y = −4.0 cm. A 3.00 kg mass is located at x = −5.0 cm and y = 2.0 cm. A 4.00 kg mass is located at x = −3.0 cm and y = −3.0 cm. Where is the center of mass (x, y)?
Solution
The center of mass (x, y) can be calculated using the following formulas:
x_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) y_cm = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
where m1, m2, and m3 are the masses and x1, x2, x3 and y1, y2, y3 are the x and y coordinates respectively.
Substituting the given values:
x_cm = [(3.00 kg * 2.0 cm) + (3.00 kg * -5.0 cm) + (4.00 kg * -3.0 cm)] / (3.00 kg + 3.00 kg + 4.00 kg) y_cm = [(3.00 kg * -4.0 cm) + (3.00 kg * 2.0 cm) + (4.00 kg * -3.0 cm)] / (3.00 kg + 3.00 kg + 4.00 kg)
Solving the above equations will give the x and y coordinates of the center of mass.
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