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Given two masses falling towards each other under gravitational attraction, do they meet at their joint center of mass, assuming other gravitational forces are negligible?
The center of mass is the point in an object or system where the mass is evenly distributed in all directions. It is the point around which an object or system will rotate if placed on a pivot.
The center of mass plays a crucial role in determining the gravitational attraction between two masses. The two masses are drawn towards each other because the center of mass of the system is in between them and exerts a force on both of them.
Yes, two masses always gravitate towards their center of mass, regardless of their distance apart. This is due to the fundamental law of universal gravitation which states that all objects with mass are attracted to each other.
No, the center of mass can be located outside the physical boundaries of an object. This is because the center of mass is determined by the distribution of mass within an object, not its physical shape or size.
The center of mass can be calculated by taking the weighted average of the positions of all the individual masses in a system. This can be represented mathematically as:
x_cm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
y_cm = (m1y1 + m2y2 + ... + mnyn) / (m1 + m2 + ... + mn)
z_cm = (m1z1 + m2z2 + ... + mnzn) / (m1 + m2 + ... + mn)
Where x, y, and z represent the coordinates of each mass, and m represents the mass of each individual object in the system.