Consider a system consisting of three masses on the x axis....

Consider a system consisting of three masses on the $x$ axis. Mass $m_{1}=1.00 \mathrm{kg}$ is at $x=1.00 \mathrm{m}$ ; mass $m_{2}=2.00 \mathrm{kg}$ is at $x=2.00 \mathrm{m}$ ; and mass $m_{3}=3.00 \mathrm{kg}$ is at $x=3.00 \mathrm{m} .$ What is the total gravitational potential energy of this system?

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Key Concepts

Newton's Law of Universal Gravitation

Newton's law of universal gravitation provides the framework for understanding gravitational attractions between masses by stating that every pair of masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This law is fundamental in deriving the formula for the gravitational potential energy between two masses, making it a key concept in analyzing gravitational systems.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in a system due to the positions of masses relative to each other in a gravitational field. It is typically calculated between two masses using a formula that involves the gravitational constant, the masses involved, and the distance between them. This concept is fundamental in understanding how energy changes as the configuration of masses varies under gravity.

Pairwise Interactions

In a system with more than two masses, the total gravitational potential energy is determined by summing the potential energy contributions from every unique pair of masses. Each interaction is calculated independently, and care must be taken to avoid double counting, which is common in multi-body gravitational systems.

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