intagration setup 1

# intagration setup 1 - "Setting up Integrals in Physics An...

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© 2001 A. John Mallinckrodt “Setting up Integrals” in Physics: An Example from Gravitation Problems that require integration in physics are difficult for introductory students not because the integrals are so difficult, but because it takes a lot of practice to become comfortable with the process of translating the physical problem statement into the corresponding mathematical integral. This is called “setting up” the integral. Consider the case of a particle or, at least, a “compact” object (meaning an object with negligible spatial extent, whose mass can reasonably be considered to be concentrated at one point like a particle) of mass m that is gravitationally interacting with an “extended” object (meaning an object whose mass is distributed over a non negligible spatial extent) of mass M . To be concrete, consider the example shown in the figure at right where a long “thin” (meaning what?) rod with a length l and a uniformly distributed total mass M interacts gravitationally with a “small” (meaning what?) object of mass m that is located a distance d away from the center of the rod along its perpendicular bisector.

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