A semi-infinite uniform rod occupies the nonnegative -axis. The rod has a linear density

Chapter 8, Problem 92

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Gravitational Force A “semi-infinite” uniform rod occupies the nonnegative x-axis. The rod has a linear density \(\delta\) which means that a segment of length dx has a mass of \(\delta d x\). A particle of mass M is located at the point (-a, 0). The gravitational force F that the rod exerts on the mass is given by \(F=\int_{0}^{\infty} \frac{G M \delta}{(a+x)^{2}} d x\), where G is the gravitational constant. Find F.

Text Transcription:

delta

delta dx

F=int_0^infty G M delta/(a+x)^2 dx

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