Recall that gravitational potential energy is GMm U(r) = (1) we'll derive some important results on gravity in classical mechanics. They are especially easier to find using the scalar potential energy, rather than the vector force. The figure below depicts a very thin spherical shell of radius R and mass M, uniformly distributed across the shell. At some point a distance r away from the centre of the shell, we have a smaller point mass m: Rde Rsine Our shell can be constructed as the collection of an infinite number of very thin circular strips/rings, such as the shaded strip depicted above. (a) What is the infinitesimal mass dM contained inside each strip? (b) What is the infinitesimal potential energy dU provided by each strip onto our mass m? (c) We can find the total U provided by the shell onto our mass m by integrating over dU in (b). What is the total potential energy U? (d) Now consider when mass m is inside the shell, as depicted below: }Raino Using a similar process as in (a) – (c), what is the total U provided by the shell onto a mass m inside the shell?

Recall that gravitational potential energy is GMm U(r) = (1) we'll derive some important results on gravity in classical mechanics. They are especially easier to find using the scalar potential energy, rather than the vector force. The figure below depicts a very thin spherical shell of radius R and mass M, uniformly distributed across the shell. At some point a distance r away from the centre of the shell, we have a smaller point mass m: Rde Rsine Our shell can be constructed as the collection of an infinite number of very thin circular strips/rings, such as the shaded strip depicted above. (a) What is the infinitesimal mass dM contained inside each strip? (b) What is the infinitesimal potential energy dU provided by each strip onto our mass m? (c) We can find the total U provided by the shell onto our mass m by integrating over dU in (b). What is the total potential energy U? (d) Now consider when mass m is inside the shell, as depicted below: }Raino Using a similar process as in (a) – (c), what is the total U provided by the shell onto a mass m inside the shell?

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter1: Relativity I

Section: Chapter Questions

Problem 4P: An airplane flying upwind, downwind, and crosswind shows the main principle of the MichelsonMorley...

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