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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?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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 Raine 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: }Raine Using a similar process as in (a) – (c), what is the total U provided by the shell onto a mass m inside the shell?
Transcribed Image Text: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 Raine 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: }Raine Using a similar process as in (a) – (c), what is the total U provided by the shell onto a mass m inside the shell?
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