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Physics / Classical Mechanics 0 / Chapter 7 / Problem 7.4

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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Consider a mass m moving in a frictionless plane that

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QUESTION:

Consider a mass m moving in a frictionless plane that slopes at an angle a with the horizontal. Write down the Lagrangian in terms of coordinates x, measured horizontally across the slope, and y, measured down the slope. (Treat the system as two-dimensional, but include the gravitational potential energy.) Find the two Lagrange equations and show that they are what you should have expected.

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QUESTION:

Consider a mass m moving in a frictionless plane that slopes at an angle a with the horizontal. Write down the Lagrangian in terms of coordinates x, measured horizontally across the slope, and y, measured down the slope. (Treat the system as two-dimensional, but include the gravitational potential energy.) Find the two Lagrange equations and show that they are what you should have expected.

ANSWER:

Step 1 of 4

The mass moving in a frictionless plane that slopes at an angle with the horizontal.

Here, is the height of the plane and is the distance of mass from the peak.

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