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Physics / Classical Mechanics 0 / Chapter 7 / Problem 7.15

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

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A mass mi rests on a frictionless horizontal table and is

Chapter 7, Problem 7.15

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QUESTION:

A mass mi rests on a frictionless horizontal table and is attached to a massless string. The string runs horizontally to the edge of the table, where it passes over a massless, frictionless pulley and then hangs vertically down. A second mass m2 is now attached to the bottom end of the string. Write down the Lagrangian for the system. Find the Lagrange equation of motion, and solve it for the acceleration of the blocks. For your generalized coordinate, use the distance x of the second mass below the tabletop.

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QUESTION:

A mass mi rests on a frictionless horizontal table and is attached to a massless string. The string runs horizontally to the edge of the table, where it passes over a massless, frictionless pulley and then hangs vertically down. A second mass m2 is now attached to the bottom end of the string. Write down the Lagrangian for the system. Find the Lagrange equation of motion, and solve it for the acceleration of the blocks. For your generalized coordinate, use the distance x of the second mass below the tabletop.

ANSWER:

Step 1 of 3

Block diagram;

Langrangian;

Here is the kinetic energy and is the potential energy.

After attaching the mass , the mass also moves as the table is frictionless;

And

……(1)

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