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Physics / Classical Mechanics 0 / Chapter 4 / Problem 4.26

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

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A mass m is in a uniform gravitational field, which exerts

Chapter 4, Problem 4.26

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QUESTION:

A mass m is in a uniform gravitational field, which exerts the usual force F = mg vertically down, but with g varying with time, g = g (t). Choosing axes with y measured vertically up and defining U = mgy as usual, show that F = V U as usual, but, by differentiating E = 4mv2 + U with respect to t, show that E is not conserved. Figure 4.25 4.30

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QUESTION:

A mass m is in a uniform gravitational field, which exerts the usual force F = mg vertically down, but with g varying with time, g = g (t). Choosing axes with y measured vertically up and defining U = mgy as usual, show that F = V U as usual, but, by differentiating E = 4mv2 + U with respect to t, show that E is not conserved. Figure 4.25 4.30

ANSWER:

Step 1 of 3

The potential energy on vertically upwards is defined as,

Then, gradient of potential energy in vertically upward can be represented in vector form as,

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