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Prove that the potential energy of a central force F =

Chapter 7, Problem 7.25

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QUESTION:

Prove that the potential energy of a central force F = krni (with n 1) is U = krn+11(n 1). In particular, if n = 1, then F = kr and U = tkr2

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QUESTION:

Prove that the potential energy of a central force F = krni (with n 1) is U = krn+11(n 1). In particular, if n = 1, then F = kr and U = tkr2

ANSWER:

Step 1 of 2

The following are given by the question:

The force,

For the central force the gradient of potential can be represented as

                                                                       

The given force has only component.

                                                                  

Integrate the above function

                                                                

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