## Physics Tutorial

#### Intro

In this short section we will

a) define conservative forces and
b) prove that such forces conserve a quantity we call energy for constant mass systems.

A conservative force is defined as:

(1) Where is a function of the coordinates.Now we multiply both sides by . We get:

(2) Where we used Newton’s second law in the first equal sign. It is left to the reader to prove:

(3) Where is the velocity. Using the equations above we have:

(4) Defining energy to be the sum of the kinetic energy and the potential energy we have:

(5) In other words , the standard conservation of energy.

#### Sample Problem

Prove

(1) #### Solution

For the first equality we have: For the second equality we have:

(1) # About The Author

 Jaime V Math And Physics From Algebra To College Calculus I have been tutoring math and physics on and off for 10 years now. I have been involved in various residential tutoring programs as well as college level teaching. I can tutor mathematics from middle school algebra all the way to college level advanced calculus. My standard teaching method is...
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