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Deriving Gravitational Energy

Deriving Gravitational Energy

Author: Jon Fishwild
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Purpose of this tutorial

Our ultimate goal is to be able to use the energy concept to make numerical predictions.  The energy concept is an alternative to the force concept and often provides a simpler approach to problems than other approaches we have learned this year.  Often a problem will illustrate a complex motion that might contain some constant velocity, some constant acceleration, and even some other type of motion we haven't studied.  In many cases we can still understand many things about a system, using the energy approach, even if we don't understand many complicated features of the system.  To that end, we need to have ways of calculating energy storage.

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Overview of Energy to Date and Setup for the Derivation

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Questions for Understanding--Part I

1. What does the energy stored in a system measure?

2. How do we calculate the amount of elastic energy stored in a system?

3. How do we calculate the amount of kinetic energy stored in a system?

4. We say that gravitational energy is path independent.  Based on the later part of the video, what do you suppose this term means?


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Deriving the Equation to Calculate Gravitational Energy

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Questions for Understanding--Part II

1. What two variables play a role in determining the amount of gravitational energy stored in a system?

2. How is the function for determining gravitational energy similar to the function for determining elastic energy?

3. How did we "steal" from our method of calculating elastic energy to calculate gravitational energy?

4. Why is the Fx graph horizontal for the gravitational energy calculation in contrast to why the Fx graph was diagonal for the elastic energy calculation?

5. Describe how the equation for calculating gravitational energy "behaves" properly in terms of how it describes the amount of gravitational energy stored in a system.

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