Where Does the Kinetic Energy Equation KE = mgR(1-cos theta) Originate?

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    Derivation
In summary, deriving an equation is a process used to understand and describe the relationship between variables in a mathematical form, allowing for predictions and conclusions to be made. This is achieved by manipulating known principles and using mathematical operations such as differentiation, integration, and substitution. Common methods for deriving equations include calculus, algebraic manipulation, and the application of physical laws and principles. It is not possible to derive an equation without making assumptions, but these assumptions should be based on sound reasoning and clearly stated. It is not necessary to derive an equation for every scientific problem, as some may already have established equations or not require a mathematical representation.
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Nash77
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For a particular homework problem, we needed to find an angle theta.

This equation was used: h = L(1 - cos theta) to solve for theta.
I guess that came from the Kinetic Energy equation KE = mgR(1-cos theta),
but where does that kinetic energy equation come from?

Is it just an equation to know, or was I supposed to have derived this from something?

Thanks,
Nash
 
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  • #2
Without seeing the particular homework problem, it's impossible to help you.
 

1. What is the purpose of deriving an equation?

The purpose of deriving an equation is to understand and describe the relationship between different variables in a mathematical form. This allows scientists to make predictions and draw conclusions based on the equation.

2. How do you derive an equation?

To derive an equation, you must start with known principles and use mathematical operations such as differentiation, integration, and substitution to manipulate the equations until you reach the desired form. This process requires a deep understanding of the principles and mathematical concepts involved.

3. What are the common methods used for deriving equations?

The common methods used for deriving equations include the use of calculus, algebraic manipulation, and the application of physical laws and principles. These methods may vary depending on the specific problem or field of study.

4. Can an equation be derived without any assumptions?

No, it is not possible to derive an equation without making any assumptions. Scientists often make assumptions to simplify a problem or to make it more manageable. However, these assumptions should be based on sound reasoning and should be clearly stated when presenting the derived equation.

5. Is it necessary to derive an equation for every scientific problem?

No, it is not necessary to derive an equation for every scientific problem. Some problems may already have established equations that can be used, while others may not require a mathematical representation. It depends on the nature of the problem and the goals of the scientific study.

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