# Why do some physics textbooks say P = dK/dt and others say P = dE/dt?

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In summary, there is a discussion about the relationship between E and K in physics. It is mentioned that some may assume E = K, but the speaker believes it is actually E = K + U. There is also a question about the definitions of P, K, and E, with the speaker providing a general definition of power and explaining that in the case of external force performing work, P = dW/dt.
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Homework Statement
I am interested in why some physics textbooks say P = dK/dt (namely morins classical mechanics) while others say that P = dE/dt (namely physics for scientists and engineers with modern physics)
Relevant Equations
P = dK/dt = dE/dt
Are they assuming that E = K in physics for scientists and engineers with modern physics, but I though E = K + U?Many thanks!

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What is P, K and E?

Is P power, is K kinetic energy and E is energy, what kind of energy?

member 731016
malawi_glenn said:
What is P, K and E?

Is P power, is K kinetic energy and E is energy, what kind of energy?
Thanks for your reply @malawi_glenn! Here I'll send you a screen shot what it says.

The text pretty much explains it.

The generic definition of power is ANY energy transfer, like transfer of heat etc.

Then in the case of an external force that is performing work, you will get P = dW/dt

member 731016
malawi_glenn said:
The text pretty much explains it.

The generic definition of power is ANY energy transfer, like transfer of heat etc.

Then in the case of an external force that is performing work, you will get P = dW/dt
Ok thank you @malawi_glenn!

## 1. Why do some physics textbooks use P = dK/dt while others use P = dE/dt?

This is because there are two different ways to define power in physics: as the rate of change of kinetic energy (K) or as the rate of change of total energy (E). Both definitions are correct and are used in different contexts depending on the problem being solved.

## 2. Which definition of power is more commonly used in physics?

The definition of power as the rate of change of total energy (P = dE/dt) is more commonly used in physics, as it takes into account all forms of energy (kinetic, potential, thermal, etc.) and is more generalizable to different systems.

## 3. When should I use P = dK/dt and when should I use P = dE/dt?

You should use P = dK/dt when dealing with systems where only kinetic energy is involved, such as a moving object. On the other hand, P = dE/dt should be used when dealing with systems where multiple forms of energy are present, such as a swinging pendulum or a chemical reaction.

## 4. Can P = dK/dt and P = dE/dt be used interchangeably?

No, P = dK/dt and P = dE/dt cannot be used interchangeably as they represent different physical quantities. Using the wrong definition of power can lead to incorrect calculations and results.

## 5. Why do some physics textbooks use different symbols for power, such as P and W?

In some cases, different symbols may be used to represent power to avoid confusion with other quantities. For example, W is often used to represent work, so P may be used to represent power to avoid confusion. However, both P and W can be used to represent power and work, respectively, as long as their units are clearly stated.

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