What are the extra terms in the k.e expression

In summary, the conversation discusses the first six terms of the classical expression for kinetic energy and their relation to the relativistic expression. The terms beyond the second are not commonly used or named in classical physics.
  • #1
Ian
88
1
Can someone please tell me what the first six terms are in the classical expression for kinetic energy.
Thanks,
Ian.
 
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  • #2
1) The kinetic energy of what?
2) Why did you post this in the general math forum?
 
  • #3
Start with the relativistic total energy (rest and kinetic):

E2=(mc2)2+p2c2

p=mv

substitute and simplify to E=mc2(1+v2/c2)1/2

then use the binomial theorem. The first term of the binomial expansion will be the rest energy, the next term will be the commonly used (1/2)mv2. The second through seventh terms are the ones you want.

Njorl
 
  • #4
Maybe it is a matter of semantics, but I wouldn't call that the "classical expression for kinetic energy", rather the "relativistic expression for kinetic energy". I guess that it's just a matter of taste...
 
  • #5
Originally posted by suyver
Maybe it is a matter of semantics, but I wouldn't call that the "classical expression for kinetic energy", rather the "relativistic expression for kinetic energy". I guess that it's just a matter of taste...

I agree. I don't think there is a standard terminology for the next few terms of the expansion. I suppose they could be called the first through fifth order corrections to the classical formula for kinetic energy.

Njorl
 
  • #6
Originally posted by Ian
Can someone please tell me what the first six terms are in the classical expression for kinetic energy.
Thanks,
Ian.

They do not correspond to any named quantity in classical physics.

This needs not be surprising. You can write any function as a linear combination of other functions in many ways (much in the way you can use different coordinate systems for describing vectors).

It turns out that, when you expand the K.E. in powers of v/c, you gain some understanding of why things look like classical mechanics when v/c<<1, but the (infinitely many) higher-order terms do not have a wide enough use to get them a name of their own; actually, had relativity not prompted this peculiar expansion of KE in terms of powers of (v/c), those terms would probably never had shown up elsewhere.
 
  • #7
I guess for the most part I would simply call them, ignored!
 

1. What are the extra terms in the k.e expression?

The extra terms in the kinetic energy (k.e.) expression are potential energy terms, such as gravitational potential energy or elastic potential energy. These terms account for the energy stored in a system due to its position or configuration.

2. Why are these extra terms included in the k.e expression?

The inclusion of potential energy terms in the k.e. expression allows for a more comprehensive understanding of the total energy of a system. It takes into account both the kinetic energy of the system (due to its motion) and the potential energy (due to its position or configuration).

3. Can the extra terms be ignored in certain situations?

No, the extra terms cannot be ignored in most situations. In order to accurately calculate the total energy of a system, both the kinetic and potential energy terms must be included. However, in certain simplified cases where potential energy is assumed to be negligible, the extra terms may be ignored.

4. How do the extra terms affect the overall energy of a system?

The extra terms contribute to the total energy of a system, which is conserved in a closed system. This means that any changes in the kinetic energy of the system will also result in changes in the potential energy, and vice versa.

5. Are there any limitations to the k.e expression with the inclusion of extra terms?

The limitations of the k.e. expression with the inclusion of extra terms depend on the specific situation and the accuracy required. In some cases, the expression may need to be modified or other energy equations may need to be used to account for additional factors, such as friction or heat. Additionally, the k.e. expression may not accurately describe the behavior of systems at the atomic or subatomic level.

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