Using Forces vs. Energy Formulas: Which is Better?

In summary, the conversation discusses the use of energy and forces in solving physics problems. It is mentioned that sometimes it is possible to use forces instead of energy, but typically using energy is less work. It is clarified that f=ma is not always true and that the concept of forces is a mathematical tool rather than something tangible. The idea of eliminating forces from equations is also mentioned, with the historical background of Newton formulating mechanics using only force and momentum. The conversation concludes with an interesting explanation of the different approaches to solving problems using either energy or forces, with an example of using calculus for the bicycle problem.
  • #1
Femme_physics
Gold Member
2,550
1
I notice that sometimes there may be 2 ways of getting to the answer -- using energy, or "forces'. Can I always just use forces?
(i.e. f=ma) instead of those energy formulas?
 
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  • #2


Evening the score! :smile:

Yes, you can always also use "forces".

It's just that when you can apply the "energy formulas", it's usually much less work.
 
  • #3


Topping you ;)

------

Can the problems I solved today, for instance, be solved with teh energy formulas?

And is

theformula.jpg


Considered an energy formula?
 
  • #4


Well, technically, f=ma is not always true. Strictly speaking,

[tex] \mathbf{F} = \frac{\partial \mathbf{p}}{\partial t} [/tex]

Take the example of a rocket. As time progresses, the rocket loses fuel and thus mass. So the force equations have to take into account not only the change in time of its velocity but also its mass.

Femme_physics said:
Topping you ;)

------

Can the problems I solved today, for instance, be solved with teh energy formulas?

And is

theformula.jpg


Considered an energy formula?

It COULD be, under the correct circumstances. You are missing the factor of mass but that may not be an issue in working some problems. But, this is showing the relationship between the final kinetic energy and the initial kinetic energy plus the added kinetic energy from work done on the object of unity mass by the application of a constant force applied along the path of motion.
 
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  • #5


Well, yes, we're talking about relatively simple problems though
 
  • #6


Femme_physics said:
Topping you ;)

------

Can the problems I solved today, for instance, be solved with teh energy formulas?

And is


Considered an energy formula?

I'll be back! :cool:



Uhh. You did solve both problems with the energy formula. :rolleyes:

And yes, that formula is an energy formula (the only one you had until now).
 
  • #7


You can think of "forces" as just a mathematical way of keeping the score, rather than something "real".

Change in mechanical energy = force x distance
Change in momentum = force x time

Eliminating "force" from those two equations is the basic idea of most of "advanced" classical (and non-classical) mechanics, but it took a few hundred years after Newton before Lagrange, Hamilton, etc figured out how to do that systematically. "Solving problems using energy instead of forces" is the first step in that direction.

Historically, in Newton's time there was no real concept of "energy", and one of the important things that Newton did was figure out the difference between vague ideas about energy and momentum. Newton formulated mechanics using only force and momentum, not energy, and most beginning mechanics courses follow the same path and take it as self-evident that "forces" are something that exist in the "real world". But the more you try to nail down what "force" really is, the harder it gets...
 
  • #8


I like Serena said:
I'll be back! :cool:
Uhh. You did solve both problems with the energy formula. :rolleyes:

And yes, that formula is an energy formula (the only one you had until now).

Is there another way to solve it?

AlephZero said:
You can think of "forces" as just a mathematical way of keeping the score, rather than something "real".

Change in mechanical energy = force x distance
Change in momentum = force x time

Eliminating "force" from those two equations is the basic idea of most of "advanced" classical (and non-classical) mechanics, but it took a few hundred years after Newton before Lagrange, Hamilton, etc figured out how to do that systematically. "Solving problems using energy instead of forces" is the first step in that direction.

Historically, in Newton's time there was no real concept of "energy", and one of the important things that Newton did was figure out the difference between vague ideas about energy and momentum. Newton formulated mechanics using only force and momentum, not energy, and most beginning mechanics courses follow the same path and take it as self-evident that "forces" are something that exist in the "real world". But the more you try to nail down what "force" really is, the harder it gets...

Thanks for that explanation :) Very interesting!
 
  • #9


Femme_physics said:
Is there another way to solve it?

The truck problem could have been solved with:

vf = vi + at
xf = xi + vi t + at2/2

The power calculation remains the same.
The bicycle problem would require calculus to do it, but you really do not want to do it that way! :smile:
 
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Related to Using Forces vs. Energy Formulas: Which is Better?

1. What is the difference between forces and energy formulas?

Forces and energy are both physical quantities that describe the behavior and interactions of objects in the natural world. Forces, measured in Newtons, are a vector quantity that describes the push or pull on an object. Energy, measured in Joules, is a scalar quantity that describes the ability of an object to do work or cause a change.

2. Which is more accurate: forces or energy formulas?

Both forces and energy formulas are accurate in their respective applications. Forces are more accurate when describing the motion and interaction of objects on a small scale, such as in mechanics. Energy is more accurate when describing the overall behavior of a system, such as in thermodynamics or electromagnetism.

3. When should I use forces instead of energy formulas?

Forces should be used when analyzing the motion and interactions of individual objects, such as in mechanics or kinematics. Forces are also useful when determining the equilibrium of a system. In these cases, energy formulas may not provide enough information about the behavior of individual objects.

4. When should I use energy formulas instead of forces?

Energy formulas should be used when analyzing the overall behavior of a system, such as in thermodynamics or electromagnetism. Energy is also useful when determining the conservation of energy in a system, as it takes into account all forms of energy, including potential and kinetic energy.

5. Can forces and energy formulas be used together?

Yes, forces and energy formulas can be used together to provide a more complete understanding of a system. Forces can be used to determine the motion and interactions of individual objects, while energy formulas can be used to analyze the overall behavior of the system and determine the conservation of energy.

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