Using Forces vs. Energy Formulas: Which is Better?

[Femme_physics]

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?

 

[I like Serena]

Evening the score!

Yes, you can always also use "forces".

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

 

[Femme_physics]

Topping you ;)

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

And is

Considered an energy formula?

 

[Born2bwire]

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

$$\mathbf{F} = \frac{\partial \mathbf{p}}{\partial t}$$

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.

Topping you ;)

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

And is

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.

 

[Femme_physics]

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

 

[I like Serena]

Topping you ;)

------

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

And is


Considered an energy formula?

I'll be back!



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

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

 

[AlephZero]

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...

 

[Femme_physics]

I'll be back!
Uhh. You did solve both problems with the energy formula.

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

Is there another way to solve it?

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!

 

[I like Serena]

Is there another way to solve it?

The truck problem could have been solved with:

v_f = v_i + at
x_f = x_i + v_i 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!