Mechanical Symmetry?

[Capiert]

Mass m vs speed_difference v "trade_off"

is very important for conservation of momentum (com).

Unfortunately conservation of energy (coe)

doesn't see (=conceptualize) things

the same way,

& instead (some sort of) a speed_squared

vs (single) mass relevance exists

(or should it?)!

E.g. How can both laws be valid,

when they seem to contradict?

Does (kinetic) energy really have

a mass vs speed_squared trade off? E.g. in collisions.

If NOT, then why do we use it (=(the) energy_construct)?

 

That's 4 questions.

Thanks in advance.

Edited December 28, 2016 by Capiert

[swansont]

KE is not conserved, except under specific conditions (e.g elastic collision, where it's conserved by definition), so the v^2 objection is moot.

[Sriman Dutta]

Both the conservation laws hold true. Besides, there's also the conversation of mass.

 

In case of collisions between two bodies having their masses as [math]m_1[/math] and [math]m_2[/math] respectively and velocities before collision as [math]u_1[/math] and [math]u_2[/math] and after collision, as [math]v_1[/math] and [math]v_2[/math] respectively, then the following equation holds true -

[math]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/math]

[Capiert]

What is moot?

Both the conservation laws hold true. Besides, there's also the conversation of mass.

 

In case of collisions between two bodies having their masses as [math]m_1[/math] and [math]m_2[/math] respectively and velocities before collision as [math]u_1[/math] and [math]u_2[/math] and after collision, as [math]v_1[/math] and [math]v_2[/math] respectively, then the following equation holds true -

[math]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/math]

That looks like only com.

[swansont]

What is moot?

You are objecting to something that's not generally true. KE is only conserved when there is no other avenue for energy loss, so it's then conserved by definition. IOW it's only conserved in a special, specific case. Your objection is moot.

[Sriman Dutta]

com=conservation of mass????

[studiot]

In Newtonian mechanics, the total mechanical energy of an isolated system is conserved.

Energy may be swapped between individual reservoirs of energy.

Often these are just Kinetic Energy and Potential Energy.

 

Further energy can be introduced into the system by outside agents, at the expense of removing the isolation constraint.

[swansont]

In Newtonian mechanics, the total mechanical energy of an isolated system is conserved.

.

As long as there's no friction.

[studiot]

As long as there's no friction.

 

Indeed this is true.

[Sriman Dutta]

Here's a simple demonstration of the law of coe.

Take a ball of mass m and at height h above the ground.

At that height: PE=mgh, KE=0, Total E=KE+PE=mgh

At midway, when ball is at a height of x above ground level, velocity of ball(v)=sqrt(2g(h-x))

PE=mgx, KE=0.5mv^2=0.5m(2g(h-x))=mgh-mgx, Total E=KE+PE=mgh

At the ground, velocity(v)=sqrt(2gh)

PE=0(since height=0), KE=0.5mv^2=0.5m(2gh)=mgh, Total E=KE+PE=mgh

[Capiert]

You are objecting to something that's not generally true. KE is only conserved when there is no other avenue for energy loss, so it's then conserved by definition. IOW it's only conserved in a special, specific case. Your objection is moot.

Please use a non_ambiguous word. (I'm unfamiliar with moot vocabulary.)

Should I assume you mean trivial or discussable? Perhaps the later?

[swansont]

Please use a non_ambiguous word. (I'm unfamiliar with moot vocabulary.)

Should I assume you mean trivial or discussable? Perhaps the later?

It's a non-issue. KE is not a generally conserved quantity. You are objecting to a fictitious problem.

[Capiert]

It's a non-issue. KE is not a generally conserved quantity. You are objecting to a fictitious problem.

So bad?

Is not KE part of the Lagrangian (PE & KE equation)?

If the parts are not dimensioned correctly

how can we expect the coe

to behave correctly?

Edited December 28, 2016 by Capiert

[swansont]

So bad?

Is not KE part of the Lagrangian (PE & KE equation)?

If the parts are not dimensioned correctly

how can we expect the coe

to behave correctly?

They have the correct dimensions. This is another non-issue

[Capiert]

They have the correct dimensions. This is another non-issue

Correct dimensions, perhaps; but conflicting proportions.

It looks like here is no place for discussion.

Is there any reason why dark energy exists?

[swansont]

Correct dimensions, perhaps; but conflicting proportions.

It looks like here is no place for discussion.

Is there any reason why dark energy exists?

Since they are variables, how do you know the proportions are "conflicting"?

 

This would be a place to discuss it, if you weren't spouting nonsense, and dark energy is not related to anything you've brought up so far in this thread.

[Capiert]

Since they are variables, how do you know the proportions are "conflicting"?This would be a place to discuss it, if you weren't spouting nonsense, and dark energy is not related to anything you've brought up so far in this thread.

If I attempt to derive the KEs from (squaring added) momentums, I find that energy does NOT always add (correctly).

I get an unusal relation which seems to agree with both (for the most part).

The excel table shows occational annomalies.

[Sriman Dutta]

[math]KE=\frac{1}{2}mv^2=\frac{1}{2}pv=\frac{p^2}{2m}[/math]

[Capiert]

Yes. mom^2~2*mE (pronounced "to me") mom squared is approximately twice the mass multiplied by the energy.

Ruffly momomentum mom=m*v, postscript numbers then apply for a non_elastic collision, when squaring both sides

(mom1+mom2)^2=(mom3)^2.

My older versions used KE~m*(v^2)/2, also applying postscript numbers.

 

The final kinetic energy

KE3#KE2+KE1

is NOT the sum of the 2, but instead

KE3~(((m1*KE1)^0.5)+((m2*KE2)^0.5)^2)/(m1+m2).

 

As you can see,

that is NOT simple addition.

 

But if masses are identical

then fewer problems happen

(= & it (=KE3 total) behaves more like simple addition of both energies)

because as it looks

energy does NOT add (properly=correctly, all the time).

Edited December 29, 2016 by Capiert

[Sriman Dutta]

Can you explain the derivation?

[Capiert]

Maybe. What would you like to know?

E.g. All the intermediate steps?

Or what does it mean?

 

Add 2 momentums mom1=m1*v1 & mom2=m2*v2

in a non_elastic collision,

so their final momentum together is mom3=m3*v3.

Before the collision

the 1st mass is m1,

the 2nd mass is m2;

& after the collision

they are stuck together

as a 3rd final mass m3=m2+m1.

Their initial speeds (before the collision) are

v1 for the 1st mass

& v2 for the 2nd mass.

After the collision

both masses (m1&m2=m3)

have a common (final) speed v3.

(All speeds are wrt earth as 0 m/s).

 

Adding both momentums gives

mom1+mom2=mom3, square both sides

(m1*v1+m2*v2)^2=(m3*v3)^2

 

Should I continue?

Or can you take it from there?

Edited December 29, 2016 by Capiert

[Tahir Gorgen]

I think the topic starter misunderstood kinteic energy. Maybey I think this because of my bad langueage.

 

You can calculate the mass, if you know the speed^2 you had and mass with a velocity. (You just divide the velocity with the mass and then take the v^^ (root) of the speed^2

 

You can do it yourselfs and see If youre rigth.

 

You can say m1+m2=m3. But v1+v2 is never v3.

 

Btw velocity is a worth they grant in kinetic energy, for objects with a mass and in movement.

 

It's not it's speed.

 

Maybey some one else can explain this.

 

The difference between speed and what kinetic energy and velocity is?

[Tahir Gorgen]

 

Edit: difide the velocity with half times the mass and than difide it with the root of the speed^2 you had.

 

If you set the velocity of 2 diferended masses. You can calculate and figure out yourself, if you are right with v1+v2=v3. I have tried it and it did'nt make a sense.

 

Mass1+(the mass of an other body/object)+ mass2=mass3

[Tahir Gorgen]

Only with the same speed, they would have a combined velocity, but I am not going to tell this, because I want to be wrong once. I hate this queue

[swansont]

If I attempt to derive the KEs from (squaring added) momentums, I find that energy does NOT always add (correctly).

I get an unusal relation which seems to agree with both (for the most part).

The excel table shows occational annomalies.

KE is not a conserved quantity. Why would you expect it to always "add correctly"?