Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: guest39538 on 26/03/2016 10:36:37
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Kinetic energy, a rather strange and mysterious concept that is seemingly mistaking displaced velocity for something else energy based.
When a roller coaster is lifted, the carriage gains relativistic mass, when the carriage is released it becomes a subject to gravity and falls down the track , when the carriage reaches the ground level instead of creating a force of impact (F=ma) , the velocity is gradually displaced by the gradient of the track , cushioning and deflecting the carriage taking away the impact. No impact, no external stopping force and according to Newton the mass will remain in motion unless there is an acting external force. When the carriage reaches the ground level it does not impact, it continues it's new velocity parallel to the ground where the grounds external force eventually brings the vehicle to an halt.
What do you think?
added- I drew it for you
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added- an ''escape'' velocity
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Sorry got carried away with my art.
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As I have explained many times before, energy is a scalar, i.e. it has no direction. Velocity is a vector. So energy is conserved (mgh = ½mv2) and momentum is conserved (ΔΣmv = 0). It's difficult to observe the latter since the two masses involved are the mass of the trolley and the mass of the earth, but you have to take it into consideration when manipulating objects in free fall.
Note that the mass of the earth, me, is implicit in g, and v = ve + vt.
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As I have explained many times before, energy is a scalar, i.e. it has no direction..
I have to disagree , energy has isotropic ''centrifugal direction'' , if it were not for electro-negativity holding electro-positivity in place, the electro-positivity would just expand isotropically from itself leaving a negative void in the center.
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A positive energy can not hold itself together without a negative hold to hold it together.
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I find it difficult to believe that when one provides energy to move a body away from a source of gravitation that that body gains mass due to E=MC^2 ?
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On further thought I have convinced myself, where does the energy come from to lift the roller coaster ? we break up a few Uranium atoms in our reactor and export the energy obtained hence the Earth must have become a little less massive.
We have a closed system so the roller coaster that receives that energy must have gained mass!.
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a=9.81m/s2 ... linearly fixed velocity constant
This is a contradiction.
The roller coaster trolley, while it is falling vertically accelerates under the force of gravity.
This means that the velocity is not fixed, but is increasing linearly.
And the distance fallen is increasing quadratically.
the carriage gains relativistic mass
electro-negativity holding electro-positivity in place
While Einstein was able to make amazing deductions from imagining electric trolley-buses traveling near the speed of light, I think it is more sensible for you to first come to terms with the kinetic energy of electrically neutral trolleys traveling nowhere near the speed of light.
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a=9.81m/s2 ... linearly fixed velocity constant
This is a contradiction.
The roller coaster trolley, while it is falling vertically accelerates under the force of gravity.
This means that the velocity is not fixed, but is increasing linearly.
And the distance fallen is increasing quadratically.
My own fault for putting an ambiguity sentence, yes the speed increases per meter, but I meant that 9 .81m/s2 is a constant rate on earth but nether mind.
the carriage gains relativistic mass
electro-negativity holding electro-positivity in place
While Einstein was able to make amazing deductions from imagining electric trolley-buses traveling near the speed of light, I think it is more sensible for you to first come to terms with the kinetic energy of electrically neutral trolleys traveling nowhere near the speed of light.
Electrically neutral does not mean that the trolley does not contain positive, kE sounds rather ''poppy cock''
What is kE apart from vivid imagination?
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What is kE apart from vivid imagination?
The purpose of physics is to build predictive mathematical models of things that happen.
Classical mechanics describes what happens to objects larger than a molecule, moving at substantially less than the speed of light, for periods between the big bang and the foreseeable future.
Three quantities are conserved in a classical interaction: mass, energy and momentum. Energy turns up in a number of forms, mostly as kinetic, potential and heat.
The formal concept of kinetic energy as ½mv2 was a stroke of brilliance in the 17th century, though the relationship between KE and PE had been surmised thousands of years earlier and used by whoever invented the bow and arrow. The conservation principle has been understood and applied by every engineer from Newcomen to NASA.
The discovery of radioactivity added a twist as it seemed that energy could appear ex nihilo but it turns out that the small correction factor E = mc2 completely accounts for the measured mass loss in nuclear decay and the observed momentum of the daughter particles.
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We have a closed system so the roller coaster that receives that energy must have gained mass!.
Relativistic mass relative to the ground.
+a=+F
An object at ground state will be x mass, raise the object and relative to the object it gains more Fn.
The speed of the fall creating an illusion that the object has gained something, the only thing gained is distance and falling acceleration Fn.
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What is kE apart from vivid imagination?
The purpose of physics is to build predictive mathematical models of things that happen.
Classical mechanics describes what happens to objects larger than a molecule, moving at substantially less than the speed of light, for periods between the big bang and the foreseeable future.
Three quantities are conserved in a classical interaction: mass, energy and momentum. Energy turns up in a number of forms, mostly as kinetic, potential and heat.
The formal concept of kinetic energy as ½mv2 was a stroke of brilliance in the 17th century, though the relationship between KE and PE had been surmised thousands of years earlier and used by whoever invented the bow and arrow. The conservation principle has been understood and applied by every engineer from Newcomen to NASA.
The discovery of radioactivity added a twist as it seemed that energy could appear ex nihilo but it turns out that the small correction factor E = mc2 completely accounts for the measured mass loss in nuclear decay and the observed momentum of the daughter particles.
Scratches his head!
What on Earth as that suppose to mean Alan with no disrespect intended, science seem to have invented their own language that doesn't come across in English.
Energy turns up in a number of forms, mostly as kinetic,
I don't get it, what ?
What is kE?
The rest energy of matter does not increase or decrease by motion, only that which is being absorbed or emitted changes relative to motion. Force of impact increases with motion, +h (height)= + force, +force delta direction = parallel distance travelled.
Ok, let us take a 1kg weight and raise it 2m in h,
F=ma
F=0.1*9.81m/s2
9.81m/s + 9.81 m/s = 19.62 m/s when it hits the floor.
F=0.1*19.62 = 1.962N
So if we Y delta X at 0h , how far will the object travel X?
1kg + 2my = ?mx
Oh and by the way, F=0.1*0m is still 0.981N the same as 1m h which is a mystery.
Fn=h0= 0.981N = (F=0.1*9.81m/s and 1m h) which is wrong somewhere.
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What is kE apart from vivid imagination?
If you get hit by a bus, it leaves very little to the imagination....
You wouldn't call the resulting damage poppycock!
Kinetic Energy = ½mv2
If the bus weighs twice as much as a mini-bus (but traveling the same speed), the KE of the bus will be twice that of the minibus.
If the minibus is traveling twice as fast as the bus, , the KE of the minibus will be twice that of the bus.
The speed of the fall creating an illusion that the object has gained something, the only thing gained is distance and falling acceleration Fn.
Another few things that the fall has produced are:
velocity or speed
Momentum = m*v
Kinetic Energy = ½mv2
Note: Normally, Force would be labelled F, and acceleration would be labelled something like a. For objects of constant mass, they are proportional.
Force of impact increases with motion, +h (height)= + force, +force delta direction = parallel distance traveled.
The force of the impact is very variable over time, depending whether the object lands on concrete, water, feathers, or has its direction changed to the horizontal by roller-coaster tracks (and so effectively lands on air). It also depends strongly on whether the trolley is more or less rigid than the thing it runs into.
While the instantaneous force of impact is very important in designing crash-resistant cars, seat-belts and air-bags, this consumes a lot of supercomputer time (and crash dummies).
Most of the time, you can determine a lot from the momentum and kinetic energy of the impact. And you can ignore relativistic mass (which is so small for a roller coaster or a bus that we can't hope to measure it).
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If you get hit by a bus, it leaves very little to the imagination....
You wouldn't call the resulting damage poppycock!
NO , I would call that force, the force of the bus was greater than my inertia, +speed = + force
No kE needed, next?
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And you can ignore relativistic mass (which is so small for a roller coaster or a bus that we can't hope to measure it).
Huh? you already measure it .
Relativistic mass is what you call kE but which is really increased relativistic weight.
The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest.
Take a 5kg object at ground state
0.5*9.81=4.905N
Now raise this object 5 m h,
0.5 * 49.05= 24.525n relativistic weight
Then convert 24.525n into a ground state mass to get the equivalent.
24.525n = 2.5 mass at ground state or 25kg approx
F=ma
2.5*9.81= 24.525n at ground state
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I would call that force, the force of the bus was greater than my inertia
Well, here is another definition of Energy:
E = F*d
Where:
- E is Energy (measured in Joules)
- F is Force (measured in Newtons)
- d is distance (measured in meters)
Now, whether this Energy is Kinetic Energy or Mechanical/Thermal energy depends on how the bus applies the force:
- If you are leaning on a stone wall, and the bus runs into you, your velocity will not change (ie stationary). The energy of the bus will go into mashing you to a pulp.
- If you are crossing the street when the bus runs into you, your velocity will change dramatically (to pretty much the original speed of the bus). The energy of the bus will get turned into your kinetic energy, plus some mechanical energy in smashing a few bones, etc. In this case, you won't get pulped quite so much (at least until you hit the ground).
+speed = + force
1kg + 2my = ?mx
I suggest that you try to attach units to everything you do (like m/s2 in your diagram for acceleration). This often reveals errors in logic, for example when you equate speed (in m/s) with force (in Newtons), or attempt to add mass (in kg) to height (in meters).
There is a very real difference between Force (Newtons) and Energy (Joules). It is similar to the difference in a car between Torque (in Newton-meters) and Power (in Joules/second).
Car lovers want a car that has high torque and high power (and generally, the car manufacturers try to deliver both in the same vehicle).
But you could imagine:
- A car with very high torque but very low power: Great pushing down walls, but not much good for anything else (like a lightweight bulldozer)
- A car with very high power, but very low torque: Great for traveling at high speeds, but it takes 5 minutes to accelerate from 0 to 100km/h.
But if you can't see the difference, you are in good company. Michael Faraday didn't distinguish the two in his work - but then he was an accomplished experimentalist, and wasn't too rigorous about getting the maths right.
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If you think "pair production", say from some gamma photon decay (e-/e+) ...... and further realize, these particles are likely quantumly entangled i.e. meaning, to exact work on one, would correspondingly cause mutual energy increase in the other - if by then, every particle in the universe has a partner, perhaps when we accelerate a given mass, may only be privvy to half the overall affect?
If the relationship between mass, energy and speed holds true (as in Einstein's iconic equation); maybe, it also applies to that of mass, energy & velocity .... only that we merely 'see' 0.5 x the jazz?
Just speculative logic, man.
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The rest energy of matter
is irrelevant to classical mechanics, in which, by definition, mass is conserved.
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The rest energy of matter
is irrelevant to classical mechanics, in which, by definition, mass is conserved.
And that means in plain English?
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Huh? you already measure it .
Relativistic mass is what you call kE but which is really increased relativistic weight.
The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest.
Take a 5kg object at ground state
0.5*9.81=4.905N
Now raise this object 5 m h,
0.5 * 49.05= 24.525n relativistic weight
Then convert 24.525n into a ground state mass to get the equivalent.
24.525n = 2.5 mass at ground state or 25kg approx
F=ma
2.5*9.81= 24.525n at ground state
No. You are on the wrong track here. I am not quite sure what track you are on, but it ain't right...
F = m*a means force = mass times acceleration
force is in units of Newtons (N = kg*m*s–2)
mass is in units of kilograms (kg)
acceleration is in units of m*s–2
therefore it makes sense that, for instance:
5 kg * 9.8 m*s–2 = 49 kg*m*s–2
it looks like what you are calling "relativistic weight" is probably work (force times distance) or potential energy (both expressed as energy)
energy (work) is in units of Joules (J = kg*m2*s–2)
so the work required to lift a 5 kg object 8 meters up against Earth's gravity is:
8 m * 5 kg * 9.8 m*s–2 = 392 kg*m2*s–2 = 392 J
note that if we apply E = m * c2, (m = E * c–2)
392 kg*m2*s–2 * (299800000 m*s–1)–2 = 0.00000000000000436 kg = 4.36 picograms
so the relativistic mass for a 5 kg object raised 8 meters above the Earth, is 5.00000000000000436 kg
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No. You are on the wrong track here. I am not quite sure what track you are on, but it ain't right...
A bit contradictory mate, you say you are not sure what I am talking about yet you claim it is not right.
F = m*a means force = mass times acceleration
force is in units of Newtons (N = kg*m*s–2)
mass is in units of kilograms (kg)
acceleration is in units of m*s–2
Huh? why are you putting - 2
Force = mass times acceleration
force is measured weight , in Newtons,
a=9.81m/s2
which means that for every meter falling it increases its acceleration *2
You lost me , I know what F=ma means, or I thought I did.
Let me confirm,
for 1kg mass we put 0.1 in the calculation for mass?
F= 0.1 * a
acceleration is 9.81m/s2
for the first meter
9.81m/s
2nd meter
9.81m/s*2
3rd meter
9.81m/s*3
?????????????
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I take it that if the energy to raise this 5Kg mass has come from an Earth bound source the Earth has also lost the same amount of relativistic mass.
Due to the daughter atoms from the spit uranium atoms having less mass and Neutrinos carrying off some.
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I take it that if the energy to raise this 5Kg mass has come from an Earth bound source the Earth has also lost the same amount of relativistic mass.
Due to the daughter atoms from the spit uranium atoms having less mass
Not at all, the energy used to raise the 5 KG is independent of the 5 kg, the energy is made to raise the 5 KG.
In experiment let me offer this , in a scrap yard there is a drive on set of scales, a weigh bridge, that weights all the old scrap cars etc, so imagine we weight a car to reveal at ground state the car has a 1 ton mass, now raise the car 5 m and drop the car on the scales, I guarantee the scales will measure a huge mass difference when the car lands on the scales.
To me, science has got a lot of different things that mean the same thing.
Mass is equivalent to Newtons. scratches head....
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Can we make these scales they would be well cool?
sorry
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Kinetic energy is 1/2 MV2. In this equation, kinetic energy is a property of mass and velocity squared.
If we look at the velocity squared term, squaring a number not only impacts the scalar, but also the vector. Squaring means a plus or minus vector direction, ends up the same, in terms of kinetic energy. Kinetic energy is not relative to direction and therefore it is not relative to any given reference, since the vectors connected to red and blue shifts are normalized by the square term.
As an experiment, we can start in empty space with zero gravity and use X fuel to generate a final velocity for our rocket. This kinetic energy will be based on an energy balance; X fuel. We can launch the first experiment moving away from the earth and then the second experiment toward the earth. Based on energy conservation, since we used the same fuel both in all experiments, both experiment will have the same kinetic energy. However, special relativity calculations will show differences in motion coming and going, relative the earth. The slowing or speeding up of space-time, due to relative reference, does not alter fuel usage, energy conservation and therefore the kinetic. These only add an energy mask to the true kinetic energy.
The lack of dependency on kinetic enemy on reference, can also be inferred from dimensional analysis. If you look at the units of kinetic energy, it is M d2/t2. It is mass times, double the units of space-time (d,t). This tells us kinetic energy is not a function of one space-time reference, but rather of two references. The real kinetic energy, based on energy conservation, is not impacted by the red or blue shift seen by different references, who may see this motion coming or going.
Kinetic energy needs to be measured against a standard that is not connected to space-time; C-ground state. At the speed of light space-time breaks down, so one reference is possible for a standard. In space-time we need to use two reference and then take an average of sorts.
I often wonder if we are properly conserving energy, when we look out at space and see the Doppler shift using one space-time reference as the standard. The result of a red shift only approach; from earth reference, would take away energy. The result will be hidden energy that needs to explained in others ways; dark energy.
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Mechanical energy, with the ability to do work, comes in two forms. Potential and kinetic energies. These are energies of motion and relate directly to the equation F=ma.
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I would call that force, the force of the bus was greater than my inertia,
Force is rate of change of inertia. You can't equate force with inertia.
And that means in plain English?
that the sum of the mass of the bus and the mass of your body is the same before and after the collision, even if bits of your body are distributed over the road and the bus. Provided the bus was travelling at less than 100,000,000 m/s, the relativistic correction is negligible for forensic purposes.
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The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest.
Not true.
The higher you lift an object, the less it weighs because the gravitational field is divergent. F= GmM/r2, if you recall.
Terminal velocity depends on the shape of a falling object, and the density and viscosity of the medium through which it falls. It's about 150 mph for a human body, from any height above a couple of hundred feet. I don't think this is what you meant.
You can calculate ground impact velocity (ignoring air resistance) by putting mgh = ½mv2, i.e. by assuming that energy is conserved. But even though the calculation is simple and the answer is always correct, I'm sure you will not believe it.
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Force is rate of change of inertia. You can't equate force with inertia.
No it is not, I totally disagree with valued reasoning.
''a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force''
In my terms a resistance to change of velocity, an object at rest on Earth has inertia, this inertia is created by the linear force of gravity, inertia how you define it is an exact equal to force and means the same thing.
F=ma in a Y axis and F=ma in a x-axis, change x to change y, inertia is just another add-on that means force, so yes I can equate inertia with force, because they are the same thing, we don't need mass, we don't need inertia, we don't need kE, Newtons of force explains all of them and is equal to them, they are all the same thing and have no differential.
A change of force is needed to change the force hold on the object, inertia is the force hold which is gravity.
In plain English, the resistance to force is a force but you call it inertia when it is Newton's.
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The higher you lift an object, the heavier it becomes relative to the ground, terminal velocity is the weight maximum limit and at its relativistic heaviest.
Not true.
The higher you lift an object, the less it weighs because the gravitational field is divergent. F= GmM/r2, if you recall.
Terminal velocity depends on the shape of a falling object, and the density and viscosity of the medium through which it falls. It's about 150 mph for a human body, from any height above a couple of hundred feet. I don't think this is what you meant.
You can calculate ground impact velocity (ignoring air resistance) by putting mgh = ½mv2, i.e. by assuming that energy is conserved. But even though the calculation is simple and the answer is always correct, I'm sure you will not believe it.
Yes by terminal velocity I meant the maximum speed something falls at, why what else could I mean?
The higher you lift an object, following the inverse square law the weight of Newton's will lessen as the gravitational force lessens, however when the object falls it regains relativists weight and the scales the object lands on will record that it gained relativistic kg (mass) .
Newton's of force is what gives an object it's mass which is equal to Newton's. (the same thing)
(F=0)=(m=0)
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No. You are on the wrong track here. I am not quite sure what track you are on, but it ain't right...
A bit contradictory mate, you say you are not sure what I am talking about yet you claim it is not right.
Imagine someone says they are trying to make chocolate mousse, and you walk into the kitchen to find them struggling with a tin of anchovies. You don't know why they are using anchovies, but you can be sure that it won't help them make the chocolate mousse...
F = m*a means force = mass times acceleration
force is in units of Newtons (N = kg*m*s–2)
mass is in units of kilograms (kg)
acceleration is in units of m*s–2
Huh? why are you putting - 2
Putting the negative sign in the exponent is equvalent to taking the reciprocal. For instance:
32 = 9
3–2 = 1/9
5*2–3 = 5/(23) = 5/8
m/s2 = m*s–2
Force = mass times acceleration
force is measured weight , in Newtons,
a=9.81m/s2
ok
which means that for every meter falling it increases its acceleration *2
no
You lost me , I know what F=ma means, or I thought I did.
Let me confirm,
for 1kg mass we put 0.1 in the calculation for mass?
F= 0.1 * a
acceleration is 9.81m/s2
for the first meter
9.81m/s
2nd meter
9.81m/s*2
3rd meter
9.81m/s*3
?????????????
no. For 1 kg, F = 1*a (and for 23 kg, F = 23*a)
An acceleration of 9.81m/s2 means that the velocity of an object (vt) after t seconds of acceleration will be whatever the velocity was at zero seconds (v0, ie before the acceleration started) plus the acceleration times t:
vt = v0 + a*t
If in object is initially not moving (v0 = 0) and then begins to fall at a = 9.81 m/s2
it will be moving at 9.81 m/s at 1 second, 19.62 m/s at 2 seconds, 29.43 m/s at 3 seconds...
EDIT: equations corrected thanks to hamdani yusuf!
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an object at rest on Earth has inertia, this inertia is created by the linear force of gravity
How do you explain that an object orbiting the Earth in free-fall (no weight) has the same inertia as the same object sitting on the Earth's surface?
Gravity is different in orbit, so how could the inertia be the same?
It is a bit of a mystery to physicists why inertial mass should be identical to gravitational mass; but it is believed that both characteristics are maintained far from an external gravitational field.
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Time for an apology. Force is rate of change of momentum. Must have left my brain in the sky.
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vt = v0 + a*t2
If in object is initially not moving (v0 = 0) and then begins to fall at a = 9.81 m/s2
it will be moving at 9.81 m/s at 1 second, 39.24 m/s at 2 seconds, 88.29 m/s at 3 seconds, 156.96 m/s at 4 seconds...
The correct formula is vt = v0 + a*t
hence at 1 second, v=9.81 m/s, at 2 seconds v=19.62, and so on.
or if you want to calculate distance st = s0 + v0*t + ½*a*t²
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vt = v0 + a*t2
If in object is initially not moving (v0 = 0) and then begins to fall at a = 9.81 m/s2
it will be moving at 9.81 m/s at 1 second, 39.24 m/s at 2 seconds, 88.29 m/s at 3 seconds, 156.96 m/s at 4 seconds...
The correct formula is vt = v0 + a*t
hence at 1 second, v=9.81 m/s, at 2 seconds v=19.62, and so on.
or if you want to calculate distance st = s0 + v0*t + ½*a*t²
You are absolutely correct--my mistake!!! [:I] I will remove this incorrect info from my original post...
I was thinking in terms of displacement, and writing velocity... as you state,
xt = x0 + v0*t + 0.5*a*t2
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no. For 1 kg, F = 1*a (and for 23 kg, F = 23*a)
The horrible persons on other forum learnt me that for 1kg you put 0.1 thank you for the correction.
You also say no for *2,
2nd meter 9.81*2= 19.62
3rd meter 19.62*2= 39.24
Is that not correct?
added- sorry correction, I did it correct in the first place
acceleration is 9.81m/s2
for the first meter
9.81m/s
2nd meter
9.81m/s*2
3rd meter
9.81m/s*3
*2 is only for the first one sorry.
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So, to answer the original question,
(1) k.e. is a scalar equal to ½mv2 and
(2) we find that if an object falls from rest through a height h in vacuo, gh = ½v2.
Which is not at all surprising for those who understand the meaning of "acceleration". The interesting bit is the discovery (phenomenologically attributed to Galileo, maths by Newton) that g = GM/r2 near the surface of a large spherical planet.
Like it or lump it, Mr Box.
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So, to answer the original question,
(1) k.e. is a scalar equal to ½mv2 and
(2) we find that if an object falls from rest through a height h in vacuo, gh = ½v2.
Which is not at all surprising for those who understand the meaning of "acceleration". The interesting bit is the discovery (phenomenologically attributed to Galileo, maths by Newton) that g = GM/r2 near the surface of a large spherical planet.
Like it or lump it, Mr Box.
Your answer is either ambiguous or something else. To me you have just said that kE is a piece of maths and does not exist as E in any sense.
I asked you what is kE?, the question is not what is the maths for kE.
A battery has energy, a mass has energy, from what I have understood, science says an objects increases in energy(kE) , so it gains more light? what is kE?
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For the hard of learning:
If you take a lump of stuff with mass m and velocity v, then you times together the mass and velocity and velocity again and halve it, you get a number that grownups call kinetic energy.
If you chop a lump of stuff so that the mass of all the bits added up comes to less than the mass you started with, and the difference is m, then m times the speed of light times the speed of light again is a number called mass-equivalent energy or rest-mass energy.
Energy only "exists" in the minds of the child-hating idiots who write the National Curriculum. For the rest of us, it is a number that tells us something about things that happen.
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Energy only "exists" in the minds of the child-hating idiots who write the National Curriculum. For the rest of us, it is a number that tells us something about things that happen.
That's what I said, so kE is not really a physical power, it is just a number so pretty meaningless and abstract.
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It may be abstract but it certainly isn't meaningless.
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Interestingly, it's what the police mostly talk about in road safety lectures. If Mr Plod understands it, and can somehow transfer that understanding to speeding teenage halfwits, it seems strange that anyone who contributes to this forum has a problem with it.
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Interestingly, it's what the police mostly talk about in road safety lectures. If Mr Plod understands it, and can somehow transfer that understanding to speeding teenage halfwits, it seems strange that anyone who contributes to this forum has a problem with it.
Oh please, I clearly understand it but like to dig deep for a deeper understanding, I have my answer, it is abstract and not really a physical thing involving energy.
Do falling objects regardless of their mass have the same terminal velocity?
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It may be abstract but it certainly isn't meaningless.
Well we could describe it mas, height, acceleration= d(x) it will travel
h*a=F
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Do falling objects regardless of their mass have the same terminal velocity?
No. Small rain drops have lower terminal velocity than bigger rain drops, even though they consist of the same material.
Terminal velocity of a falling object is achieved when down force by gravity equals up force by air resistance, hence it is affected by many factors, e.g. air pressure, temperature, humidity, and the object's density, form, orientation, size, etc.
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I clearly understand it but like to dig deep for a deeper understanding
There's nothing deeper to understand. The kinetic energy of a mass m moving at velocity v is ½mv2. It's a useful concept because (by experiment) energy is conserved in classical physics, so we can use it to predict what happens when our moving object interacts with something else.
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I clearly understand it but like to dig deep for a deeper understanding
There's nothing deeper to understand. The kinetic energy of a mass m moving at velocity v is ½mv2. It's a useful concept because (by experiment) energy is conserved in classical physics, so we can use it to predict what happens when our moving object interacts with something else.
I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle. Is it F=ma?
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Except that kinetic energy that is constant has no acceleration. Therefore there is zero force. As well as having stated F=ma, Newton also has a first law which precludes acceleration. You should look it up. It describes states with no forces acting on an object. So that an object at rest remains at rest and an object with constant speed carries on in a straight line with the same constant speed. Because NO FORCES ARE ACTING UPON THE OBJECT!
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Except that kinetic energy that is constant has no acceleration.
A piece of maths has no acceleration or velocity or anythng else for that matter because it is abstract. I think you mean the object in motion will remain in motion unless acted upon by external forces. An object in spacial motion away from an inertial reference frame, remains without force until it impacts another body . A falling body that the force is redirected of, will continue in a parallel motion until the potential force disperses an dis lost to the external force of gravity.
→
p=F
p0=Fn
var(p)=var(Fn)
Newtons third law ''the ground pushes back'',
It is positive energy that pushes back and is the resistance to compression.
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I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.
This thread is discussing conservation of Energy (of which Kinetic Energy and Potential Energy are two forms), under the influence of a gravitational field.
Emmy Noether came up with a very general concept which links conservation laws to symmetries in nature.
The Conservation of Energy (and its component Kinetic Energy) is proved in the following example:
http://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:_Conservation_of_energy
Occasionally, conservation of momentum comes up in this thread - this is another principle which can be proved by Noether's theorem.
Do falling objects regardless of their mass have the same terminal velocity?
"raindrops falling through air to reach terminal velocity" is a complex system in which it is extremely hard to add up all the tiny contributions of kinetic energy which are distributed amongst all the individual air molecules. So if you wish to understand kinetic energy, look at objects falling in a vacuum (or the proverbial cannonballs falling from the leaning tower of Pisa) - it is so much easier to analyze.
You can see something real, without being diverted into fractal flurries of turbulence which dissipate lots of energy and get you nowhere.
p0=Fn etc
The mathematical notation used in Noether's Theorem may look superficially similar to some equations previous posted in this thread. It is not.
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I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.
This thread is discussing conservation of Energy (of which Kinetic Energy and Potential Energy are two forms), under the influence of a gravitational field.
Emmy Noether came up with a very general concept which links conservation laws to symmetries in nature.
The Conservation of Energy (and its component Kinetic Energy) is proved in the following example:
http://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:_Conservation_of_energy
Occasionally, conservation of momentum comes up in this thread - this is another principle which can be proved by Noether's theorem.
Do falling objects regardless of their mass have the same terminal velocity?
"raindrops falling through air to reach terminal velocity" is a complex system in which it is extremely hard to add up all the tiny contributions of kinetic energy which are distributed amongst all the individual air molecules. So if you wish to understand kinetic energy, look at objects falling in a vacuum (or the proverbial cannonballs falling from the leaning tower of Pisa) - it is so much easier to analyze.
You can see something real, without being diverted into fractal flurries of turbulence which dissipate lots of energy and get you nowhere.
p0=Fn etc
The mathematical notation used in Noether's Theorem may look superficially similar to some equations previous posted in this thread. It is not.
That is new to me, I have no idea what it means yet.
I had this thought though after looking at the link
Φ→← = Φ←→ = 4/3 pi r³
>Φ→← = <4/3 pi r³
>Φ←→ = >4/3 pi r³
E=>Φ→←
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I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle. Is it F=ma?
Kind of.
Energy = work = force x distance = (mass x acceleration) x distance = mass x ½(velocity change)2, if you think about it.
Classical physics really is very simple. It's all about precise definitions of mathematical quantities, and finding the conservation laws that apply to them. And as I've said many times before, dimensional analysis will always resolve any mistakes or misunderstandings.