When an object is accelerating without resistance, why does it take more and more energy to accelerate it the same amount?
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Anonymous2007-06-26 14:55 ID:QzvFPsV/
momentum is just product of mass and velocity, so for a constant mass to get more momentum, it requires greater velocity. It takes energy to accelerate a mass to that greater velocity. A small mass would need more velocity than a large mass for their momentums to be equal, as in 2x6 = 3x4, where a 2 needs a 6 multiplied to become 12, but the 3 only needs a 4 mulitplied to be 12.
#2 You can't sustain acceleration without energy transfer. F=ma, to accelerate a mass, you require a force to be applied, and the application of force that has effect over a distance is energy transfer. When you stop applying the force, you aren't feeding the acceleration anymore.
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Anonymous2007-06-26 15:13 ID:x4OGrSVl
why does it take more and more energy to accelerate it the same amount?
Because you also need to accelerate the energy you've put in.
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Anonymous2007-06-26 15:35 ID:QzvFPsV/
#2 oh I guess I didn't really answer what you asked, I have to figure that out.
>>3 >>4
Why is the difference so substantial? 3 ms^-1 is a negligible fraction of the speed of light. Yet the energy needed to accelerate the object from 2 m/s to 3 m/s is 5 times higher than the energy needed to accelerate the object from standing to 1 m/s.
We have 2 observers, one travelling at 1m/s and the other standing still. One observer would note that object 1 expended a total of 4.5 joules to increase it's velocity by 3 m/s, whilst the other would note that object 1 expended 2.5 joules to increase it's velocity by 3m/s. Which one is right?
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Anonymous2007-06-28 12:12 ID:jIRGu75M
Just to clarify, the observer travelling at 1m/s would note down this.
Starting at V=-1 the objct would expend 0.5 joules to slow down to v=0, it would then need 2 joules to get to v=2. All relative to the observer.
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Anonymous2007-06-29 10:10 ID:ZQ43Q90x
Can't anyone answer me?
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Anonymous2007-06-29 10:54 ID:3+3Pe10V
Work(energy) is integral of force over distance
Integral F.S
. is the dot product, S is distance moved.
As the velocity increases the distance grows.
F=ma, constant force produces constant acceleration. Now as the velocity grows the acceleration stays the same but the distance traveled grows quite fast, as the S increases so does the work.
>>5
They're both right. Kinetic energy is not invariant under reference frame transformations. As your data suggests, differences of kinetic energy are also not invariant under reference frame transformations. The easiest way to see this is that any moving object has kinetic energy, but in the reference frame of the object, it has 0 kinetic energy.
With regards to the initial questions, they're obviously true mathematically. However, I don't think I can give a "physical" reason anytime soon :( I'll think about it.