Is there an intuitive way to grasp why kinetic energy is proportional to the square of velocity instead of just linear?
I know it's a novice thing, but I'd like something without equations.
I've seen the "throwing something upwards reaches the square of the height" analogy, but that just changes one question for another (why is double the height double the potential energy?).
I've also seen the "you have to move faster to keep pushing an object at the same force"
For example, the pistons of a combustion engine need to move ever faster to maintain acceleration, thus consuming more gas.
This last one appeals to me. Is it "correct"?
Kinetic energy
Eli James
Zachary Butler
It's the definiton that comes from work. Do some calculus on w = F * dr
Jayden Brooks
Doe a rocket engine push with the same force constantly? Does that mean it delivers a constant amount of energy to the vehicle per unit of time?
If so, why does the vehicle's energy increase quadratically?
Joseph Davis
shutup pleb brainlet, if its not intuitive now it will never be
Anthony Butler
>Doe a rocket engine push with the same force constantly? Does that mean it delivers a constant amount of energy to the vehicle per unit of time?
No, but the mass of the rocket decreases with time (as rocket fuel is consumed).
James Hill
1. This is only true for closed system (i.e. constant mass).
2. It is derived from momentum and the second law of motion.
Grayson Sanchez
look up your question in physics stack exchange, I kind of remember some Israeli guy gave a very good answer not using work which would be circular and stupid but symmetry
Luke Butler
Can you sculpt an answer out of this starting point?:
An object falls and as it does it accelerates to about 10 m/s in the first second, then to about 20 m/s in the second second.
In the first second though, the object din't fall 10 meters though, it fell a distance equal to the average acceleration, which is exactly half, which is 5m. This is because half the time it was going slower than 5 m/s and half the time it was going faster than 5m/s. You can see how it equals out. We'll call this distance 1 block/rectangle/square/ whatever.
Now, in the second second, the object is already going 10m/s (even though it has traveled only 5m). Therefore, it will cover AT LEAST 10m more. It will accelerate from 10m/s to 20m/s, meaning its average velocity will be right smack dab in the middle: 15m/s. So therefore it will cover 15 more meters in this time.
How far has the bad bitch gone in these two seconds? 20m. thats a total of four times what it traveled the first second. Wow! it has conquered 1 hurdle in the first second but 4 hurdles in the first two seconds! that means its accumulating hurtles a lot faster w/ each passing second, and they continue to build up.
The same thing happens with kinetic energy hurtles that are accumulated by speed as it increases. Just turn the analogy (above) on its side, and you see that speeds that are increasing are not just gaining more steam as they go faster, they are hording and collecting the energy from the speeds they had before, which were naturally not as potent at the speeds they just gained.
Also, doubling a larger speed does not change your speed by the same amount as doubling a smaller speed. Doubling from 5 to 10mph changes your speed by 5. Doubling again from 10 to 20 changes your speed by 10. (This is just to kind of get a feel of the concept)
(cont)
Xavier Myers
(Cont)
So: a car starts out and has conquered 1 hurdle of KE at 5mph. doubling the speed doesn't erase this conquered hurdle, but effectively adds 3 more as the KE's smoothly transition through the averages. Therefore the total is 4 hurdles conquered by the time it reaches 10mph.
Liam Mitchell
The first answer here is the best treatment of this question I've ever seen.