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Comment by andrewla | Hacker News Reader

My intuition rings false on this -- I don't think this is right. In a vacuum, ignoring the rocket equation (that is, assuming ejected reaction mass is negligible compared to projectile mass), the energy required to produce the 120 -> 96 mph change is the same as that required to go from 24 -> 0. This works out in conservation of energy because the ejected mass has kinetic energy of its own.

In the case of you landing, I don't think energy balance is the way to look at it; each of the collisions that slows you down will transfer some energy to the ground. In terms of force, the force is dependent only on the acceleration, so it comes down to how long each impact lasts. If each "bounce" or "thud" lasts the same amount of time (I don't know if this is realistic) then each one will transfer 1/5th of the force, as the article says.

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Your intuition is wrong.

Potential energy is linear with height. AKA it takes the same energy to climb from floor 1 to 2 as 2 to 3.

Gravity is 32 feet per second per second aka you gain speed over time. In a vacuum 0 to 32 feet per second takes 1 second, 32 to 64 feet per second takes 1 seconds, 64 to 96 takes 1 second etc.

However, in the first second you fall 16 feet. in the next second you fall 38 feet because you where falling at the start of that second. Thus, it takes more energy to increase your speed.

PS: What's confusing about rockets, is your fuel has momentum. So, when use it your consuming the energy it took to get that fuel up to speed with you. Further, at low speed most of the energy goes into the exhaust not the rocket.

>However, in the first second you fall 16 feet. in the next second you fall 38 feet because you where falling at the start of that second. Thus, it takes more energy to increase your speed...

Doesn't make sense. Care to explain? Are you saying it takes less energy to take an object from 0 to 10m/s than it requires to take it from 10m/s to 20m/s?

That's exactly correct. Consider the equation for kinetic energy:

    E = 1/2 m*v^2

The energy to go from 0-10 m/s is the difference in this value (for 1kg e.g.):

    dE = E1 - E0 = 1/2(10^2) - 1/2(0^2) = 50J

To go from 10m/s to 20m/s:

    dE = E2 - E1 = 1/2(20^2) - 1/2(10^2) = 200 - 50 = 150J

In fact by solving for velocity you can figure out what happens if you put another 50J into your object that's already going 10m/s:

    v = sqrt(2*E) = sqrt(200) = 14.1m/s

When you double the energy, you only get 1.4 times the speed.

Uhh, that's just what happens it does not need to make sense.

You can find plenty of examples but that's about it. Ex: You hold a gun in your hand and shoot it, the gun kicks back because momentum is concerved. But, the bullet is a lot more dangerous than the gun because while it has the same momentum it's got a lot more energy. Now, it hits a bullet proof vest. The vest still hits the person wearing the vest but because it obsorbed the energy it feels like a strong punch instead of making a hole in them.

Suppose a 10 m/s gust of solar-wind accelerates a space-balloon from 0 m/s to 10 m/s. And suppose I want to further accelerate the balloon from 10 m/s to 20 m/s.

A second gust at 10 m/s is NOT enough to further accelerate the balloon to 20 m/s. Because the wind and the balloon are now travelling at the same speed. It follows intuitively that the second gust should contain more kinetic energy than the first gust.

Thats correct, it actually does. Somewhat counterintuitively. Some explanation at https://www.reddit.com/r/askscience/comments/40bi9z/why_is_t...

It makes more sense to ask "does an object moving 20m/s have more energy than the same object moving 10m/s?" The answer is obviously yes; so how much more?

Since KE = (1/2)mv^2 we can just do the math.

Say m=2 so we're just left looking at the v^2 terms:

120^2 - 96^2 >? 24^2 - 0^2

5184 >? 576

So yes, the KE difference between 120 and 96 is greater than the difference between 24 and 0.

doing the math is seldom enough ;)

*KE == kinetic energy

kinetic energy: "energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes."

in normal person terms: the energy of moving, or ~exercise, in a parallel world :)

The answer is that you gain velocity by shooting rocket fuel out the back. The energy that the fuel loses is proportional to the the square of the speed of the rocket as well, so everything works out fine. The mass of the rocket fuel is small, but it's not negligible, especially considering that kinetic energy is far more concerned with velocity than with mass.

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