3 ms·

>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 e

>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?

hughes 10y ago
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.
craigds 10y ago
Thats correct, it actually does. Somewhat counterintuitively. Some explanation at https://www.reddit.com/r/askscience/comments/40bi9z/why_is_the_amount_of_work_required_to_accelerate/ https://www.reddit.com/r/askscience/comments/40bi9z/why_is_t...
noonespecial 10y ago
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?
Retric 10y ago
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.
Double_Cast 10y ago
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.

hughes 10y ago

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.

craigds 10y ago

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

noonespecial 10y ago

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?

Retric 10y ago

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.

Double_Cast 10y ago

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.