4 ms·

> 120 divided by 5 = 24. Not bad! 24 mph is only a bit faster than the speed at which experienced parachutists land. This is of course being a little silly, bu

by sfeng 10y ago

> 120 divided by 5 = 24. Not bad! 24 mph is only a bit faster than the speed at which experienced parachutists land. This is of course being a little silly, but it does get the physics wrong. Your energy is proportional to the square of your speed, so you have 25x more energy to dissipate at 120 mph, not 5x. Even if your five point landing was perfect, each of the five 'hits' is the equivalent of a landing at just under 60 mph, not 24.

andrewla 10y ago
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.
- Retric 10y ago
  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.
  - babyrainbow 10y ago
    >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.
- nananonymous 10y ago
  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.
  - q_revert 10y ago
    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 :)
- ouid 10y ago
  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.
mathattack 10y ago
The article is humor. Let's not get too technical on the math. Of course you're going to be a pancake if you hit the earth at 120mph, even if you find a way to split the damage 120 ways.

by sfeng 10y ago

andrewla 10y ago

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.

Retric 10y ago
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.
- babyrainbow 10y ago
  >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.
nananonymous 10y ago
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.
- q_revert 10y ago
  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 :)
ouid 10y ago
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.

mathattack 10y ago

The article is humor. Let's not get too technical on the math. Of course you're going to be a pancake if you hit the earth at 120mph, even if you find a way to split the damage 120 ways.