You have a sled on top of a hill where it slides down and continues on flat surface. Part of the flat surface is ice and we assume it has no friction. Otherwise the ground has friction and will slow the sled down.The sled has a rocket booster which, when ignited, will push the sled forward with certain force for a constant amount of time.Here comes a paradox that I've been thinking about. If the rocket is ignited on the point A, the sled is able to slide a longer distance while the rocket is boosting because the ice has no friction. We know that energy is equal to force multiplied by distance, so the sled ends up with more kinetic energy in the option A. But if the rocket is ignited on the point B, now the distance travelled while the rocket is boosting is shorter because the snow has friction unlike the ice. So force multiplied by distance is less than in the option A which means the sled has now less energy.The energy content of the rocket is constant but the sled gains a different amount of energy from the rocket depending on where you ignite it. Am I missing something or does this break physics?
>>17015677Friction dissipates as heat. I'm not sure I understand what the paradox is.
>>17015682In one scenario the sled goes a further distance before coming to a stop compared to the other despite the fact that it used the same amount of energy.
Adding to what is said in >>17015682You should also take a look at the distinction between conservativeand non-conservative forces.
>>17015686Right, and that energy removed by friction is converted to heat.Again, where's the paradox?
>>17015688Doesn't the sled which goes further lose therefore more energy by friction? So the energy lost is not always the same as the initial energy. That's the paradox.
>>17015690Both sleds will go equally far though, because the friction force times distance has to equal the same kinetic energy in both cases.When the rocket is boosting while the sled experiences friction, the force in work = force × distance over a given distance increases.
>>17015690After all, when you push an object with high friction, the force of your push isn't readily apparent from the acceleration and mass of the object.
>>17015677I don't know where you think the paradox is. Working against a static resistive force like sliding friction or gravity can result in lot of seemingly different outcomes depending on how and where the energy is spent. For instance if you had a 2 rockets one which burns for 1g for 10 seconds and one that burns for 2g for 5 seconds (or two of the same 1g 5 second rockets one launched parallel and one in series) both of those have the same amount of force or energy inside of them but only one can actually lift off the ground. It's the same thing in your example. If you use the no friction zone to accelerate you can go further but since sliding friction doesn't work based on distance but time both sleds stop at the same time (counting from when they pass point B). Easily enough to imagine that your sled has speed of say 5 and the rocket can increase the speed by 5 over 5 seconds and the friction then in turn takes away 1 speed every second. Both sleds would stop after the friction applies on them for 10 seconds. The rocket does do more "work" in A than in B but at the same time the friction also does more work in A than it does in B.Rockets "energy content" is measured as their maximum effort, you can always do worse than the maximum by fighting against something like air, gravity or the ground friction in this case.
>>17015677If you use energy at the right time, it's better?
>>17015686>>17015690There's no physical law that says you must go further if you spend more energy.
>>17015677Consider the case where the rocket energy is extremely high and short lived and the "ground friction" has some dynamic characteristics. In this case, the rocket ignited while on the frictionless surface could travel far less distance that the other option. An example of this is boundary differences when a very fast object enters water and tears apart versus the same object slowly speeding up in water. Your hypothetical has significant degenerate cases. I can't address the problem because>problem is in yo head>problem space is ill defined>conditionals are ambiguous
>>17015677You are confusing distance with work gain and loss. There is no force applied at point A when you apply the force at B, therefore you cannot include that distance in the computation of work done. As long as the time the rocket is fired is the same in both scenarios, and the sled comes to a complete stop, AND as long as you add in the energy of the hill, Energy in equals energy out. So if you fire the rocket at A, it will be going faster at B, and will stop applying force earlier, but you include the distance between A and B in your energy computation.If you fire the rocket at B, you cannot include the distance between A and B in your computation of energy, because no force was applied.
>>17015677Well>>17015686what are you talking about? Show your work and prove it.
