20 upvotes, 4 direct replies (showing 4)
View submission: Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
If I am in a spaceship and the ship is accelerating at 1g then that ship needs to expend a large amount of energy to maintain that acceleration.
Stood on the surface of the earth I am still subject to the same acceleration - where does the energy come from to maintain that 1g.
Both are accelerations - one as a result of converting fuel - the other as a consequence of the warping of spacetime by the mass of the earth.
But it seems you get 'something for nothing' once the initial warping of spacetime is achieved - the acceleration is constant.
What am I missing?
Comment by SenorMcNuggets at 20/07/2022 at 15:22 UTC*
38 upvotes, 0 direct replies
The difference lies in the framing of your question, both literally and figuratively. In the frame of the Earth, your mechanical energy is not changing while you stand there.
Sure, you’re experiencing a gravitational force of mg, but if you’re standing still on earth’s surface, it’s because there is an equal and opposite normal force pushing back up. You are not accelerating (F = ma = N - mg = 0).
So the initial question is a bit off base, but let’s try and change the comparison.
If we instead reframe your question such that you are *falling* near earth’s surface, then we get that acceleration of 1g (ignoring air resistance), by removing that normal force (F = ma = -mg). In this case there is a shift of energy. Just like the rocket is taking chemical potential energy and turning it into kinetic energy, as you fall, gravitational potential energy is being converted into kinetic energy.
Comment by SonOfOnett at 20/07/2022 at 15:35 UTC
12 upvotes, 2 direct replies
Adding to what the other commenter says and regarding your “something for nothing” intuition:
Consider that once the object has fallen to the surface of the earth and is no longer accelerating (because the net force on it is zero) that it has “used up” its gravitational potential energy, or “used up” its fuel in your other example. You’d need to raise it back up above the surface to “refuel it with potential energy”
Comment by xi_jin_penis at 21/07/2022 at 00:19 UTC
0 upvotes, 0 direct replies
You can have arbitrarily large forces/acceleration with no change in energy, I used to have the same misconception that energy was the ability to cause a force, it isn't. It is when you have a non-zero net force on an object in which the energy of the object changes. In a rocket, chemical energy is converted into thermal energy, leaving really hot gasses that are very high pressure. The rocket accelerates forwards because the gasses accelerate backwards, ie the gasses lose KE, and so the rocket must gain KE. We are only able to consider that there is a change in energy because we consider the exhaust gasses and rocket to be distinct objects, it would be impossible to have a lone object experience a net force, due to newton's third law. A person on earth is being pushed away from the earth as much as they are being pulled towards it, so the net force is zero, so the persons energy is constant
Comment by RudeHero at 21/07/2022 at 01:29 UTC
0 upvotes, 0 direct replies
i believe you're confusing energy with force
that's where your overall confusion stems from. energy and force are entirely different concepts