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I've been pondering this today. Say you have a moving vehicle, with enough space to move around in (say, an empty moving truck). How fast would it have to be going for you to jump and go flying across it, like falling?

I thought I'd start with an effect similar to gravity, so using F=ma & F=.5mv^2 and equating them you get 2a = v^2. But subbing in for a and resolving for v gives ~4.4ms^-2 or just under 10mph. This seems a little on the small side, so I guess my questions are:

How fast would you actually need to be going to get a similar effect? And what did I do wrong?

Cheers.

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  • $\begingroup$ What? If you are inside a moving truck, you are moving with the same velocity as the truck. You can't jump in the air and fly across it unless it is accelerating quite fast. You don't really want that. $\endgroup$
    – ACuriousMind ♦
    Commented Mar 23, 2015 at 16:53
  • $\begingroup$ Your calculations are wrong (you set force=energy, which is like saying "my clock reads five meters" - it doesn't make sense!) And your units are incorrect (your speed is a measure of acceleration). Are you expectong someone to fly towards the back of a moving truck when they jump? This is incorrect! If you jump on an airplane you notice nothing special different than jumping on the ground. $\endgroup$
    – user12029
    Commented Mar 23, 2015 at 16:55
  • $\begingroup$ ... Well that explains a lot. Dumb moment, thanks guys. $\endgroup$
    – Overt_Agent
    Commented Mar 23, 2015 at 16:56
  • $\begingroup$ @niallmcfc been there...done that...keep on asking..only way to find out all the best $\endgroup$
    – user74893
    Commented Mar 23, 2015 at 17:39
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    $\begingroup$ @NeuroFuzzy but my clock does read 5 meters.... <.< $\endgroup$
    – Jim
    Commented Mar 24, 2015 at 18:26

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You will not "fly" inside the vehicle unless it is accelerated (and even then you will simply be pushed to the back unless the vehicle acclerates very quickly and by a huge amount). This is actually the (Gallilean) principle of relativity: a state of rest is indistinguishable from a state of constant velocity motion by the observer who is moving/ stationary. There is no absolute motion.

In regards to your question, the vehicle would have to accelerate at about 9.807 m/s^2 for you to experience a "fake gravity" effect (directed opposite the motion of the car) equivalent to that experienced towards the center of the Earth. This is the principle of equivalence that was used by Einstein to formulate GR. But if the acceleration is 0, you will stay where you are inside the vehicle, as your body is also moving at the same velocity as the vehicle. You will "feel" that you are at rest. The only way you can "fly" inside is if the vehicle is undergoing acceleration (which is quite absolute), which your body will resist (inertia) and you will be pushed behind. As to where you went wrong, I have no idea where v came from in your equation. The force equals to the rate of change of momentum, that is $$F=\frac{dmv}{dt}=m\frac {dv}{dt}=ma$$ (I've used the classical assumption that mass stays constant for simplicity) As you can clearly see, the magnitude of the velocity in itself has no impact on the force.

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