Timeline for Problem with an exercise: position and velocity of a thrown sphere with non uniform acceleration
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2015 at 23:28 | comment | added | Imago | @Floris, I begin to make the connection, though I guess I am still a good way away from understanding. I try to get the way to formulas, that describe $ v_i $ , i = 1,2,3,4,5 with: $ 0 < v_1 < v_2 = v_{firstcosmicvelocity} < v_3 < v_4 = v_{secondcosmicvelocity} < v_5 $ Also find out the position x of the sphere at a given time t. So far I can follow MonkeysUncle's post to the end, but I find it hard to completely "nail" the problem.. so that I could say that I understood everything. At least now I know how the sphere "behaves" for a given $v_i$ ... | |
| Feb 24, 2015 at 23:16 | comment | added | Floris | @Imago - isn't that the problem you are trying to solve? Motion of an object in an inverse square law field? The link gives the (very messy) inverse of the equation that MonkeysUncle derived - namely, $y(t)$; as such I thought it complemented the answer given here nicely. | |
| Feb 24, 2015 at 20:16 | comment | added | Imago | @Floris, I fail to see what the inverse square law gravitational field has to do with my problem or how it takes MonkeysUncle's answer any further. May elaborate? | |
| Feb 24, 2015 at 19:21 | comment | added | Floris | See also en.wikipedia.org/wiki/… | |
| Feb 24, 2015 at 15:53 | comment | added | Imago | Ah, yes, that makes sense. I just try to get a better understanding of those matters, what happens for $v_1 $ to $v_5$, namely : $0 < v_1 < v_{firstcosmicvelocity} = v_2 < v_3 < v_4 = v_{secondcosmicvelocity} < v_5 $ I find it just difficult to get proper material as one can't even find something good on the internet. Most materials just cover the very basics, but as soon as one wants to get a better understanding, those materials fail :/ | |
| Feb 24, 2015 at 15:33 | comment | added | MonkeysUncle | You get those by plugging in the initial conditions. When $C_1$ pops up, plug in $v(0)$ and $x(0)$ to find it's value. In the final expression, plug in $t=0$ and $x(0)$ to find $C_2$. If you don't know a numerical value for $v_0$, just keep it as $v_0$ and you get a $C_1$ value that depends on initial velocity. Just make sure to include that the most general solution can't have $v_0=v_{esc}$, because that changes the last differential equation you have to solve. | |
| Feb 24, 2015 at 15:26 | vote | accept | Imago | ||
| Mar 3, 2015 at 17:42 | |||||
| Feb 24, 2015 at 15:17 | comment | added | Imago | Thank you a lot. I could follow all your steps, though I wonder, how one should handle $ C_1 $ and $ C_2 $. Do they have a certain value? If yes, which one and how would you get those? | |
| Feb 24, 2015 at 14:48 | history | answered | MonkeysUncle | CC BY-SA 3.0 |