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Mechanics 3 Edexcel Intergration question

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Question 6 part B
I cant seem to understand the limits used on the intergration, the boundary conditions are rather vague, "initial speed is 4m/s". Do we just assign this as 0m? does this calculate the relative distance? help pls.

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Reply 1
Avatar for Zacken
Zacken
22
Original post by shehab77
...


If you find this particular method slightly hard to follow, then you can adopt the slightly longer method which is to calculate the general solution.

i.e: we have ∫10000v28000−v3 dv=∫ dx\displaystyle \int \frac{10000v^2}{8000 - v^3} \, \mathrm{d}v = \int \, \mathrm{d}x which gets us x=−10003ln⁡∣8000−v3∣+cx = -\frac{1000}{3} \ln |8000-v^3| + c


Then you use the condition v=4v=4 when t=x=0t=x=0 to find cc. And then you can find xx when v=8v=8.
Reply 2
Avatar for shehab77
shehab77
OP
Thanks a lot! I did that, but dont know where I went wrong. Also you missed a zero in x=-10000/3....
Reply 3
Avatar for Zacken
Zacken
22
Original post by shehab77
Thanks a lot! I did that, but dont know where I went wrong. Also you missed a zero in x=-10000/3....


Wait, are you saying it's sorted now or...? :tongue:

Yeah, I did. Typo on my part.
Original post by shehab77
...


For v:
The limits on v are clear at 4 and 8.

For x:
Since we are looking for relative distance, wherever she starts, she goes a distance D, say.

For ease of computation, we can set our limits as 0 and D, corresponding to the velocities 4 and 8 respectively.

But we're not actually told that x=0 when v=4. We could set the limits to s and s+D, and it would still work.
Reply 5
Avatar for shehab77
shehab77
OP
Original post by Zacken
Wait, are you saying it's sorted now or...? :tongue:

Yeah, I did. Typo on my part.


Yep its sorted!


Original post by ghostwalker
For v:
The limits on v are clear at 4 and 8.

For x:
Since we are looking for relative distance, wherever she starts, she goes a distance D, say.

For ease of computation, we can set our limits as 0 and D, corresponding to the velocities 4 and 8 respectively.

But we're not actually told that x=0 when v=4. We could set the limits to s and s+D, and it would still work.


Relative distance is what I was looking for! Thanks guys! M3 on 18th May, still have complete Statics of rigid bodies chapter to go :colondollar:

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