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October 31st, 2017, 09:31 AM   #1
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Calculate mass along thread (line-integral)



I've tried to solve this 4 times already, what am I doing wrong?
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October 31st, 2017, 09:41 AM   #2
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You're doing it wrong :P

There's no force here to dot with $dr$

You just have to calculate the differential length along the string and multiply it by the density. I.e.

$m = \displaystyle \int_0^1 ~(1+t)\left\|\dfrac{dr}{dt}\right \|~dt$

see if you can chug through the integral.
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October 31st, 2017, 11:44 AM   #3
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integral of (1+t)sqrt(9 + 36t + 36t^2) ?

**** me this is the second exercise in this subject, doing mega complex integrals is not part of the course.

Is there a simpler way?
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October 31st, 2017, 12:03 PM   #4
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Quote:
Originally Posted by Addez123 View Post
integral of (1+t)sqrt(9 + 36t + 36t^2) ?

**** me this is the second exercise in this subject, doing mega complex integrals is not part of the course.

Is there a simpler way?
$\left\| \dfrac{dr}{dt} \right \| = \sqrt{9+36t^2 + 36t^4} = 3+6t^2,~t \in [0,1]$
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