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Calc III:
Determine how much work was done by an object in moving along an arc of the cycloid given by:
Image attached
 one year ago
 one year ago
Calc III: Determine how much work was done by an object in moving along an arc of the cycloid given by: Image attached
 one year ago
 one year ago

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calcIIIstudentBest ResponseYou've already chosen the best response.0
I'm completely lost on this one, I don't even know what formula to use.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1344456883598:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1344456975045:dw change everything into t's ... since parameter is given, it should be easy to find it.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
the other method, ... check if the field is conservative or not, if the field is conservative, the difference in the potential should give you the work done.
 one year ago

calcIIIstudentBest ResponseYou've already chosen the best response.0
Well, the field is conservative, and the parameter is 0 to pi, but what I'm not understanding is what to do with the F*dr
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
for a conservative field, dw:1344457305326:dw isn't this definition of conservative field?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1344457452297:dw moreover F = div V
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
\[\int\limits_C\vec F\cdot d\vec r=\int_a^b\vec F(\vec r(t))\cdot\vec r'(t)dt\]I don't see where you need \(\nabla f\) in this problem...
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
so this is going to involve the fundamental theorem for line integrals
 one year ago

calcIIIstudentBest ResponseYou've already chosen the best response.0
Also this is a friend of mines test result (I'm studying for finals) and I have no idea what she did.
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
\[\int\limits_C\nabla f\cdot d\vec r=f(\vec r(b))f(\vec r(a))\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
she did what i suggested ... first find the curl of field (to make sure that it is conservative) though it isn't necessary.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
if the field is conservative, and you know the potential ... the line integral of Field along the path (or so called work done in physics) = change in potential ...
 one year ago

calcIIIstudentBest ResponseYou've already chosen the best response.0
If finding the curl wasn't necessary, then where did she get these numbers from?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1344458019983:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1344458032365:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1344458052253:dw use those values of t's ... and find the x coordinate and y coordinate. at t=0 and t=pi
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
Work is defined as\[W=\int\limits_C\vec F\cdot d\vec r=\int\limits_C\nabla f\cdot d\vec r=f(\vec r(b))f(\vec r(a))\]the potential function for the conservative vector field is\[f=\frac13x^3+\frac13y^3\]and the line is\[\vec r(t)=\langle3(t\sin t),3(1\cos t),\rangle\]we have\[\vec r(\pi)=\langle3\pi,6\rangle\]\[\vec r(0)=\langle0,0\rangle\]
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
so\[W=\int\limits_C\vec F\cdot d\vec r=\int\limits_C\nabla f\cdot d\vec r=f(\vec r(\pi))f(\vec r(0))\]\[\left(\frac13(3\pi)^3+\frac136^3\right)0=9\pi^3+72\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
this way is super easy ... if you are preparing for finals ... try to work on both methods.
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
yes, always learn more than one way when possible !
 one year ago

colorfulBest ResponseYou've already chosen the best response.2
btw when I said "work is defined as" I only meant the first part of the expression\[W=\int\limits_C\vec F\cdot d\vec r\]the next part only follows if the force \(\vec F\) is conservative:\[W=\int\limits_C\vec F\cdot d\vec r=\int\limits_C\nabla f\cdot d\vec r=f(\vec r(b))f(\vec r(a))\]
 one year ago

calcIIIstudentBest ResponseYou've already chosen the best response.0
Sorry, my internet crashed. But yeah, that pretty much summed up all my questions. Thanks!
 one year ago
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