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calcIIIstudent
Group Title
Calc III:
Determine how much work was done by an object in moving along an arc of the cycloid given by:
Image attached
 2 years ago
 2 years ago
calcIIIstudent Group Title
Calc III: Determine how much work was done by an object in moving along an arc of the cycloid given by: Image attached
 2 years ago
 2 years ago

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calcIIIstudent Group TitleBest ResponseYou've already chosen the best response.0
I'm completely lost on this one, I don't even know what formula to use.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1344456883598:dw
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

calcIIIstudent Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
for a conservative field, dw:1344457305326:dw isn't this definition of conservative field?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1344457452297:dw moreover F = div V
 2 years ago

colorful Group TitleBest 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...
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.2
so this is going to involve the fundamental theorem for line integrals
 2 years ago

calcIIIstudent Group TitleBest 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.
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.2
\[\int\limits_C\nabla f\cdot d\vec r=f(\vec r(b))f(\vec r(a))\]
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

experimentX Group TitleBest 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 ...
 2 years ago

calcIIIstudent Group TitleBest ResponseYou've already chosen the best response.0
If finding the curl wasn't necessary, then where did she get these numbers from?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1344458019983:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1344458032365:dw
 2 years ago

experimentX Group TitleBest 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
 2 years ago

colorful Group TitleBest 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\[\vec r(\pi)=\langle3\pi,6\rangle\]\[\vec r(0)=\langle0,0\rangle\]
 2 years ago

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

colorful Group TitleBest ResponseYou've already chosen the best response.2
questions?
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.2
yes, always learn more than one way when possible !
 2 years ago

colorful Group TitleBest 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:\[W=\int\limits_C\vec F\cdot d\vec r=\int\limits_C\nabla f\cdot d\vec r=f(\vec r(b))f(\vec r(a))\]
 2 years ago

calcIIIstudent Group TitleBest ResponseYou've already chosen the best response.0
Sorry, my internet crashed. But yeah, that pretty much summed up all my questions. Thanks!
 2 years ago
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