If work is given by the $1$-form $3dx+4dy-dz$, find all points that can be reached from the origin without...
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I have no idea how to approach this question. There's no mention of how "work" functions in my notes.
As an attempt I listed the points $$(pm3, pm4,pm1)$$ but it's a guess.
differential-forms
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
asked Dec 13 '18 at 16:34
JamesJames
154
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closed as unclear what you're asking by amWhy, BigbearZzz, Rebellos, platty, KReiser Dec 14 '18 at 2:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
I have no idea how to approach this question. There's no mention of how "work" functions in my notes.
As an attempt I listed the points $$(pm3, pm4,pm1)$$ but it's a guess.
differential-forms
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
asked Dec 13 '18 at 16:34
JamesJames
154
$endgroup$
closed as unclear what you're asking by amWhy, BigbearZzz, Rebellos, platty, KReiser Dec 14 '18 at 2:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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Work is a product of force and displacement. So I am guessing you're supposed to find out points where it integrates back to $0$. Also please use MathJax in the title, as without it there is very limited amount of help you'll get
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– Sauhard Sharma
Dec 13 '18 at 16:47
add a comment |
$begingroup$
I have no idea how to approach this question. There's no mention of how "work" functions in my notes.
As an attempt I listed the points $$(pm3, pm4,pm1)$$ but it's a guess.
differential-forms
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
asked Dec 13 '18 at 16:34
JamesJames
154
$endgroup$
I have no idea how to approach this question. There's no mention of how "work" functions in my notes.
As an attempt I listed the points $$(pm3, pm4,pm1)$$ but it's a guess.
differential-forms
differential-forms
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
asked Dec 13 '18 at 16:34
JamesJames
154
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
asked Dec 13 '18 at 16:34
JamesJames
154
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
edited Dec 13 '18 at 17:13
Shubham Johri
4,666717
4,666717
asked Dec 13 '18 at 16:34
JamesJames
154
asked Dec 13 '18 at 16:34
JamesJames
154
asked Dec 13 '18 at 16:34
JamesJames
154
154
closed as unclear what you're asking by amWhy, BigbearZzz, Rebellos, platty, KReiser Dec 14 '18 at 2:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by amWhy, BigbearZzz, Rebellos, platty, KReiser Dec 14 '18 at 2:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Work is a product of force and displacement. So I am guessing you're supposed to find out points where it integrates back to $0$. Also please use MathJax in the title, as without it there is very limited amount of help you'll get
$endgroup$
– Sauhard Sharma
Dec 13 '18 at 16:47
add a comment |
$begingroup$
Work is a product of force and displacement. So I am guessing you're supposed to find out points where it integrates back to $0$. Also please use MathJax in the title, as without it there is very limited amount of help you'll get
$endgroup$
– Sauhard Sharma
Dec 13 '18 at 16:47
$begingroup$
Work is a product of force and displacement. So I am guessing you're supposed to find out points where it integrates back to $0$. Also please use MathJax in the title, as without it there is very limited amount of help you'll get
$endgroup$
– Sauhard Sharma
Dec 13 '18 at 16:47
$begingroup$
Work is a product of force and displacement. So I am guessing you're supposed to find out points where it integrates back to $0$. Also please use MathJax in the title, as without it there is very limited amount of help you'll get
$endgroup$
– Sauhard Sharma
Dec 13 '18 at 16:47
add a comment |
1 Answer
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active
oldest
votes
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HINT: You want points $P$ so that $int_0^P 3,dx+4,dy-dz = 0$. Note first that the integral is path-independent. Why? Indeed, you can find a function $f$ so that $df = 3,dx+4,dy-dz$, and then the integral is equal to $f(P)-f(0)$.
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
HINT: You want points $P$ so that $int_0^P 3,dx+4,dy-dz = 0$. Note first that the integral is path-independent. Why? Indeed, you can find a function $f$ so that $df = 3,dx+4,dy-dz$, and then the integral is equal to $f(P)-f(0)$.
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
$endgroup$
add a comment |
$begingroup$
HINT: You want points $P$ so that $int_0^P 3,dx+4,dy-dz = 0$. Note first that the integral is path-independent. Why? Indeed, you can find a function $f$ so that $df = 3,dx+4,dy-dz$, and then the integral is equal to $f(P)-f(0)$.
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
$endgroup$
add a comment |
$begingroup$
HINT: You want points $P$ so that $int_0^P 3,dx+4,dy-dz = 0$. Note first that the integral is path-independent. Why? Indeed, you can find a function $f$ so that $df = 3,dx+4,dy-dz$, and then the integral is equal to $f(P)-f(0)$.
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
$endgroup$
HINT: You want points $P$ so that $int_0^P 3,dx+4,dy-dz = 0$. Note first that the integral is path-independent. Why? Indeed, you can find a function $f$ so that $df = 3,dx+4,dy-dz$, and then the integral is equal to $f(P)-f(0)$.
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
answered Dec 13 '18 at 17:50
Ted ShifrinTed Shifrin
63.1k44489
63.1k44489
add a comment |
add a comment |
$begingroup$
Work is a product of force and displacement. So I am guessing you're supposed to find out points where it integrates back to $0$. Also please use MathJax in the title, as without it there is very limited amount of help you'll get
$endgroup$
– Sauhard Sharma
Dec 13 '18 at 16:47