The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N...
Problem :
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N The magnitude of the two forces are
(a) 13,5
(b) 12,5
(c) 14,4
(d) 11,7
My approach :
We can take two forces as $|P| ; |Q|$ as per the given condition
$|P| +|Q| =18N $ ( sum of two forces) ; $ |R| = |P+Q| = 12 N $
angle formed by smaller force is at $90^{circ}$.. Please suggest how to go further from here... thanks..
vector-spaces
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
add a comment |
Problem :
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N The magnitude of the two forces are
(a) 13,5
(b) 12,5
(c) 14,4
(d) 11,7
My approach :
We can take two forces as $|P| ; |Q|$ as per the given condition
$|P| +|Q| =18N $ ( sum of two forces) ; $ |R| = |P+Q| = 12 N $
angle formed by smaller force is at $90^{circ}$.. Please suggest how to go further from here... thanks..
vector-spaces
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
This problem is poorly worded. It sounds like the forces are supposed to be vectors but the problem begins "The sum of two forces is 18 N", which is a scalar. In your approach you are interpreting the start of the problem to mean the sum of the magnitudes of the two forces is 18N. I'm blaming the author of the problem, not necessarily you. Fortunately the question is multiple choice so if you get an answer that matches a choice it is likely you interpreted the problem in the intended manner.
– Stefan Smith
Dec 18 '13 at 4:30
You might try converting all the equations and facts you've written down into equations involving dot products: $sqrt{Pcdot P}+sqrt{Qcdot Q}=18$, $(P+Q)cdot(P+Q)=144$, $Pcdot(P+Q)=0$. Then see if you can find some useful algebraic manipulations of these equations.
– Gerry Myerson
Dec 18 '13 at 4:46
add a comment |
Problem :
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N The magnitude of the two forces are
(a) 13,5
(b) 12,5
(c) 14,4
(d) 11,7
My approach :
We can take two forces as $|P| ; |Q|$ as per the given condition
$|P| +|Q| =18N $ ( sum of two forces) ; $ |R| = |P+Q| = 12 N $
angle formed by smaller force is at $90^{circ}$.. Please suggest how to go further from here... thanks..
vector-spaces
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
Problem :
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N The magnitude of the two forces are
(a) 13,5
(b) 12,5
(c) 14,4
(d) 11,7
My approach :
We can take two forces as $|P| ; |Q|$ as per the given condition
$|P| +|Q| =18N $ ( sum of two forces) ; $ |R| = |P+Q| = 12 N $
angle formed by smaller force is at $90^{circ}$.. Please suggest how to go further from here... thanks..
vector-spaces
vector-spaces
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
asked Dec 18 '13 at 4:19
sultansultan
4,302450116
4,302450116
This problem is poorly worded. It sounds like the forces are supposed to be vectors but the problem begins "The sum of two forces is 18 N", which is a scalar. In your approach you are interpreting the start of the problem to mean the sum of the magnitudes of the two forces is 18N. I'm blaming the author of the problem, not necessarily you. Fortunately the question is multiple choice so if you get an answer that matches a choice it is likely you interpreted the problem in the intended manner.
– Stefan Smith
Dec 18 '13 at 4:30
You might try converting all the equations and facts you've written down into equations involving dot products: $sqrt{Pcdot P}+sqrt{Qcdot Q}=18$, $(P+Q)cdot(P+Q)=144$, $Pcdot(P+Q)=0$. Then see if you can find some useful algebraic manipulations of these equations.
– Gerry Myerson
Dec 18 '13 at 4:46
add a comment |
This problem is poorly worded. It sounds like the forces are supposed to be vectors but the problem begins "The sum of two forces is 18 N", which is a scalar. In your approach you are interpreting the start of the problem to mean the sum of the magnitudes of the two forces is 18N. I'm blaming the author of the problem, not necessarily you. Fortunately the question is multiple choice so if you get an answer that matches a choice it is likely you interpreted the problem in the intended manner.
– Stefan Smith
Dec 18 '13 at 4:30
You might try converting all the equations and facts you've written down into equations involving dot products: $sqrt{Pcdot P}+sqrt{Qcdot Q}=18$, $(P+Q)cdot(P+Q)=144$, $Pcdot(P+Q)=0$. Then see if you can find some useful algebraic manipulations of these equations.
– Gerry Myerson
Dec 18 '13 at 4:46
This problem is poorly worded. It sounds like the forces are supposed to be vectors but the problem begins "The sum of two forces is 18 N", which is a scalar. In your approach you are interpreting the start of the problem to mean the sum of the magnitudes of the two forces is 18N. I'm blaming the author of the problem, not necessarily you. Fortunately the question is multiple choice so if you get an answer that matches a choice it is likely you interpreted the problem in the intended manner.
– Stefan Smith
Dec 18 '13 at 4:30
This problem is poorly worded. It sounds like the forces are supposed to be vectors but the problem begins "The sum of two forces is 18 N", which is a scalar. In your approach you are interpreting the start of the problem to mean the sum of the magnitudes of the two forces is 18N. I'm blaming the author of the problem, not necessarily you. Fortunately the question is multiple choice so if you get an answer that matches a choice it is likely you interpreted the problem in the intended manner.
– Stefan Smith
Dec 18 '13 at 4:30
You might try converting all the equations and facts you've written down into equations involving dot products: $sqrt{Pcdot P}+sqrt{Qcdot Q}=18$, $(P+Q)cdot(P+Q)=144$, $Pcdot(P+Q)=0$. Then see if you can find some useful algebraic manipulations of these equations.
– Gerry Myerson
Dec 18 '13 at 4:46
You might try converting all the equations and facts you've written down into equations involving dot products: $sqrt{Pcdot P}+sqrt{Qcdot Q}=18$, $(P+Q)cdot(P+Q)=144$, $Pcdot(P+Q)=0$. Then see if you can find some useful algebraic manipulations of these equations.
– Gerry Myerson
Dec 18 '13 at 4:46
add a comment |
1 Answer
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I agree the problem is poorly worded. the two forces are $F1$ and $F2$. The vector labeled Sum is their sum. We have $|F2|^2=|Sum|^2+|F2|^2=144+|F1|^2$ and I believe you are supposed to assume $|F1|+|F2|=18$ with solution $|F1|=13,|F2|=5$
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
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oldest
votes
active
oldest
votes
I agree the problem is poorly worded. the two forces are $F1$ and $F2$. The vector labeled Sum is their sum. We have $|F2|^2=|Sum|^2+|F2|^2=144+|F1|^2$ and I believe you are supposed to assume $|F1|+|F2|=18$ with solution $|F1|=13,|F2|=5$
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
add a comment |
I agree the problem is poorly worded. the two forces are $F1$ and $F2$. The vector labeled Sum is their sum. We have $|F2|^2=|Sum|^2+|F2|^2=144+|F1|^2$ and I believe you are supposed to assume $|F1|+|F2|=18$ with solution $|F1|=13,|F2|=5$
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
add a comment |
I agree the problem is poorly worded. the two forces are $F1$ and $F2$. The vector labeled Sum is their sum. We have $|F2|^2=|Sum|^2+|F2|^2=144+|F1|^2$ and I believe you are supposed to assume $|F1|+|F2|=18$ with solution $|F1|=13,|F2|=5$
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
I agree the problem is poorly worded. the two forces are $F1$ and $F2$. The vector labeled Sum is their sum. We have $|F2|^2=|Sum|^2+|F2|^2=144+|F1|^2$ and I believe you are supposed to assume $|F1|+|F2|=18$ with solution $|F1|=13,|F2|=5$
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
answered Dec 18 '13 at 5:10
Ross MillikanRoss Millikan
292k23197371
292k23197371
add a comment |
add a comment |
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This problem is poorly worded. It sounds like the forces are supposed to be vectors but the problem begins "The sum of two forces is 18 N", which is a scalar. In your approach you are interpreting the start of the problem to mean the sum of the magnitudes of the two forces is 18N. I'm blaming the author of the problem, not necessarily you. Fortunately the question is multiple choice so if you get an answer that matches a choice it is likely you interpreted the problem in the intended manner.
– Stefan Smith
Dec 18 '13 at 4:30
You might try converting all the equations and facts you've written down into equations involving dot products: $sqrt{Pcdot P}+sqrt{Qcdot Q}=18$, $(P+Q)cdot(P+Q)=144$, $Pcdot(P+Q)=0$. Then see if you can find some useful algebraic manipulations of these equations.
– Gerry Myerson
Dec 18 '13 at 4:46