Center of Mass of an L-shaped object!?
-1
$begingroup$
We have a square with side $A$ and we remove from one of its corners a square with side $Blt A$.
Questions:
1) What is the center of mass of this object?
2)What is the ratio of B/A such that the center of mass is inside the object?
(we need to use the formula with the integrals $$Ycm = frac{int ydm}{int dm}$$ and $$Xcm = frac{int xdm}{int dm}$$)
It was a question in a test I had recently at the university and it puzzled many people, myself included and I want to know the solution to it.
Thank you for your help!
euclidean-geometry physics
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
$endgroup$
add a comment |
-1
$begingroup$
We have a square with side $A$ and we remove from one of its corners a square with side $Blt A$.
Questions:
1) What is the center of mass of this object?
2)What is the ratio of B/A such that the center of mass is inside the object?
(we need to use the formula with the integrals $$Ycm = frac{int ydm}{int dm}$$ and $$Xcm = frac{int xdm}{int dm}$$)
It was a question in a test I had recently at the university and it puzzled many people, myself included and I want to know the solution to it.
Thank you for your help!
euclidean-geometry physics
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
$endgroup$
$begingroup$
I forgot to edit something and it appeared as a simple sentence.
$endgroup$
– Negafilms Origins
Jan 1 at 14:36
$begingroup$
Can downvoters please (i} give their reasons (ii) give the questioner a chance to fix any problems (iii) remind themselves what the code of conduct says about new contributors? Thanks.
$endgroup$
– timtfj
Jan 1 at 15:38
$begingroup$
I think you're going need to put a bit more background in (your own thoughts on it or the thoughts that came up among your puzzled ckassmates, for a start.) And make it clear how the question is primarily about maths rather than physics. (Physics itself is considered off-topic, but maths used in physics can be on-topic.)
$endgroup$
– timtfj
Jan 1 at 15:44
$begingroup$
This problem is primarily about the math involved and clever and insightful thinking (like math), rather than the physics used, which is basic level and not that complicated to need explaining. The knowledge needed is a simple formula for density and Euclidean geometry. So I don't really consider it to be off-topic.
$endgroup$
– Negafilms Origins
Jan 1 at 16:17
$begingroup$
I completely agree, but there's a tendency for "physics questions" to get a negative reaction despite really being maths questions. In this case I'd try treating the removed square as an object with negative mass, so you've still got two squares.
$endgroup$
– timtfj
Jan 1 at 16:33
add a comment |
-1
-1
-1
0
$begingroup$
We have a square with side $A$ and we remove from one of its corners a square with side $Blt A$.
Questions:
1) What is the center of mass of this object?
2)What is the ratio of B/A such that the center of mass is inside the object?
(we need to use the formula with the integrals $$Ycm = frac{int ydm}{int dm}$$ and $$Xcm = frac{int xdm}{int dm}$$)
It was a question in a test I had recently at the university and it puzzled many people, myself included and I want to know the solution to it.
Thank you for your help!
euclidean-geometry physics
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
$endgroup$
We have a square with side $A$ and we remove from one of its corners a square with side $Blt A$.
Questions:
1) What is the center of mass of this object?
2)What is the ratio of B/A such that the center of mass is inside the object?
(we need to use the formula with the integrals $$Ycm = frac{int ydm}{int dm}$$ and $$Xcm = frac{int xdm}{int dm}$$)
It was a question in a test I had recently at the university and it puzzled many people, myself included and I want to know the solution to it.
Thank you for your help!
euclidean-geometry physics
euclidean-geometry physics
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
edited Jan 1 at 16:17
Negafilms Origins
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
asked Jan 1 at 14:28
Negafilms OriginsNegafilms Origins
164
164
$begingroup$
I forgot to edit something and it appeared as a simple sentence.
$endgroup$
– Negafilms Origins
Jan 1 at 14:36
$begingroup$
Can downvoters please (i} give their reasons (ii) give the questioner a chance to fix any problems (iii) remind themselves what the code of conduct says about new contributors? Thanks.
$endgroup$
– timtfj
Jan 1 at 15:38
$begingroup$
I think you're going need to put a bit more background in (your own thoughts on it or the thoughts that came up among your puzzled ckassmates, for a start.) And make it clear how the question is primarily about maths rather than physics. (Physics itself is considered off-topic, but maths used in physics can be on-topic.)
$endgroup$
– timtfj
Jan 1 at 15:44
$begingroup$
This problem is primarily about the math involved and clever and insightful thinking (like math), rather than the physics used, which is basic level and not that complicated to need explaining. The knowledge needed is a simple formula for density and Euclidean geometry. So I don't really consider it to be off-topic.
$endgroup$
– Negafilms Origins
Jan 1 at 16:17
$begingroup$
I completely agree, but there's a tendency for "physics questions" to get a negative reaction despite really being maths questions. In this case I'd try treating the removed square as an object with negative mass, so you've still got two squares.
$endgroup$
– timtfj
Jan 1 at 16:33
add a comment |
$begingroup$
I forgot to edit something and it appeared as a simple sentence.
$endgroup$
– Negafilms Origins
Jan 1 at 14:36
$begingroup$
Can downvoters please (i} give their reasons (ii) give the questioner a chance to fix any problems (iii) remind themselves what the code of conduct says about new contributors? Thanks.
$endgroup$
– timtfj
Jan 1 at 15:38
$begingroup$
I think you're going need to put a bit more background in (your own thoughts on it or the thoughts that came up among your puzzled ckassmates, for a start.) And make it clear how the question is primarily about maths rather than physics. (Physics itself is considered off-topic, but maths used in physics can be on-topic.)
$endgroup$
– timtfj
Jan 1 at 15:44
$begingroup$
This problem is primarily about the math involved and clever and insightful thinking (like math), rather than the physics used, which is basic level and not that complicated to need explaining. The knowledge needed is a simple formula for density and Euclidean geometry. So I don't really consider it to be off-topic.
$endgroup$
– Negafilms Origins
Jan 1 at 16:17
$begingroup$
I completely agree, but there's a tendency for "physics questions" to get a negative reaction despite really being maths questions. In this case I'd try treating the removed square as an object with negative mass, so you've still got two squares.
$endgroup$
– timtfj
Jan 1 at 16:33
$begingroup$
I forgot to edit something and it appeared as a simple sentence.
$endgroup$
– Negafilms Origins
Jan 1 at 14:36
$begingroup$
I forgot to edit something and it appeared as a simple sentence.
$endgroup$
– Negafilms Origins
Jan 1 at 14:36
$begingroup$
Can downvoters please (i} give their reasons (ii) give the questioner a chance to fix any problems (iii) remind themselves what the code of conduct says about new contributors? Thanks.
$endgroup$
– timtfj
Jan 1 at 15:38
$begingroup$
Can downvoters please (i} give their reasons (ii) give the questioner a chance to fix any problems (iii) remind themselves what the code of conduct says about new contributors? Thanks.
$endgroup$
– timtfj
Jan 1 at 15:38
$begingroup$
I think you're going need to put a bit more background in (your own thoughts on it or the thoughts that came up among your puzzled ckassmates, for a start.) And make it clear how the question is primarily about maths rather than physics. (Physics itself is considered off-topic, but maths used in physics can be on-topic.)
$endgroup$
– timtfj
Jan 1 at 15:44
$begingroup$
I think you're going need to put a bit more background in (your own thoughts on it or the thoughts that came up among your puzzled ckassmates, for a start.) And make it clear how the question is primarily about maths rather than physics. (Physics itself is considered off-topic, but maths used in physics can be on-topic.)
$endgroup$
– timtfj
Jan 1 at 15:44
$begingroup$
This problem is primarily about the math involved and clever and insightful thinking (like math), rather than the physics used, which is basic level and not that complicated to need explaining. The knowledge needed is a simple formula for density and Euclidean geometry. So I don't really consider it to be off-topic.
$endgroup$
– Negafilms Origins
Jan 1 at 16:17
$begingroup$
This problem is primarily about the math involved and clever and insightful thinking (like math), rather than the physics used, which is basic level and not that complicated to need explaining. The knowledge needed is a simple formula for density and Euclidean geometry. So I don't really consider it to be off-topic.
$endgroup$
– Negafilms Origins
Jan 1 at 16:17
$begingroup$
I completely agree, but there's a tendency for "physics questions" to get a negative reaction despite really being maths questions. In this case I'd try treating the removed square as an object with negative mass, so you've still got two squares.
$endgroup$
– timtfj
Jan 1 at 16:33
$begingroup$
I completely agree, but there's a tendency for "physics questions" to get a negative reaction despite really being maths questions. In this case I'd try treating the removed square as an object with negative mass, so you've still got two squares.
$endgroup$
– timtfj
Jan 1 at 16:33
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
I don't think the large square has had a small square removed from it. I think it has had a small negative-mass square added to it, and that there are now two squares. So the question is about the combined centre of mass of two nice symmetrical objects, one of which has negative mass.
Being inside the L shape means being inside the large square and outside the small one.
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
$endgroup$
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
add a comment |
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1 Answer
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1 Answer
1
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1
$begingroup$
I don't think the large square has had a small square removed from it. I think it has had a small negative-mass square added to it, and that there are now two squares. So the question is about the combined centre of mass of two nice symmetrical objects, one of which has negative mass.
Being inside the L shape means being inside the large square and outside the small one.
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
$endgroup$
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
add a comment |
1
$begingroup$
I don't think the large square has had a small square removed from it. I think it has had a small negative-mass square added to it, and that there are now two squares. So the question is about the combined centre of mass of two nice symmetrical objects, one of which has negative mass.
Being inside the L shape means being inside the large square and outside the small one.
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
$endgroup$
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
add a comment |
1
1
1
$begingroup$
I don't think the large square has had a small square removed from it. I think it has had a small negative-mass square added to it, and that there are now two squares. So the question is about the combined centre of mass of two nice symmetrical objects, one of which has negative mass.
Being inside the L shape means being inside the large square and outside the small one.
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
$endgroup$
I don't think the large square has had a small square removed from it. I think it has had a small negative-mass square added to it, and that there are now two squares. So the question is about the combined centre of mass of two nice symmetrical objects, one of which has negative mass.
Being inside the L shape means being inside the large square and outside the small one.
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
edited Jan 1 at 16:51
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
answered Jan 1 at 16:44
timtfjtimtfj
2,483420
2,483420
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
add a comment |
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
I understand this logic and I have seen something similar with a circle and it wall well and fine and I understand the solution, but in this particular problem I am stuck. Moreover, from intuition and a trick I learned, the center of mass is in the diagonal of the big square where the square with negative mass exists.
$endgroup$
– Negafilms Origins
Jan 1 at 18:12
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOrigins It doesn't have to be in the small square—if the small one is vanishingly small, the centre of mass will be the centre of the large square. I think you need an expression for the position of the centre of mass on the diagonal, and one for the position of the small square"s innermost corner, as distances from the centre of the large square.
$endgroup$
– timtfj
Jan 1 at 18:25
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
@NegafilmsOriginsThen if the centre of mass is further out than the corner of the small square is, it's inside the small square and outside the L.
$endgroup$
– timtfj
Jan 1 at 18:28
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
$begingroup$
Firstly, I said it is in the diagonal and lastly, what is the math to solve it?
$endgroup$
– Negafilms Origins
Jan 1 at 18:34
add a comment |
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$begingroup$
I forgot to edit something and it appeared as a simple sentence.
$endgroup$
– Negafilms Origins
Jan 1 at 14:36
$begingroup$
Can downvoters please (i} give their reasons (ii) give the questioner a chance to fix any problems (iii) remind themselves what the code of conduct says about new contributors? Thanks.
$endgroup$
– timtfj
Jan 1 at 15:38
$begingroup$
I think you're going need to put a bit more background in (your own thoughts on it or the thoughts that came up among your puzzled ckassmates, for a start.) And make it clear how the question is primarily about maths rather than physics. (Physics itself is considered off-topic, but maths used in physics can be on-topic.)
$endgroup$
– timtfj
Jan 1 at 15:44
$begingroup$
This problem is primarily about the math involved and clever and insightful thinking (like math), rather than the physics used, which is basic level and not that complicated to need explaining. The knowledge needed is a simple formula for density and Euclidean geometry. So I don't really consider it to be off-topic.
$endgroup$
– Negafilms Origins
Jan 1 at 16:17
$begingroup$
I completely agree, but there's a tendency for "physics questions" to get a negative reaction despite really being maths questions. In this case I'd try treating the removed square as an object with negative mass, so you've still got two squares.
$endgroup$
– timtfj
Jan 1 at 16:33