A key question could be something like, "What properties of vectors did you see in the lab?", and key idea would be that the sum of all forces in our lab would equal out to be zero. Sum of Forces x = 0 = Equilibrium, Sum of Forces y = 0 = Equilibrium, and Sum of all Forces would equal out to be zero as well, causing the ring to stay balanced as we witnessed.
After completing this lab, my group and I discussed the differences between the graphical method and the algebraic method. Obviously both the graphical and algebraic "procedures" work but we realized it came down to "comfort level". For example, I prefer using the algebraic method because i find that getting an equation and then just plugging in numbers is a lot simpler. We discovered that the purpose of this lab is to gain experience in working with vector quantities. The lab involves the demonstration of the process of the addition of several vectors to form a resultant vector. If several forces with different magnitudes and directions act at a point its net effect can be represented by a single resultant force. This resultant force can be found using a special addition process known as vector addition. Rachel Rha
A key idea is that there is more than one method to do this lab. You can do it graphically or algebraically while still getting relatively the same answers. Not only can you do It that way, but there are also different methods within those methods. Lizzie and I both had the same answers but she drew triangles and I solved an equation. This lab also showed how the magnitude and direction of two vectors resulted in a resultant. This lab also proved the ideas that vectors are commutative. It also got us using trig functions. Emma
One of the main things that my group and I found out as we went through the lab was that there truly is not one single way to get to an answer. Yes, there are the two methods (graphical and algebraic), however there are also different approaches within these methods. Vectors are commutative (another key idea that was further developed in this lab), so they could be translated in multiple different ways when using the graphical method. As long as the magnitude and direction stayed the same, a vector could be moved any way so that finding the resultant would be easier. When it came to the algebraic method, I also noticed a couple different things. There was the simplest way of merely taking the formula and plugging in the numbers. Some people also drew a picture to get a visual and then plugged in soh cah toa formulas based on the picture. Along with these things, some important things during this lab were the concepts of component vectors, resultant vectors, and equilibrium vectors. The given vectors were the components, and they had to be combined to find the resultant, their total sum. A key idea was that resultants and equilibriums are equal but opposite. So, once one was found on the force table, it merely had to be flipped over to find the other. The equilibrium vector was a third component that would allow the total resultant to equal zero. It could only be reached once both the vertical and horizontal forces of each vector would equal zero (Fx=Ax+Bx+Cx=0, Fy=Ay+By+Cy=0).
This lab had many key ideas with it. It showed how graphical and algebraic methods produce nearly the same answers. We verified this by comparing the drawings we made to the charts we completed. One major factor in ensuring the same results was that in each case the vectors equaled zero. There were times, though, in which my answers were about a hundredth away from zero. I concluded that this was an issue of accuracy and precision. I might have measured incorrectly on the graph. I could have also misjudged the value of the angles when doing the algebraic method. This lab helped familiarize the class with vectors and vector addition. When vectors are graphically drawn head to tail, the resultant vector can easily be produced to represent the sum of the values. When we know certain pieces of information about the vectors, we can use the information to find x and y components that ultimately offer the sum. In conclusion, this lab helped the class discuss and understand vector addition.
The force table lab further proved that vectors can be added both graphically, using the head to tail method, and algebraically. Both methods should produce the same exact result or results extremely close to one another--taking into consideration the margin of human error. It is difficult to compare the results knowing the slight chance of error with the graphical method. The angles, lengths and how parallel a vector is to its original drawing when translated all needed to be noted when comparing the two methods. The algebraic method is more accurate because it requires a definite equation and the variables that were solved for mathematically. There is a lesser chance of error when solving algebraically and it is also easier to correct mistakes when you know where you went wrong. When tested in a real world situation using the force tab, strings and weights, we found that the length of the strings (which in our case varied between all four), did not have any affect on the lab. However, the differing masses did. Key ideas from this lab are vectors must be added head to tail, vectors can be translated if the direction and magnitude stay the same, and when the sum of all forces of vectors adds up to be zero, the vectors are in a state of equilibrium.
This lab has given us many key ideas on how the force table lab works. it had showed us that we can solve for vectors using the graphical or algebraic methods. When using the graphical method you have to create drawings by adding vectors head to tail. When you draw it you will eventually get a resultant, Then you have to create a key and measure them to get your answer. When using the algebraic method you have to use cos to find your x's and sin to find your y's. Both of these methods work very well, so it mostly depends on personal choice. Another idea that this lab had showed us was that the forces of the vectors would be 0. This means that the vectors are in equilibrium. That would make sense because in order for the ring to stay still the forces would have to equal out. Also when we tried to do this lab in the real world our numbers were a little different. Since the equations made sense on paper it worked out in the real world. There were different probably because in some cases the paperclips were perpendicular to the rings. Other than that everything turned out well. Mahfuz-ul Hasan
This lab showed how vectors can be added graphically as well as algebraically. They are both ways to solve for the sum of vectors. However, in this lab we found one to be better than the other. Algebraically is more reliable because it is dealing with numbers and it relies only on human error and not instrument error for the most part. Adding them graphically can be affected by the ruler used, the pencil used, if the line is a little too long, or if the angle is even the slightest off. It has too many little things that could go wrong with the instrument used as well as human error compared to adding algebraically. But over all the answers were basically the same. Adding the vectors in real life confirmed our answers we found graphically and algebraically. It showed how all of the vectors added to zero causing a state of equilibrium. This means there was no acceleration, and the total sum of the forces was zero. We also found in our lab that length of the string did not matter. The only thing that mattered was mass and the angle. Therefore, another key idea was found in this lab. Vectors have magnitude and direction that cannot be ignored. The mass and angle of the vectors affected the answer and both needed to be right in order to achieve the desired result. In all this lab demonstrated the methods of adding vectors as well as certain properties of vectors like magnitude and direction.
The Force Table lab had a couple of key aspects. One, is that there is more than one way to solve vector problems. In this lab, we solved the problems both graphically and algebraically. Personally, solving it algebraically is less time consuming and to me seems more accurate. However, solving it graphically gives me a visual and makes finding the resultant easy. The resultant being the opposite direction with the same magnitude of C, or an unknown vector, is also an important concept. Another key aspect we got from the lab are the equations Ax+Bx+Cx=0 and Ay+By+Cy=0. This equation is definitely one we will use all year long and driving it from a real work example makes it easier to understand. Kelly Glenn
In the Force Table Lab, we learned how to reliably add vectors two ways: graphically and algebraically. Since both methods work, either one can be used, or both can be used to make sure the answer is truly correct. As for the vectors themselves, we learned that in order to add multiple vectors, they need to be lined up head to tail. Just like adding normal numbers, vectors are commutative (3+1=4, and 1+3=4); also, vectors going in the exact same direction can be combined, just like how 2x+2x+5x can become 4x+5x. So two vector both pointing east with a magnitude of 5 cm can be combined to create one bigger vector with a magnitude of 10 cm, still going east. The opposite can be done too, for vectors can be broke down into super simple components. Lastly, when graphically solving, it does not matter what vector is translated in order to create a triangle with three vectors. The resultant and it's opposite (C) should still be the same. All the vectors on the table should have a net force of zero (there can be a percent error, however) to show they are in equilibrium. John Mairone
“Hey, if you’re not making mistakes you’re not learning!” Mr. Crane once told me. This lab was all about trial and error once brought into experiment in the real world. Even though all of our measurements graphically and algebraic made sense, we were still slightly off in the real world. We didn’t bother so much, because it was 1/100thish off so it really didn’t impact the lab greatly. I learned that if your work on paper is accurate in real life it should work. The Force Table Lab also showed us many other things. Key information in this lab was the two vectors plus the third vector added to zero. This explains why the ring stayed perfectly in the center, showing that both sided are equal in the amount of force they are exerting, but in opposite directions. Key information that I found based on my reports was that the mass of one of the weights would always be greater than the other two and that it would always be in the opposite hemisphere of the other two. This lab came out with the same results if you did it graphically, alegerabraicly, or in reality. What you want to do depends on which one you think is the easiest. What I think most people made a mistake on in actually doing the lab is forgetting to count the wait of the weight-hanger itself. Everything of the lab made sense after actually doing the lab and seeing how it works. Altogether this lab taught us many things about forces and vectors. -Neil Patel
One of the key ideas of the force is to determine the relationships between the vectors from the angles and magnitude provided. This lab taught us how to get a resultant and its direction from other magnitudes. There were two ways to add vectors: algebraic method, or graphical method. I found the algebraic method simpler, because I believe that the algebraic method gives more certainty to the results of the vectors. However, from my point of view, I believed that both graphical and algebraic methods are needed in order to complete the lab. You need more of a graph to understand the direction and the angles of the vectors. For me, algebra is an easier way to solve for magnitudes. Well, that's my opinion. I was very happy to see our calculations work in the "real world experiment" on Friday. It was amazing that our "head to tail", "Pythagorean theorem", "law of cosines", and "angle calculations" made the weights balance out. And of course we had some errors to the decimals but none of the weight vectors moved (shook a little). Lastly, whenever we were confused, we made sure that for the x component and the Y component A+B+C=0. This really helped us find the missing x and y components. One of the key questions was :How To Find The Magnitude?" The answer is this: break down the magnitude into x and y components, make a table, and use the Pythagorean theorem to solve for the displacement. -Rajat Baul
One of the key ideas that the Force Table Lab clearly portrayed is that there is not only one single way to complete the lab. In this lab, answers could be found by doing the lab graphically or doing the calculations algebraically. Whether doing the lab one way or the other, nearly the same answers were found for every case. It also helps that there were two ways to do the lab so that you could check the answers of one method by doing the other method. In the graphical method, the vectors were added head to tail, and in the algebraic method, sines and cosines were used. The results in both methods were very close, but may have been slightly different due to human error which was more often in the graphical method. This lab also helped get us more familiar with trig functions and reinforced the ideas of adding vectors head to tail and getting a resultant. -Nicole Dib
The two key ideas of this lab was adding vectors graphically and algebraically, and within these two key ideas, there were smaller, sub-key components. In the graphical method, it further showed and proved the method of adding vectors graphically (although it was later found that this method is not as accurate as the algebraic method). Vectors need to be added head to tail, and in order to do that in the lab for most cases, the vectors needed to be translated. Translation of vectors, another key idea, requires the same exact magnitude and direction for vectors while being translated throughout the graph. Another key idea that was stressed was that the Resultant Vector (which was often appearing with the use of Pythagorean Theorem by two component vectors, A and B, when attempting to find Vector C) = -Vector C. Another key idea introduced through the graphical method was that Vector A + Vector B + Vector C [+ Vector D] = 0. In order for this to occur, an equilibrium or balance of all of the vectors in the real world, all of the vectors’ sum had to be 0. As for algebraically, most of the ideas were already familiar to me. This included the cosine, sine, tangent functions, F=ma, a^2+b^2=c^2, Vector A + Vector B + Vector C [+ Vector D] = 0, and tan^-1(y/x)=angle or direction of the vector. It was just a matter of choosing the right ones to apply in the lab. As mentioned above, graphically adding vectors was found not to be as accurate as performing the addition methods algebraically. If the graphing had been done on a larger scale, however, it would have been more accurate (a larger scale = less of human error). At the same time, the algebraic method proved to be the most accurate. Lauren
A key question could be something like, "What properties of vectors did you see in the lab?", and key idea would be that the sum of all forces in our lab would equal out to be zero. Sum of Forces x = 0 = Equilibrium, Sum of Forces y = 0 = Equilibrium, and Sum of all Forces would equal out to be zero as well, causing the ring to stay balanced as we witnessed.
ReplyDeleteAfter completing this lab, my group and I discussed the differences between the graphical method and the algebraic method. Obviously both the graphical and algebraic "procedures" work but we realized it came down to "comfort level". For example, I prefer using the algebraic method because i find that getting an equation and then just plugging in numbers is a lot simpler. We discovered that the purpose of this lab is to gain experience in working with vector quantities. The lab involves the demonstration of the process of the addition of several vectors to form a resultant vector. If several forces with different magnitudes and directions act at a point its net effect can be represented by a single resultant force. This resultant force can be found using a special addition process known as vector addition.
ReplyDeleteRachel Rha
A key idea is that there is more than one method to do this lab. You can do it graphically or algebraically while still getting relatively the same answers. Not only can you do It that way, but there are also different methods within those methods. Lizzie and I both had the same answers but she drew triangles and I solved an equation. This lab also showed how the magnitude and direction of two vectors resulted in a resultant. This lab also proved the ideas that vectors are commutative. It also got us using trig functions.
ReplyDeleteEmma
One of the main things that my group and I found out as we went through the lab was that there truly is not one single way to get to an answer. Yes, there are the two methods (graphical and algebraic), however there are also different approaches within these methods. Vectors are commutative (another key idea that was further developed in this lab), so they could be translated in multiple different ways when using the graphical method. As long as the magnitude and direction stayed the same, a vector could be moved any way so that finding the resultant would be easier. When it came to the algebraic method, I also noticed a couple different things. There was the simplest way of merely taking the formula and plugging in the numbers. Some people also drew a picture to get a visual and then plugged in soh cah toa formulas based on the picture. Along with these things, some important things during this lab were the concepts of component vectors, resultant vectors, and equilibrium vectors. The given vectors were the components, and they had to be combined to find the resultant, their total sum. A key idea was that resultants and equilibriums are equal but opposite. So, once one was found on the force table, it merely had to be flipped over to find the other. The equilibrium vector was a third component that would allow the total resultant to equal zero. It could only be reached once both the vertical and horizontal forces of each vector would equal zero (Fx=Ax+Bx+Cx=0, Fy=Ay+By+Cy=0).
ReplyDeleteThis lab had many key ideas with it. It showed how graphical and algebraic methods produce nearly the same answers. We verified this by comparing the drawings we made to the charts we completed. One major factor in ensuring the same results was that in each case the vectors equaled zero. There were times, though, in which my answers were about a hundredth away from zero. I concluded that this was an issue of accuracy and precision. I might have measured incorrectly on the graph. I could have also misjudged the value of the angles when doing the algebraic method. This lab helped familiarize the class with vectors and vector addition. When vectors are graphically drawn head to tail, the resultant vector can easily be produced to represent the sum of the values. When we know certain pieces of information about the vectors, we can use the information to find x and y components that ultimately offer the sum. In conclusion, this lab helped the class discuss and understand vector addition.
ReplyDeleteThe force table lab further proved that vectors can be added both graphically, using the head to tail method, and algebraically. Both methods should produce the same exact result or results extremely close to one another--taking into consideration the margin of human error. It is difficult to compare the results knowing the slight chance of error with the graphical method. The angles, lengths and how parallel a vector is to its original drawing when translated all needed to be noted when comparing the two methods. The algebraic method is more accurate because it requires a definite equation and the variables that were solved for mathematically. There is a lesser chance of error when solving algebraically and it is also easier to correct mistakes when you know where you went wrong. When tested in a real world situation using the force tab, strings and weights, we found that the length of the strings (which in our case varied between all four), did not have any affect on the lab. However, the differing masses did. Key ideas from this lab are vectors must be added head to tail, vectors can be translated if the direction and magnitude stay the same, and when the sum of all forces of vectors adds up to be zero, the vectors are in a state of equilibrium.
ReplyDeleteThis lab has given us many key ideas on how the force table lab works. it had showed us that we can solve for vectors using the graphical or algebraic methods. When using the graphical method you have to create drawings by adding vectors head to tail. When you draw it you will eventually get a resultant, Then you have to create a key and measure them to get your answer. When using the algebraic method you have to use cos to find your x's and sin to find your y's. Both of these methods work very well, so it mostly depends on personal choice. Another idea that this lab had showed us was that the forces of the vectors would be 0. This means that the vectors are in equilibrium. That would make sense because in order for the ring to stay still the forces would have to equal out. Also when we tried to do this lab in the real world our numbers were a little different. Since the equations made sense on paper it worked out in the real world. There were different probably because in some cases the paperclips were perpendicular to the rings. Other than that everything turned out well.
ReplyDeleteMahfuz-ul Hasan
This lab showed how vectors can be added graphically as well as algebraically. They are both ways to solve for the sum of vectors. However, in this lab we found one to be better than the other. Algebraically is more reliable because it is dealing with numbers and it relies only on human error and not instrument error for the most part. Adding them graphically can be affected by the ruler used, the pencil used, if the line is a little too long, or if the angle is even the slightest off. It has too many little things that could go wrong with the instrument used as well as human error compared to adding algebraically. But over all the answers were basically the same. Adding the vectors in real life confirmed our answers we found graphically and algebraically. It showed how all of the vectors added to zero causing a state of equilibrium. This means there was no acceleration, and the total sum of the forces was zero. We also found in our lab that length of the string did not matter. The only thing that mattered was mass and the angle. Therefore, another key idea was found in this lab. Vectors have magnitude and direction that cannot be ignored. The mass and angle of the vectors affected the answer and both needed to be right in order to achieve the desired result. In all this lab demonstrated the methods of adding vectors as well as certain properties of vectors like magnitude and direction.
ReplyDeleteThe Force Table lab had a couple of key aspects. One, is that there is more than one way to solve vector problems. In this lab, we solved the problems both graphically and algebraically. Personally, solving it algebraically is less time consuming and to me seems more accurate. However, solving it graphically gives me a visual and makes finding the resultant easy. The resultant being the opposite direction with the same magnitude of C, or an unknown vector, is also an important concept. Another key aspect we got from the lab are the equations Ax+Bx+Cx=0 and Ay+By+Cy=0. This equation is definitely one we will use all year long and driving it from a real work example makes it easier to understand. Kelly Glenn
ReplyDeleteIn the Force Table Lab, we learned how to reliably add vectors two ways: graphically and algebraically. Since both methods work, either one can be used, or both can be used to make sure the answer is truly correct. As for the vectors themselves, we learned that in order to add multiple vectors, they need to be lined up head to tail. Just like adding normal numbers, vectors are commutative (3+1=4, and 1+3=4); also, vectors going in the exact same direction can be combined, just like how 2x+2x+5x can become 4x+5x. So two vector both pointing east with a magnitude of 5 cm can be combined to create one bigger vector with a magnitude of 10 cm, still going east. The opposite can be done too, for vectors can be broke down into super simple components. Lastly, when graphically solving, it does not matter what vector is translated in order to create a triangle with three vectors. The resultant and it's opposite (C) should still be the same. All the vectors on the table should have a net force of zero (there can be a percent error, however) to show they are in equilibrium.
ReplyDeleteJohn Mairone
“Hey, if you’re not making mistakes you’re not learning!” Mr. Crane once told me. This lab was all about trial and error once brought into experiment in the real world. Even though all of our measurements graphically and algebraic made sense, we were still slightly off in the real world. We didn’t bother so much, because it was 1/100thish off so it really didn’t impact the lab greatly. I learned that if your work on paper is accurate in real life it should work. The Force Table Lab also showed us many other things. Key information in this lab was the two vectors plus the third vector added to zero. This explains why the ring stayed perfectly in the center, showing that both sided are equal in the amount of force they are exerting, but in opposite directions. Key information that I found based on my reports was that the mass of one of the weights would always be greater than the other two and that it would always be in the opposite hemisphere of the other two. This lab came out with the same results if you did it graphically, alegerabraicly, or in reality. What you want to do depends on which one you think is the easiest. What I think most people made a mistake on in actually doing the lab is forgetting to count the wait of the weight-hanger itself. Everything of the lab made sense after actually doing the lab and seeing how it works. Altogether this lab taught us many things about forces and vectors.
ReplyDelete-Neil Patel
One of the key ideas of the force is to determine the relationships between the vectors from the angles and magnitude provided. This lab taught us how to get a resultant and its direction from other magnitudes. There were two ways to add vectors: algebraic method, or graphical method. I found the algebraic method simpler, because I believe that the algebraic method gives more certainty to the results of the vectors. However, from my point of view, I believed that both graphical and algebraic methods are needed in order to complete the lab. You need more of a graph to understand the direction and the angles of the vectors. For me, algebra is an easier way to solve for magnitudes. Well, that's my opinion. I was very happy to see our calculations work in the "real world experiment" on Friday. It was amazing that our "head to tail", "Pythagorean theorem", "law of cosines", and "angle calculations" made the weights balance out. And of course we had some errors to the decimals but none of the weight vectors moved (shook a little). Lastly, whenever we were confused, we made sure that for the x component and the Y component A+B+C=0. This really helped us find the missing x and y components. One of the key questions was :How To Find The Magnitude?" The answer is this: break down the magnitude into x and y components, make a table, and use the Pythagorean theorem to solve for the displacement. -Rajat Baul
ReplyDeleteOne of the key ideas that the Force Table Lab clearly portrayed is that there is not only one single way to complete the lab. In this lab, answers could be found by doing the lab graphically or doing the calculations algebraically. Whether doing the lab one way or the other, nearly the same answers were found for every case. It also helps that there were two ways to do the lab so that you could check the answers of one method by doing the other method. In the graphical method, the vectors were added head to tail, and in the algebraic method, sines and cosines were used. The results in both methods were very close, but may have been slightly different due to human error which was more often in the graphical method. This lab also helped get us more familiar with trig functions and reinforced the ideas of adding vectors head to tail and getting a resultant. -Nicole Dib
ReplyDeleteThe two key ideas of this lab was adding vectors graphically and algebraically, and within these two key ideas, there were smaller, sub-key components. In the graphical method, it further showed and proved the method of adding vectors graphically (although it was later found that this method is not as accurate as the algebraic method). Vectors need to be added head to tail, and in order to do that in the lab for most cases, the vectors needed to be translated. Translation of vectors, another key idea, requires the same exact magnitude and direction for vectors while being translated throughout the graph. Another key idea that was stressed was that the Resultant Vector (which was often appearing with the use of Pythagorean Theorem by two component vectors, A and B, when attempting to find Vector C) = -Vector C. Another key idea introduced through the graphical method was that Vector A + Vector B + Vector C [+ Vector D] = 0. In order for this to occur, an equilibrium or balance of all of the vectors in the real world, all of the vectors’ sum had to be 0. As for algebraically, most of the ideas were already familiar to me. This included the cosine, sine, tangent functions, F=ma, a^2+b^2=c^2, Vector A + Vector B + Vector C [+ Vector D] = 0, and tan^-1(y/x)=angle or direction of the vector. It was just a matter of choosing the right ones to apply in the lab. As mentioned above, graphically adding vectors was found not to be as accurate as performing the addition methods algebraically. If the graphing had been done on a larger scale, however, it would have been more accurate (a larger scale = less of human error). At the same time, the algebraic method proved to be the most accurate.
ReplyDeleteLauren