Objectives
After studying the material of this chapter, you should be able to:1. Represent the magnitude and direction of a vector using a protractor and ruler.
2. Multiply or divide a vector quantity by a scalar quantity.
3. Use the methods of graphical analysis to determine the magnitude and direction of the vector resultant in problems involving vector addition or subtraction of two or more vector quantities. The graphical methods to be used are the parallelogram method and the tip to tail method.
4. Use the trigonometric component method to resolve a vector components in the x and y directions.
5. Use the trigonometric component method to determine the vector resultant in problems involving vector addition or subtraction of two or more vector quantities.
6. Use the kinematics equations of Chapter Two along with the vector component method of Chapter Three to solve problems involving two dimensional motion of projectiles.
Links:
Vector Addition & Components
Vector Lab Checklist:
- Each person must turn in a complete lab.
- All work & calculations must be shown for case 1
- A Results summary of all 5 cases
- Discussion Section: Overall results/improvements/ questions
Review:
Mr. Crane, for the Force Table lab, I do not know what inverse trigonometric functions are, or how to use them. I also do not know how to program my calculator to use them.
ReplyDeleteWait, I may have figured it out...
DeleteActually I am still confused
DeleteAwesome I will show you how to do this in class and give you a little mini lesson...
ReplyDeleteVECTOR ISLAND "Summarize the KEY IDEAS from the activity"
ReplyDeleteUGH Addition is commutative so I should be able to add vectors in any order? Also are there any strategies you may have learned not in the directions?
DeleteOKAY so I'm going to say that I was at first hesitant about doing the lab (I was extremely lazy the other day and really did not feel like interacting with anything except three slices of pizza), but the entire process turned out to be very interesting. After looking over the directions, I realized what the point of the lab must be, because I was also thinking about properties of adding vectors. With any form of addition, the commutative property can always be used. Why should that rule be any different when adding vectors? Through the lab, we all realized that no matter how you add vectors, they will always end up with the same result. It's just a treasure map. No matter which direction you take in which order, 'X' will always mark the spot. Specifically, that was the main idea. We also had a couple other ideas reinforced for us, such as the idea of human error. The different paths leading to the resultant were taken by different people, so different outcomes should be expected (although the outcomes shouldn't be too far from each other!) We also had another idea reinforced that really applies itself to this class: "You can get points for anything. Write down everything that could possibly be important. You never know what things you might get points for." It was a good idea for us to label the paths, showing the number of paces that each vector represented. It truly clarified the unique ways in which everyone got to the same 'X' at the very end. Those small details really worked to solidify the drawings. That can be transferred to other areas of the class as a year-long strategy. Another strategy? Keep all work neat. Luckily, my partner and I both had kept our lines and writing very fine and clean, in order to avoid confusion with our sometimes intersecting paths. One last idea to close this wordy paragraph? Even the seemingly dumbest, most elementary activities can teach us the most. I got more from this project that I'm sure most of us thought we would.
DeleteThe Vector Island activity focused on the idea that vector addition is commutative. This means that the vectors can be added in any order. To do this, a frame of reference must be determined to decide which values are positive and which are negative. From here, the vectors can simply be added. The lab also showed that drawing a diagram and adding the vectors are two different strategies that bear nearly the same results. Any error is because of the measuring device and the person using it.
ReplyDeleteI understand the concept of vectors adding up to zero and cancelling each other out, however I only vaguely remember "sin" and "cos" from math last year, so I am having some difficulty with the lab. Can anyone explain to me how these apply and function when it comes to force vectors??
ReplyDeleteThe Vector island activity shows that when adding vectors, it does not matter what order the vectors are in. Addition is commutative. When having two vectors in different directions, you still add them but one will be negative and one will be positive. You should label which way is positive and which way is negative. When drawing the map, the difference between precision and accuracy became clear. When we measured the amount of paces we needed to draw, we were accurate, but not necessarily precise. This is because a ruler is not perfect; therefore, making measurements not exact. Also, drawing a diagram showed the rule that vectors are connected head to tail.
ReplyDeleteThe vector island activity gave a visual explanation to the fact that when adding vectors, it does not matter what order the vectors are in because adding is commutative. When given multiple vectors, it does not matter which order you add the components in because you will end up with the same resultant. The most important rule is to align the vectors head to tail. If given drawn vectors it is important to establish which direction is positive and which is negative. Also, the lab showed us that when drawing the vectors on the map, it is important to be as accurate and precise with your measurements as possible in order to make yours and your partners vector maps end at the same spot. Some people faced the problem of theirs and their partner's resultant vector maps being different, and that error is most likely due to inaccurate or not precise measurements.
ReplyDeleteThe Vector Island Activity taught us that when you graphically add vectors, it does not matter what order you chose to follow them if you start from the same starting point. As long as you accurately add the vectors head to tail, you will produce the same result.
ReplyDeleteIs this due tommorow?
ReplyDelete-NP
The Force Table Lab is due on October 7th.
DeleteThis comment has been removed by the author.
ReplyDeleteI just noticed the case numbers on the Force Table Lab.
Delete-Addition is commutative, so the order doesn't matter.
ReplyDelete-If the same numbers are used, others will get similar or the same results.
-If the vectors are added from head to tail, you should get the correct answer.
The vector island activity showed how addition of vectors is commutative. It does not matter what order they are added in. This was proved because two people did the same activity. Both people used the same set of vectors but in different orders. The end result was the same place on the map for both people. The order with which the vectors were added did not matter. Another key idea is how to find the resultant. The total sum is from the starting point to the end point once all the vectors are drawn and added. This is the resultant of the components, vectors, being added.
ReplyDeleteThe Pirate's Treasure: Vector Island Treasure Map activity reminded us of the simple lesson that addition is commutative. The Commutative Property is a fundamental building block of math, but it only works for addition and multiplication. As we completed the activity we worked to see if vector addition did not depend on order, similar to scalar addition. The only reason the vectors may not have lined up would be because of human error.
ReplyDeleteThe Vector Island activity demonstrated a commonly known and accepted characteristic of addition - that it is commutative. It proved that this characteristic is even applicable to vectors. By correctly applying the crucial rule of adding the vectors head to tail and accurately measuring the paces, (regardless of what order the partners performed the steps on the map), it resulted in extremely close, if not exact, results (human error is also a factor). It also proved the importance of diagramming, in which one can visually see results and connections in activities and problems. This activity visually proved that vectors can be added graphically, with negative vectors pointing west and south and positive vectors pointing north and east.
ReplyDeleteThe Vector Island Activity helps you to understand the following points...
ReplyDelete1. Vectors have magnitude and direction
2. Vector addition is communtative (ex. a+b=b+a)
3. You are able to group parallel. Errors and add them (This will reduce errors)
4. Larger scales= less error (more sig figs)