#$&*
Phy 231
Your 'cq_1_16.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A rubber band has no tension until it reaches a length of 7.5 cm. Beyond that length its tension increases by .7 Newtons for every additional centimeter of length.
What will be its tension if its endpoints are at the points (5 cm, 9 cm) and (10 cm, 17 cm) as measured on an x-y coordinate system?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
length^2=5cm^2+8cm^2= 89cm^2
length=9.43cm
length beyond 7.5cm=9.43cm-7.5cm=1.93cm
tension equals 1.93cm*.7N=1.35N
#$&*
What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
I'm not sure what this question means-- do we name the vector? It is a ve
@&
@&
A vector can be specified by giving its angle and magnitude or its components.
*@
*@
#$&*
What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
The magnitude of the vector is its length, 9.43cm.
#$&*
What vector do you get when you divide this vector by its magnitude? (Specify the x and y components of the resulting vector).
answer/question/discussion: ->->->->->->->->->->->-> scussion:
A vector of 9.43cm divided by its 9.43 magnitude = 1.
#$&*
The new vector should have magnitude 1. When you divide a vector by its magnitude the result is a vector with magnitude 1. We call a vector of magnitude 1 a unit vector. What vector do you get when you multiply this new vector (i.e., the unit vector) by the tension?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
We get a vector of magnitude 1.35N
#$&*
What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
The only way I can think of to do this is find the original angle.
tan(theta) = 8/5
theta=58deg
sin(58deg)=y/1.35
.84*1.35=y
y=1.13
cos(58deg)=x/1.35
.52*1.35=x
x=.702
#$&*
This new vector is called the tension vector. It is a force vector which represents the tension. A force vector can be specified by its components, or equivalently by its magnitude and direction.
** **
30 minutes, but only because it took me a long time to figure out that my new graphing calculator was set to Radians. Ouch!
** **
I'm not clear on the terminology of naming vectors. I know this is discussed early in our textbook, but it's not sinking in for me. I don't know how to specify the angle (especially using typewriter notation), or if we always need to, necessarily.
@&
Check my note on specifying the vector.
You did get the angle and magnitude of the vector.
Also be very sure you have worked through Introductory Problem Set problems 5.1 - 5.5, which presents the fundamental concepts of vectors in a simple and concise manner. You pretty much know what you need to know, but you can probably benefit from seeing the notation.
Check out the discussion at the link below as well. No revision is necessary unless you have questions.
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
*@