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PHY 201
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.
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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: ->->->->->->->->->->->-> :
Length equals:
+-sqrt((x2-x1)^2+(y2-y1)^2),
+-sqrt((10cm-5cm)^2+(17cm-9cm)^2),
+-sqrt(25cm^2+64cm^2),
+-9.4cm,
We will use +9.4cm because we are determining the
length of the rubber band.
9.4cm-7.5cm=1.9cm,
1.9*.7N=1.33N
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What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
The line that connects to two points. I'm not sure
@& A vector can be specified by its x and y components, or by its magnitude and angle with the positive x axis.
The force is parallel to the rubber band, and you know the components of its length vector. So you can calculate its angle with the positive x axis.*@
what the question is asking. I could say the vector
is AB, saying the first point is A and the second
point is B.
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What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
The magnitude is 9.4 cm.
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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: ->->->->->->->->->->->-> :
If you divide this vector by its magnitude you will
have a vector with a magnitude of 1. Points of
(5,9),(6,10).
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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: ->->->->->->->->->->->-> :
?
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What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
?
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30 min.
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@& See my notes, then check the link. No revision is necessary as long as you understand, which I believe you will.
*@
&#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. &#