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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.
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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: ->->->->->->->->->->->-> :
slope = (17 cm – 9 cm) / (10 cm – 5 cm) = 1.6
Tension = (0.7 N)*(1.6) = 1.12 N
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
The vector is from the first point (5 cm, 9 cm) to the second point (10 cm, 17 cm)
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
magnitude = sqrt(x^2 + y^2)
x = 10 cm – 5 cm = 5 cm
y = 17 cm – 9 cm = 8 cm
magnitude = sqrt(5cm^2 + 8 cm^2)
magnitude = 9.43
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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: ->->->->->->->->->->->-> :
(5 cm, 9 cm) / 9.43 and (10 cm, 17 cm) / 9.43
Which gives you:
(0.53 cm, 0.954 cm) for one point of the new vector and (1.06 cm, 1.8 cm) for another point of the new vector.
the first would be
(5 cm, 9 cm) / (9.43 cm).
The numbers would be the same but the cm divides out, making the unit vector (.53, .846), not (.53 cm, .846 cm).
A unit vector, interestingly, has no units.
Therefore the unit vector:
1.8 cm – 0.954 cm = 0.846 cm
1.06 cm – 0.53 cm = 0.53 cm
Unit vector = (0.53 cm, 0.846 cm)
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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: ->->->->->->->->->->->-> :
Unit vector = (0.53 cm, 0.846 cm)
Tension = 1.12 N
(0.53 cm, 0.846 cm)*(1.12 N)
New vector: (0.5936 N*cm, 0.94752 N*cm)
The tension would be based on the length of the vector from one point to the other, not on the slope of that graph. So your 1.12 N is probably not correct. However your use of the vectors, and the unit vectors, is very good.
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
The x components of the new vector is the horizontal displacement*tension of 0.5936 N*cm and the y components of the new vector is the vertical displacement*tension of 0.94752 N*cm
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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.
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About 30 minutes
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Good, but there are a couple of things you'll want to revise. Shouldn't give you any trouble at all, nor take you long.
&#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. &#