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phy121
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: ->->->->->->->->->->->-> :
we plot the points (5cm,9cm) and (10cm,17cm). We draw a vector line for the x component from 5 to 10 giving it a length of 5 cm. we draw a vector line from 9 cm to 17 cm giving it length 8 cm. We then sketch in the hypotenuse to finish this triangle. We are told that a rubber band has no tension until it reaches 7.5 cm and that after that point, each additional 1cm of length increases tension by 17 NEwtons. To find the length of the rubber band we use Pythagorean theoem and sqroot (5^2 + 8^2) = 9.43 cm. 9.43-7.5 = 1.93 * .7 = 1.351 newtons for the tension
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
vector from (5cm, 9cm) to (10cm 17cm) is 5cm in x direction and 8 cm in y direction
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
magnitude is found by the pythagorean theorem which we previously found to be 9.43 cm angle is arctan (8/5) = 58 degrees
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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: ->->->->->->->->->->->-> :
dividing the vector by its magnitude gives <5cm, 8cm> / 9.4 = .53 x componenet and .85 y component
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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: ->->->->->->->->->->->-> :
<.53, .85> * 1.35 = .7155 x direction 1.1475 y direction
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Good. However be sure you include units. Numbers without units are often pretty much meaningless and difficult to keep track of.
The tension would be 1.35 Newtons, so the components would be .72 N and 1.15 N.
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
.7155 x direction 1.1475 y direction with an angle of arctan (1.1475/.7155)=58 degrees
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&#Good responses. See my notes and let me know if you have questions. &#