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course Phy 121
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:
The distance that the rubber band is stretched can be found by creating a right triangle with the rubber band as the hypotenuse. Band length = sqrt(8^2+5^2)=9.43cm
distanced stretched=9.43cm-7.5cm=1.93cm
1.93*.7N=1.35N
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What is the vector from the first point to the second?
answer/question/discussion:
(17cm-9cm),(10cm-5cm)=(8cm.5cm)
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What is the magnitude of this vector?
answer/question/discussion:
sqrt(8^2+5^2)=9.43cm
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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:
.89,.53
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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:
(.89,.53)*1.35N=(1.2,.72)
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What are the x and y components of the new vector?
answer/question/discussion:
(1.2,.72)
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