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PHY 231
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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 first
(17-9)^2 + (10-5)^2 = c^2
c = 9.4 cm
9.4 - 7.5 = 1.9 cm
1.9cm(.7) =1.3 N
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
5i + 8j + 0k from subtracting from the coordinates,
Angle is: tan^-1(rise/run)
Angle is 58 deg
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
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: ->->->->->->->->->->->-> :
.53i + 0.85j + 0k
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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: ->->->->->->->->->->->-> :
0.69i + 1.12j + 0k
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
0.69, 1.12
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