Phy 201
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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?
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9cm – 7.5cm = 2.5cm * .7N = 1.75
17cm – 7.5cm = 9.5cm * .7N = 6.65
You need to use the Pythagorean Theorem to find the length of the rubber band, and then use what you learned from Introductory Problem Set 5 in Assignment 14.
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• What is the vector from the first point to the second?
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• What is the magnitude of this vector?
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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).
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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?
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• What are the x and y components of the new vector?
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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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20 min
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