course phy 121
3/14 at 4:45 p.m.
Asst 16 Question 1--------------------------------------------------------------------------------
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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:
On the x coordinate, there is only a difference of 5 cm; however, on the y coordinate there is a difference of 8 cm which means this is surpassing the 7.5 cm limit. If the
tension increases by .7 for every cm and there is an increase of .5, this means that the tension increases by 3.5. I don't know if this is making sense of this or not.
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What is the vector from the first point to the second?
answer/question/discussion:
Using the Pythagorean theorem and squaring the sides of the triangle and then taking the square root, it appears that it is 9.43 cm. It is going from (5,9) to (10, 17).
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What is the magnitude of this vector?
answer/question/discussion:
9.43 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:
I honestly don't understand because I'm assuming this is 9.43/9.43. ???
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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:
3.5 assuming that my thinking above is right.
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What are the x and y components of the new vector?
answer/question/discussion:
I don't know.
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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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Revised: 06 Feb 2010 17:12:21 -0500"
Vectors have x and y components.
You correctly applied the Pythagorean Theorem to get the magnitude of the vector, but didn't get the parts related to vector components.
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