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?
answer/question/discussion: ->->->->->->->->->->->-> :
I took the points and plotted them on a graph. Then, I drew a triangle from the two points and calculated the legs of the triangle, which were 5 cm as the base and 8 cm as the height. Then, used the Pythagorean theorem to find the hypotenuse, which was 9.4 cm. So, the tension after the 7.5 cm is the subtraction from the hypotenuse 9.4 cm from the 7.5 cm: 9.4 – 7.5 = 1.9 cm, so almost 2 cm past the time when the rubber band gains tension. 2 cm * .7 N = 1.4 N.
The end points of the vector will have around 1.4 N of tension.
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
The vector from the first point to the second is the use of the Pythagorean theorem: sqrt(5^2 + 8^2) = 9.4 cm.
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
The magnitude of the vector is 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: ->->->->->->->->->->->-> :
When I divide the vector into the magnitude I get 1: 9.4 cm / 9.4 cm = 1 cm.
A vector has magnitude and direction. You haven't specified direction.
9.4 cm / (9.4 cm ) = 1, not 1 cm. The cm units divide out.
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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: ->->->->->->->->->->->-> :
I have a unit vector, and when I multiply that by the tension I get: 1 cm * 1.4 N = 1.4 cm.
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
I am not sure how to get the new x and y components from the new vector.
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30 minutes
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&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
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