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PHY 201
Your 'cq_1_16.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Samantha Rogers
PHY 201
Seed 16.1
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 length of the vector can be solved using the Pythagorean theorem. The coordinates are connected in a straight line, the hypotenuse. The change in the x-component is the base, 5 cm ( 10 - 5 ). The change in the y-value is the y-component, the length of the long side, 8 cm ( 17 - 9 ). The length of the vector can be found using the Pythagorean theorem. If a^2 + b^2 = c^2, then, 5^2 + 8^2 = c^2. Thus, 89 ( 25 + 64 ) = c^2. And since the square root of 89, the length of a side, cannot be negative, the answer will be roughly a positive 9.4 cm, the length of the rubber band. 9.4-7.5 = 1.9, the additional length of the rubber band. Thus, the tension will be about 1.33 Newtons ( 1.9 * .7 ).
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
The points of the vector are ( 5 cm, 9 cm ) and ( 10 cm, 17 cm ). I will now adjust my subsequent answers based on this response.
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
The magnitude of the vector is around 9.4.
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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: ->->->->->->->->->->->-> :
The unit vector has a magnitude of 1, in the same direction as the original vector. Thus, if the original vector has a magnitude of about 9.4 cm, then to make a unit vector, you divide all of the legs of the triangle by 9.4 to be proportional as well.
5 cm( 10 cm - 5 cm )/ 9.4 cm = .53
8 cm ( 17 cm - 9 cm )/ 9.4 cm = .85
( .53, .85 )
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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: ->->->->->->->->->->->-> :
You get a new vector, because you are multiplying a scalar quantity by a vector quantity. The vector has the same alignment/position in space ( angle of direction as compared to the unit vector ) in space, yet its new magnitude is 1.33.
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
multiply them by the tension force to get the new x and y coordinates of the vector of magnitude 1.33.
Original Unit Vector: ( .53, .85 )
1.33 N * Original Vector ( .705, 1.13 )
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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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30 minutes
&#Very good responses. Let me know if you have questions. &#
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6/24/2012 10:10