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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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I will re-do. I just need some help, please point me in the correct direction.
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10 min
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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: ->->->->->->->->->->->-> :
squ (5 - 10)^2 + ( 9- 17) ^2 = 25 + 64 = 89 cm
@& The magnitude of the vector will be sqrt( (5 - 10)^2 + (9 - 17) ^ 2)
sqrt( (5 - 10)^2 + (9 - 17) ^ 2) = sqrt( 25 + 64) = sqrt(89).
Note that you are missing some parentheses in your expression, though you have the right idea.
You also left of the sqrt operator on your second and third steps, so you never actually got the magnitude. You have to follow the order of operations throughout.
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61cm/7.5cm =11.86 cm
@& You don't indicate how you got 61 cm, or 7.5 cm, or why you would be dividing these quantities. However do note that, while the result isn't necesssarily related to this situation, 61 cm / (7.5 cm) = 8.2. The cm would divide out of this calculation.
In any case this calculation doesn't give you the length of the rubber band. Your previous calculation, if done correctly, will give you the length.*@
11.86 x .7N = 8.3 N
@& The rubber band has a length, but it doesn't exert a force throughout its length.
The length isn't 11.86 cm, but if it was, you would have to consider the fact that it exerts no tension until its length reaches 7.5 cm. You would not multiply its entire length by .7 N / cm. You would multiply its length in excess of 7.5 cm by .7 N / cm.*@
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
11.36
What is the definition of a vector?
@& Have you worked through Introductory Problem Set 5, as I believe has been assigned? You might not know what a vector is until you have done so.
A vector has a magnitude (in this case the magnitude would be the length of the vector, which you find using the Pythagorean Theorem as you started to do in the fisrt step; the length of this vector will be between 9 and 10 cm), and an angle. The angle is the angle made by the rubber band with the positive x direction, and is found as instructed in Intro Problem Set 5.
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
How do you solve for the magnitude? Is that the slope?
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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: ->->->->->->->->->->->-> :
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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: ->->->->->->->->->->->-> :
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
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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.
@& You started out with the right calculation for the length of the rubber band, but you didn't complete that calculation correctly. You shouldn't have much trouble correcting that.
You also need to have done Introductory Problem Set 5 in order to know what a vector is and how to do the vector calculations.
See my notes and do submit a revision as indicated below.
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Be sure to include the entire document, including my notes.
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