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: ->->->->->->->->->->->-> : We need to find the length of the hypotenuse of the triangle made by these points using a^2+b^2=c^2
a=10-5 or 5 cm b=17-9 or 8
so 5^2+8^2=c^2 means that c= 9.43cm
so if the distance is 9.43cm, it is 1.93cm over the length that would have no tension, so we would multiply 1.93cm(.7N) to get 1.35N of tension
What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> : We know the distance of the vector, so we need to find the angle/direction. We can do this by taking tan(8/5) which gives an angle of about 60 degrees north of the horizontal.
What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> : The magnitude is its length which we found using the Pathagorium theorem above. We found its length was 9.43cm.
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: ->->->->->->->->->->->-> : You get a normalized vector where the magnitude is 1. I am not sure how to figure out the points. A guess would be that since the magnitude of our vector was 9.43, we should put all our units over 9.43 to get a magnitude of one. How would we do this?
What vector do you get when you multiply this new vector by the tension?
answer/question/discussion: ->->->->->->->->->->->-> : I really do not know what I should do here. We may get the original vector or maybe the vector of tension instead of the total vector?
What are the x and y coordinates of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> : Again I dont know how to do this?
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25 mins
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Very good. Check out the link for the last couple of answers. No need for revision unless you have questions.
&#Please compare your solutions with the expanded discussion at the link
Solution
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