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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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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: ->->->->->->->->->->->-> :
From 5 cm to 9 cm, the tension would be 9 cm - 7.6 cm = 1.4 cm * 0.7 N/cm = 0.98 N
At 10 cm the tension would be 1.68 N(10 cm - 7.6 cm = 2.4 cm * 0.7 N/cm = 1.68 N). Between 17 cm and 10 cm, the tension would be 7 cm * 0.7 N/cm = 4.9 N. Therefore, the total tension at 17 cm would be 4.9 N + 1.68 N = 6.58 N.
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Not a bad attempt, but from the point (5 cm, 9 cm) to (10 cm, 17 cm) you can construct a right triangle with legs of 5 cm and 8 cm, whose hypotenuse begins at the first point and ends at the second.
The length of this hypotenuse will be the distance between the points.
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• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
Bare with me, I am not sure if the vector is supposed to be based on force (0.98 N and 6.58 N) or based on the displacements. I am assuming displacements.
Vector A with x & y components of 5 cm (x) and 9 cm (y)
Vector B with x & y components of 10 cm (x) and 18 cm (y)
The x component of the vectors is 5 cm + 10 cm = 15 cm.
The y component of the vectors is 9 cm + 18 cm = 27 cm.
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If you draw an arrow from the first point to the second, its length will be less than 15 cm, and quite a bit less that 27 cm.
The x and y components of the vector will both be less than its length.
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• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
Using Pythagorean theorem, the magnitude is equal to sqrt(a^2 + b^2) = sqrt((15)^2 + (27)^2) = 30.9 cm
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That would be the magnitude of a vector whose x and y components are 15 cm and 27 cm, but those components don't describe the vector for this situation.
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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: ->->->->->->->->->->->-> :
Okay, I must not be understanding vector terminology very well, or i started off incorrectly.
Vector A would have the x & y components 5 cm and 9 cm, this is one vector
Vector B would have the x & y components 10 cm and 18 cm, and would make up the second vector.
The sum of the x component and y component will give me a third vector known as the Resultant Vector with x component of 15 cm and y component of 27 cm. I used Pythahegorean theorem to get the magnitude of the Resultant vector.
(15, 27) / 30.9 = (1/30.9)(15, 27) = (0.49, 0.87) give or take some rounding errors. The magnitude of this would be sort((0.49)^2 + (0.87)^2) = 0.998
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You probably need to review the assignment related to Introductory Problem Set 5 before making your revisions on this problem.
We have a point with coordinates 5 cm and 9 cm, and another point with coordinates 10 cm and 18 cm, but we don't have a vector of either of the descriptions you give.
This should be clear upon reviewing that Intro Problem Set assignment.
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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: ->->->->->->->->->->->-> :
Okay, I am pretty much close to a magnitude of 1. I guess I wasn't supposed to figure out the resultant vector, but only do vector A. Vector A give me a magnitude of 10.3. (5, 9) / 10.3 = (0.49, 0.87), which gives me a vector magnitude of 1. Multiply this new vector by the total tension associated with that vector of 0.98 N, and I get 0.98(0.49, 0.87) = (0.48, 0.85) This new vector gives me a magnitude of 0.98.
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A vector with x and y components 5 and 9, respectively, could run from the origin to the point (5, 9), and a unit vector in the same direction would be (.49, .87). So you've got a good calculation there.
However none of these questions are related to either of those vectors.
The two vectors relevant to this question are the vector from (5 cm, 9 cm) to (10 cm, 18 cm), and the unit vector in the same direction.
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• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
x component is 0.49 and the y component is 0.85
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You'll need to revise this. I believe you got started with the wrong idea. You do appear to have a lot of correct ideas that once applied to the question as stated should lead you to a good solution.
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