Phy 231
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.
** **
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: ->->->->->->->->->->->-> :
length: sqrt((10-5)^2 + (17-9)^2) = 9.43cm
9.43cm-7.5cm = 1.93 additional cm
Tension = 1.93cm * .7N = 1.351 J
Very good, but the units would be
Tension = 1.93cm * .7N/cm = 1.351 N
#$&*
• What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
10-5cm = 5cm
17cm-9cm = 8cm
5i + 8j
#$&*
• What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
magnitude = sqrt( 5^2 + 8^2) = 9.43 cm
#$&*
• What vector do you get when you divide this vector by its magnitude? (Specify the x and y components of the resulting vector).
answer/question/discussion: ->->->->->->->->->->->-> :
x component = 5 / 9.43 = .530
y component = 8 / 9.43 = .848
vector = .530i + .848j
#$&*
• 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: ->->->->->->->->->->->-> :
( .530i + .848j) * 1.351 = .716i + 1.15j
With units:
( .530i + .848j) * 1.351 N = .716 N * i + 1.15 N * j.
#$&*
• What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
x component: .716 cm
y component: 1.15 cm
The units would be Newtons.
#$&*
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.
** **
20 minutes
Excellent work, but be sure to see my notes (and check out the discussion at the link) regarding the units. You will have no trouble understanding.
&#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
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#