#$&*
Phy 231
Your 'cq_1_16.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A rubber band has no tension until it reaches a length of 7.5 cm. Beyond that length its tension increases by .7 Newtons for every additional centimeter of length.
What will be its tension if its endpoints are at the points (5 cm, 9 cm) and (10 cm, 17 cm) as measured on an x-y coordinate system?
answer/question/discussion: ->->->->->->->->->->->-> :
0.7 N / 1 cm = 0.7 N / 0.01 m
(0.7N / 0.01 m) * 'ds
(0.7 N / 0.01 m * 0 m = 0N
(0.7N / 0.01 m) * 0.015 m - 1.05 N
(0.7N / 0.01 m) * 0.025 m = 1.75 N
(0.7N / 0.01 m) * 0.095 m = 6.65 N
#$&*
What is the vector from the first point to the second?
answer/question/discussion: ->->->->->->->->->->->-> :
vector = (xf - xo) + (yf - yo) = (9 cm - 5 cm) +(1.05N - 0N) = 4 cmi + 1.05 N j
#$&*
@&
4 cm * i + 1.05 N * j is not a vector. Its components do not have the same units.
*@
What is the magnitude of this vector?
answer/question/discussion: ->->->->->->->->->->->-> :
mag = 'sqrt (x^2 + y^2) = 'sqrt (4cm ^2 + 1.05N^2) = 4.135 N cm
@&
sqrt(cm^2 + N^2) is not N cm. This expression cannot be simplified, so the unit would be just sqrt(cm^2 + N^2).
*@
#$&*
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: ->->->->->->->->->->->-> :
4 cm / 4.135 N cm + 1.05 N / 4.135 N cm = 0.967 Ni + 0.2539 cmj
#$&*
The new vector should have magnitude 1. When you divide a vector by its magnitude the result is a vector with magnitude 1. We call a vector of magnitude 1 a unit vector. What vector do you get when you multiply this new vector (i.e., the unit vector) by the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
mag = 'sqrt( 0.967^2 + 0.254^2) = 0.999 = 1
New vector time Tension @ 9 cm
1.05 N *( 0.967 i + 0.254 j) = 1.02i + 0.267j
#$&*
What are the x and y components of the new vector?
answer/question/discussion: ->->->->->->->->->->->-> :
1.02 i + 0.267j
#$&*
*#&!
@&
You got off on the wrong foot near the beginning of the problem.
(0.7N / 0.01 m) * 0.095 m = 6.65 N is a correct calculation. After that your vectors don't have consistent units so they aren't really vectors. You can't have a vector whose x component is a distance and whose y component is a force.
The components of the requested vector are both displacements.
Give this one another try.
*@