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course phy 201
12-27 3:30
Three Rubberband System
You measured the x and y coordinates of the ends of three rubber band chains, all three of which were attached to a central paper clip. You also measured the tension in each chain by opposing it to your ‘colored’ calibrating chain.
You should have reported your analysis of this activity, according to instructions outlined in previous class notes. Outline of the procedure:
· find the displacement vector from the paperclip end of each rubber band chain to the other end
· use the displacement vector to get a unit vector in the direction of the tension
· find the tension force from the length of the ‘colored’ calibrating chain
· for each chain multiply the unit vector by the tension force to get the tension vector
· add up the x components of all three tension vectors, and do the same for the y components
· compare your results with the ideal result
You should include a copy of your report here. If you have submitted it you may include a copy of the document from your Access Page.
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measurements in cm
( x , y)
(18.5,37)
(44,42.5)
(53.5,24)
(54,23.2)
(57,21.5)
(81,8.5)
vector 1 vector 2 vector 3
(x) 53.5-18.5=35 53.5-44=9.5 81-57=24
(y) 24-37=-13 24-42.5=-18.5 8.5-21.5=-13
sqrt(35^2+(-13)^2)=32.5 sqrt(9.5^2+(-18)^2)=20.8 sqrt(24^2+(13)^2)=27.3
x comp y comp x comp of lgth y comp of lgth calib lgth force(in dominos) force*ycomp of lgth force*xcomp of lgth
RB 1 53.5-18.5=35 24-37=-13 35/37.3=.94 -13/37.3=-.35 33 cm 5 5 dom*.35cm=-1.75 dom cm 5dom*.94cm=4.7
RB 2 53.5-44=9.5 24-42.5=-18.5 9.5/20.8=.46 -18.5/20.8=-.89 28 cm 2 2 dom*-.89=-.78 2 dom*.46=.92
RB 3 81-57=24 8.5-21.5=-13 24/27.3=.88 -13/27.3=-.48 32.8 cm 5 5 dom*-.48=-2.4 5 dom*.88=4.4
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The points on the central paperclip appear to be
(53.5,24)
(54,23.2)
(57,21.5)
Each vector should be calculated by subtracting the coordinates on the central paperclip from the coordinates of the other endpoint.
The 'far endpoints' of the three rubber bands would be
(18.5,37)
(44,42.5)
(81,8.5)
It isn't completely clear which of these goes with which point on the central paperclip, but the differences in the coordinates of the central-clip points don't vary a lot, so your results are overall plausible. However you should have stated which two points go with which rubberband chain. You appear to have used (53.5, 24) for two different chains.
The more important error is the order of subtraction. You subtracted in the correct order for one of the three vectors, but not the other two. The main effect is that the components two of your vectors have the wrong signs.
Other than the signs, most of your calculations are correct, and are well-done.
Can you correct the signs, and perhaps a couple of other more minor errors, and resubmit?
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