Wright State University Lake Campus/2019-9/Oil drop kinematics

Wright State University Lake Campus/2019-9/Phy 1050/Notes How Things Work (HTW)
Wright State University Lake Campus/2019-9/Phy 1110/Notes College Physics (CP1)


Initial effort by HTW

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08-28W

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  1. Mozart D-minor piano 126-132 beats per minute. We got 150 beats/min. Is this a big deal? 150/129=1.16
  2. https://www.youtube.com/watch?v=7QgOBbKl0eY


Buzzwords (vocabulary): inclined plane  ... rise and run  ... uniform sphere  ... Galileo's rule of 1, 3, 5, 7  ... uncertainty/error

08-29R

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Took data on solid sphere rolling down incline

At beat t=-1 ball was relased. Distances from release point shown shown in centmeters for three trials (a,b,c). We conducted four trials. The rise was 3.1±.1 cm, and the hypotenus was 138±1 cm. I am not sure where the ball was released: 0 cm or 0.5cm?

The accelerations are shown on the right, it seems to be the median suggests that it's 14 + or - 4 cm/s2.

t a b c * Dt (sec) a b c h ell frac 7/5 a(med) g(meas)
0 2 2 2 * 1.6
1 32 30 33 * 1.6 10 13.75 23.125 3 138 1.4 13.75 885.5
2 78 80 101 * 1.6 13.125 20 2.5 3 138 1.4 13.125 845.25
3 145 162 173 * 1.6 cm/s/s cm/s/s cm/s/s a(ave) is: 13.75

08-30F

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Same Mozart. From this we conclude that the syncopation error will probably be small. In other words, why switch to more boring music if it doesn't get us better results?

bars sec bars/sec beats/min sec/bar
15 26 0.576923077 138.4615385 1.7333
29 45 0.644444444 154.6666667 1.5517
3 4.97 0.60362173 144.8692153 1.6567
15 23 0.652173913 156.5217391 1.5333
15 26.3 0.570342205 136.8821293 1.7533
0.609501074 146.2802578 ave 1.6457
0.037654083 9.036979948 sddev 0.101
6% 6% sd/ave
25% 25% off by 1 beat
13% 13% half beat
6% 6% sd/ave
25% 25% off by 1 beat
13% 13% half beat

Data by 1110

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https://tools.wmflabs.org/excel2wiki/

0 a1 a2 a3 c1 c1 c1 b1 b2 b3
1 40 50 46 25 30 32 4.5 4 4
2 90 125 122 85 79 97 62 53 45
3 182 200 200 151 163 179 152 158 131

Formulas

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Accelerated motion

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  where the moment of inertia of a solid sphere is  , and,

  is the ratio of height to track-length. A good way to evaluate our accuracy is to solve this for g and see how close it is to the accepted result of approximately 980 cm/s2. For the exact value of g at your location, visit https://www.sensorsone.com/local-gravity-calculator/.

In "How-things-word" we did the algebra to get:

 

Calculating acceleration

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It can be shown that for three consecutive locations   along straight line:

 

See also Wikipedia:Finite difference coefficient