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

• Youtube: Oil drop diagrams Note provocative comment about using videos instead of teachers.
• Pilot pages: Phy1010 . HTW
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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

08-28W

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

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

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

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

Accelerated motion

$a={\frac {g\sin \theta }{1+{\frac {I}{MR^{2}}}}}$ where the moment of inertia of a solid sphere is $I={\tfrac {2}{5}}MR^{2}$, and,

$\sin \theta =h/\ell$ 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:

$g={\frac {7}{5}}{\frac {\ell }{h}}a$

Calculating acceleration

It can be shown that for three consecutive locations $(x_{0},x_{1},x_{2})$ along straight line:

$a={\frac {\Delta v}{\Delta t}}={\frac {x_{2}-2x_{1}+x_{0}}{\Delta t^{2}}}$

See also Wikipedia:Finite difference coefficient