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Gdetermination.maple.txt
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Gdetermination.maple.txt
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MethodS For Determining G.
Restart and set constant values to be used.
> restart;
This is the lierature value for G
> litValue:=6.67384 * 10^(-11);
-11
6.673840000 10
Taking 30.01 to be the depth of the housing, I can half that and take away 1mm
from an estimate.
The estimate is that the rod holding the two m1 masses is approximately 2mm in
diameter.
Since it is holding the mirror in front of it.
> Lo:=(630.5+14+15)*10^(-3);
0.6595000000
> b:=((63.01+30.1)*10^(-3))/2;
0.04655500000
Taken from the first swing S:=20.96*10^(-3);
> S:=20.939*10^(-3);
0.02093900000
> alpha := arctan(S/Lo)/2;
0.01586957422
Alpha is much less than 1.
> L1 := S*Lo/(2*alpha);
0.4350863580
Beta is not that nuch less than 1.
> beta:=arccos(Lo/L1);
0.9764157875 I
opposite over hypoteneuse for Beta
> L:=L1/Lo;
0.6597215436
Error from L
> ((L-Lo)/L)*100;
0.03358138023
> T:=608.353;
608.353
> d:=49.3*10^(-3);
0.04930000000
> m2:=1.5085;
1.5085
> m1:=0.015;
0.015
Moment of Inertia of the wee masses m1;
> 2*m1*d^2;
0.00007291470000
Deflection
> G:=(S,T)->(Pi^2* S * b^2*d)/ (T^2 * m2*L);
2 2
Pi S b d
(S, T) -> ----------
2
T m2 L
> evalf(G(S,T));
-11
5.995397393 10
Correction factor.
> K:= (b^3)/(b^2 + (4*d^2))^(3/2);
0.07783286727
> Gfin1:=evalf(G(S,T)/(1-K));
-11
6.501421684 10
Gives the percentage accuracy.
> pe1:=((litValue-Gfin1)/Gfin1);
0.02652009428
> error1:=(Gfin1*pe1)/10^(-11);
0.1724183160
Acceleration
> ao:=(4.4010*10^(-3)*d)/(60*60*L);
-8
9.135558871 10
> G2:=(b^2*ao)/ (2*(m2)*(1-K));
-11
7.116768405 10
> evalf(G2);
-11
7.116768405 10
Gives the percentage accuracy. Error on acceleration value (using 2.5% erorr
0.77*10^{-11}
> pe2:=evalf(abs(litValue-G2)/G2);
0.06223729364
> evalf(G2*pe2);
-12
4.429284050 10
Determining G Errors
> restart;
> G:=(S,T)->(Pi^2* S * b^2*d)/ (T^2 * m2*L);
2 2
Pi S b d
(S, T) -> ----------
2
T m2 L
> errGrad:=0.6297/(3600);
0.0001749166667
> dT:=diff(G(S,T),T);
2 2
2 Pi S b d
- ------------
3
T m2 L
> dS:=diff(G(S,T),S);
2 2
Pi b d
--------
2
T m2 L
> db:=diff(G(S,T),b);
2
2 Pi S b d
-----------
2
T m2 L
> dd:=diff(G(S,T),d);
2 2
Pi S b
--------
2
T m2 L
> dL:=1*10^(-3);
1
----
1000
> dL:=diff(G(S,T),L);
2 2
Pi S b d
- ----------
2 2
T m2 L
> dm2:=diff(G(S,T),m2);
2 2
Pi S b d
- ----------
2 2
T m2 L
Put in the constant values now.
> T:=608.353;
608.353
> d:=49.3*10^(-3);
0.04930000000
> m2:=1.5085;
1.5085
> b:=((63.01+30.1)*10^(-3))/2;
0.04655500000
> L:=(630.5+14+15)*10^(-3);
0.6595000000
> val:=sqrt((0.02)^2+(dd*errd)^2+(db*errb)^2+(0.011)^2+(dL*errL)^2+(0.01)^2);
/ -17 4 2 2 -16 4 2 2
\0.000621 + 3.465153510 10 Pi S errd + 1.554331494 10 Pi S errb
-19 4 2 2\
+ 1.936362742 10 Pi S errL /^(1/2)
> errd:=(0.1*10^(-3));
0.0001000000000
> errb:=0.1*10^(-3);
0.0001000000000
> errS:=20.96*10^(-3)*0.02;
0.0004192000000
> errL:=0.1*10^(-3);
0.0001000000000
> errm2:=0.01*m2;
0.015085
Just using the first calculation here to keep it simple.
> S:=20.96*10^(-3);
0.02096000000
Percentage error on G.
> hyevalf(val)*100;
/ (1/2)\
|/ -28 4\ |
100 hyevalf\\0.000621 + 8.359337633 10 Pi / /