Question

So 30.4 Uslape 8. The slope of this graph is related to the value of g Table 3 152 117.5 73 Measured L= L = L= Slope Std-dev %U.** length (m) 1520 Mazs 0.730.035090.304 (of slope) tio (sec) 128 902132 1045 13,73 10:41 10.2643 T(sec) 2.30.12.132/1.600 1.3231,00 m/5 T (sec) 15.7214.545.2.771.8851.1686 Uslope=3(std-dev)/VN ** %U, =100%( Uslope /slope) Referring to equation (3), where: slope* g/(47°) . Thus: gpendulum = (47°)* slope Spendulum = 10:43 _units M/S2

Answer 1

Plotting L(on y-axis) and T² on x-axis in excel, adding trandline and dislplaying the equation on graph and setting intersept to zero.

The equation will be:

y=0.2633x; Hence, slope will be 0.2633

For individual points, find the ratio L/T² , those will be individual slopes S_i

Hence, S₁= 0.2661

S₂=0.2585

S₃=0.2635

S₄=0.2652

S₅=0.2601

and the mean slope is, S=0.2633

Now, standard deviation of slope will be:

$\sigma=\sqrt{\frac{\sum_{i=1}^{5}(S_i-S)^2}{5}}$

$\sigma=\sqrt{\frac{ 0.0031^2+0.0048^2+0.0002^2+0.0019^2+0.0032^2}{5}}$

$\sigma=10^{-4}\sqrt{\frac{ 31^2+ 48^2+ 2^2+ 19^2+ 32^2}{5}}$

$\sigma=10^{-4}\sqrt{\frac{ 961+ 2304+ 4+ 361+ 1024}{5}}$

$\sigma=10^{-4}\sqrt{930.8}$

$\sigma=0.0031$

Now, $U_{slope}=\frac{3\sigma}{\sqrt{5}}=\frac{3 *0.0031}{\sqrt{5}}=0.0042$

%$U_{g}=100*\frac{U_{slope}}{S}=100*\frac{0.0042}{0.2633}=1.595percent$

$g_{pendulum}=4\pi^2*S=4\pi^2*0.2633=10.39m/s^2$