| Wydział budownictwa | Fotometr Bunsena | 08.03.2009 |
|---|---|---|
| Ćw. Nr 6 | Mateusz Lukas | Ocena: |
POPRAWA
$$I_{\text{teoret}} = \frac{m \bullet r^{2}}{2} = \frac{0,078 \bullet {0,156}^{2}}{2} = 0,000949\ \ \lbrack kg \bullet m^{2}\rbrack$$
$$\delta = \frac{\left| I_{D} - I_{T} \right|}{I_{T}} = \frac{\left| 0,0060965 - 0,000949 \right|}{0,000949} = 5,42413$$
-Niepewność pomiarowa dla tarczy:
$$\mathbf{I}_{\mathbf{t}}\mathbf{=}\frac{\mathbf{m \bullet g \bullet R \bullet r}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}}\mathbf{\bullet}\mathbf{T}^{\mathbf{2}}$$
$$\sqrt{\left( \frac{\mathbf{g \bullet R \bullet r \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(m)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet r \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(R)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet R \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(r)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet R \bullet r}\mathbf{\bullet 2}\mathbf{T}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(T)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{L - 4\pi}\left( \mathbf{m \bullet g \bullet R \bullet r \bullet}\mathbf{T}^{\mathbf{2}} \right)}{\left( \mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{L} \right)^{\mathbf{2}}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(L)}^{\mathbf{2}}}$$
$$\mathbf{\ }\sqrt{\left( \frac{\mathbf{9,81 \bullet 0,149 \bullet 0,066 \bullet}\mathbf{1,768}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,1)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{1,6258 \bullet 9,81 \bullet 0,066 \bullet}\mathbf{1,768}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{1,6258 \bullet 9,81 \bullet 0,149 \bullet}\mathbf{1,768}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{1,6258 \bullet 9,81 \bullet 0,149 \bullet 0,066}\mathbf{\bullet 2 \bullet 1,768}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,1)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57 - 4\pi(}\mathbf{1,6258 \bullet 9,81 \bullet 0,149 \bullet 0,066 \bullet}\mathbf{1,768}^{\mathbf{2}}\mathbf{)}}{{\mathbf{(4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57)}}^{\mathbf{2}}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{= 0,00}\mathbf{8609}$$
-Niepewność pomiarowa dla Fe:
$$\mathbf{I}_{\mathbf{\text{Fe}}}\mathbf{=}\frac{\mathbf{m \bullet g \bullet R \bullet r}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}}\mathbf{\bullet}\mathbf{T}^{\mathbf{2}}$$
$$\sqrt{\left( \frac{\mathbf{g \bullet R \bullet r \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(m)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet r \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(R)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet R \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(r)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet R \bullet r \bullet 2}\mathbf{T}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(T)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{L - 4\pi}\left( \mathbf{m \bullet g \bullet R \bullet r \bullet}\mathbf{T}^{\mathbf{2}} \right)}{\left( \mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{L} \right)^{\mathbf{2}}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(L)}^{\mathbf{2}}}$$
$$\mathbf{\ }\sqrt{\left( \frac{\mathbf{9,81 \bullet 0,149 \bullet 0,066 \bullet}{\mathbf{1,}\mathbf{462}}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,1)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{2,4079}\mathbf{\bullet 9,81 \bullet 0,066 \bullet}\mathbf{1,462}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{2,4079}\mathbf{\bullet 9,81 \bullet 0,149 \bullet}\mathbf{1,462}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{2,4079}\mathbf{\bullet 9,81 \bullet 0,149 \bullet 0,066 \bullet 2 \bullet}\mathbf{1,462}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,1)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57 - 4\pi(}\mathbf{2,4079}\mathbf{\bullet 9,81 \bullet 0,149 \bullet 0,066 \bullet}\mathbf{1,462}^{\mathbf{2}}\mathbf{)}}{{\mathbf{(4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57)}}^{\mathbf{2}}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{= 0,008}\mathbf{8}$$
-Niepewność pomiarowa dla Al:
$$\mathbf{I}_{\mathbf{\text{Al}}}\mathbf{=}\frac{\mathbf{m \bullet g \bullet R \bullet r}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}}\mathbf{\bullet}\mathbf{T}^{\mathbf{2}}$$
$$\sqrt{\left( \frac{\mathbf{g \bullet R \bullet r \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(m)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet r \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(R)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet R \bullet}\mathbf{T}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(r)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{m \bullet g \bullet R \bullet r \bullet 2}\mathbf{T}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet L}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(T)}^{\mathbf{2}}\mathbf{+}\left( \frac{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{L - 4\pi}\left( \mathbf{m \bullet g \bullet R \bullet r \bullet}\mathbf{T}^{\mathbf{2}} \right)}{\left( \mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{L} \right)^{\mathbf{2}}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(L)}^{\mathbf{2}}}$$
$$\mathbf{\ }\sqrt{\left( \frac{\mathbf{9,81 \bullet 0,149 \bullet 0,066 \bullet}{\mathbf{1,}\mathbf{258}}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,1)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{3,6949}\mathbf{\bullet 9,81 \bullet 0,066 \bullet}\mathbf{1,258}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{3,6949}\mathbf{\bullet 9,81 \bullet 0,149 \bullet}\mathbf{1,258}^{\mathbf{2}}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{3,6949}\mathbf{\bullet 9,81 \bullet 0,149 \bullet 0,066 \bullet 2 \bullet}\mathbf{1,258}}{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,1)}^{\mathbf{2}}}\mathbf{+}\sqrt{\left( \frac{\mathbf{4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57 - 4\pi(}\mathbf{3,6949}\mathbf{\bullet 9,81 \bullet 0,149 \bullet 0,066 \bullet}\mathbf{1,258}^{\mathbf{2}}\mathbf{)}}{{\mathbf{(4}\mathbf{\pi}^{\mathbf{2}}\mathbf{\bullet 0,57)}}^{\mathbf{2}}} \right)^{\mathbf{2}}\mathbf{\bullet u}\mathbf{(0,001)}^{\mathbf{2}}}\mathbf{= 0,0}\mathbf{10185}$$
Na dokładność pomiarów miały wpływ takie czynniki jak:
- pomiar odległości (niedokładność związana z odczytem podziałki suwmiarki),
- pomiar okresu drgań na który wpływ miała chwila uruchomienia i zatrzymania stopera,
a także dokładność odczytu jego wskazań,
Na dokładność pomiaru I miał dodatkowo wpływ błąd związany z pomiarem masy tarczy
i krążków. Najmniejszy moment bezwładności posiada krążek żelazny jest to krążek, który miał najmniejsza wagę a wynika z tego, że najmniejszy moment bezwładności ma ciało o najmniejszej wadze.