courses:phy101l:2
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| courses:phy101l:2 [2023/06/17 10:10] – asad | courses:phy101l:2 [2023/10/15 04:02] (current) – asad | ||
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| ====== 2. Gravitational acceleration from a pendulum ====== | ====== 2. Gravitational acceleration from a pendulum ====== | ||
| + | [[https:// | ||
| ===== - Introduction and theory ===== | ===== - Introduction and theory ===== | ||
| + | {{https:// | ||
| + | |||
| For a simple pendulum | For a simple pendulum | ||
| Line 8: | Line 11: | ||
| For a compound pendulum | For a compound pendulum | ||
| - | $$ T = 2\pi \sqrt{\frac{K^2/l+l}{g}} $$ | + | $$ T = 2\pi \sqrt{\frac{\frac{K^2}{l}+l}{g}} $$ |
| and, hence, a compound pendulum is equivalent to a simple pendulum if | and, hence, a compound pendulum is equivalent to a simple pendulum if | ||
| Line 15: | Line 18: | ||
| which is a quadratic equation with two solutions $l_1$ and $l_2$ where $l_1+l_2=L$ and $l_1l_2=K^2$. | which is a quadratic equation with two solutions $l_1$ and $l_2$ where $l_1+l_2=L$ and $l_1l_2=K^2$. | ||
| + | |||
| + | You have to find gravitational acceleration $g$ and radius of gyration $K=\sqrt{l_1l_2}$. | ||
| ===== - Method and data ===== | ===== - Method and data ===== | ||
| + | |||
| + | ==== - Data table ==== | ||
| + | ^ Hole no. ^ Distance [cm] ^ Trial ^ Time for 10 oscillations [s] ^ | ||
| + | | 1 | 10 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 2 | 20 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 3 | 30 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 4 | 40 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 6 | 60 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 7 | 70 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 8 | 80 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| + | | 9 | 90 | 1 | | | ||
| + | |:::|:::| 2 | | | ||
| ===== - Graphical analysis ===== | ===== - Graphical analysis ===== | ||
| - | ===== - Results | + | ===== - Calculating g ===== |
| + | Find $R$ from here: https:// | ||
| + | |||
| + | $$ g = \frac{GM}{R^2} $$ | ||
| ===== - Discussion and conclusion ===== | ===== - Discussion and conclusion ===== | ||
| + | Answer the following questions in Discussion. | ||
| + | - Why the angle of deflection of the pendulum should not be large? | ||
| + | - Why are the periods at 10, 30, 70 and 90 cm similar? | ||
| + | - Why do you get two symmetric curves after plotting $T$ as a function of $l$. | ||
| + | - If your were periods at 10, 30, 70 and 90 cm were not as similar as expected, discuss why this happened? | ||
courses/phy101l/2.1687018201.txt.gz · Last modified: by asad