Describe the experimental procedure for determining the Earth's gravitational field strength using a simple pulley system, including a diagram and assumed values.

Here is the solution for the experiment "Determining the Earth's Gravitational Field Strength Using a Simple Pulley System", using assumed values as requested:

Diagram

\begin{tikzpicture}[scale=1.0] % Clamp stand \draw[thick] (0,0) -- (0,5); \draw[thick] (-1,5) -- (1,5); \draw[thick] (0,0) -- (2,0); \node at (0.5,5.3) {Clamp}; \node at (1,0.3) {Stand}; % Pulley \draw[thick] (0,4.5) circle (0.5); \draw[thick] (0,4.5) -- (0,5); \node at (0.8,4.5) {Pulley}; % String \draw[thick] (0,4) -- (-2,4); \draw[thick] (0,4) -- (2,4); % Mass m1 \draw[thick] (-2,4) -- (-2,3); \draw[thick, fill=gray!50] (-2,3) rectangle (-2.5,2.5); \node at (-2.25,2.2) {$m_1$}; % Mass m2 \draw[thick] (2,4) -- (2,1); \draw[thick, fill=gray!50] (2,1) rectangle (2.5,0.5); \node at (2.25,0.2) {$m_2$}; % Metre Rule \draw[thick] (2.8,0) -- (2.8,4); \foreach \y in {0,1,2,3,4} \draw (2.8,\y) -- (2.9,\y) node[right] {\y}; \node at (3.2,2) {Metre Rule (m)}; % Height h \draw[<->] (2.6,1) -- (2.6,4) node[left, midway] {$h$}; % Stopwatch \draw[thick] (-3,0.5) rectangle (-2,1.5); \node at (-2.5,1) {Stopwatch}; \end{tikzpicture}

Procedure

1. Set up the apparatus as shown in the diagram. Ensure the pulley is frictionless and the string is light and inextensible.
2. Measure the masses of the two mass holders, $m_1$ and $m_2$, using an electronic balance. Adjust them so that $m_1 > m_2$.
3. Attach $m_1$ and $m_2$ to the ends of the string, passing the string over the pulley.
4. Adjust the position of $m_1$ to a suitable initial height ($h$) above the ground, using the metre rule.
5. Release the system from rest and simultaneously start the stopwatch.
6. Stop the stopwatch when $m_1$ hits the ground. Record the time $t$.
7. Repeat steps 4-6 for the same height $h$ at least three times to obtain an average time.
8. Vary the height $h$ (e.g., $0.2 \text{ m}, 0.3 \text{ m}, 0.4 \text{ m}, 0.5 \text{ m}, 0.6 \text{ m}$) and repeat steps 5-7 for each height.
9. For each height, calculate the average time $t$ and then $t^2$.

Observations/Results

• Assumed mass $m_1 = 0.55 \text{ kg}$
• Assumed mass $m_2 = 0.45 \text{ kg}$
• Total mass $M = m_1 + m_2 = 0.55 \text{ kg} + 0.45 \text{ kg} = 1.0 \text{ kg}$
• Difference in mass $\Delta m = m_1 - m_2 = 0.55 \text{ kg} - 0.45 \text{ kg} = 0.1 \text{ kg}$

Height $h$ (m)	Time $t_1$ (s)	Time $t_2$ (s)	Time $t_3$ (s)	Average Time $t$ (s)	$t^2$ (s$^2$)
0.2	0.64	0.63	0.64	0.64	0.41
0.3	0.78	0.79	0.78	0.78	0.61
0.4	0.90	0.91	0.90	0.90	0.81
0.5	1.01	1.