A student investigated the damping of a rotational pendulum using the apparatus shown - Edexcel - A-Level Physics - Question 3 - 2023 - Paper 6

To plot the graph:

1. Calculate ln(θ) for each angle θ in the table:

   n	θ/°	ln(θ)
   10	124	4.820
   20	82	4.400
   30	55	3.988
   40	37	3.610
   50	25	3.219
   60	16	2.772

2. Draw axes with appropriate scaling, labeling the x-axis as n and the y-axis as ln(θ).

3. Plot the points for ln(θ) against n accurately.

4. Draw the best fit line through the points.

To find the value of z:

1. Determine the gradient of the best fit line plotted on the graph. Use two clear points (e.g., (10, 4.820) and (60, 2.772)).

2. The slope (gradient) is given by:

   z = -rac{ ext{change in } ext{ln}( heta)}{ ext{change in } n}

3. Plug in the respective values and compute z. This will yield the value of z, which will be negative.

To verify the student's claim, we must compare the value of θ₀ that we calculated from the y-intercept of the ln(θ) vs. n graph:

1. The y-intercept ln(θ₀) gives the initial value of θ.

2. To find θ₀, we raise e to the power of the y-intercept value:

   $$heta₀ = e^{ ext{y-intercept}}$$

3. Evaluate θ₀ to see if it is greater than 180°.

4. If θ₀ > 180°, then the student's claim is correct. If θ₀ ≤ 180°, the claim is incorrect.