Blog

Free-fall Lab

1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2 Points)

Suppose you are using external resources; include the reference. It would be best if you had any relevant formulas and explanations of each term. You may use the rich formula tools embedded here.

2) Hypothesis: In an If /Then statement, highlight the purpose of the experiment.

For instance: If two same shape objects with different masses are dropped from the same height, they will hit the ground simultaneously. (2 points)

Post-lab section:

3) Attach your analysis here, including any table, chart, or plot image. (3 Points)

4) Attach the image of any table, chart, or plot here. (4 points)

Each part is 2 points.

Table 1 and the calculation of the percent error.

Table 2 and the calculation of the percent error.

5) Attach the image of samples of your calculation here. (2 points)

6) In a paragraph between 100 and 150 words, explain what you Learn. What conclusion can you draw from the results of this lab assignment? (2 points)

7) In one sentence, compare the results of the experiment with your Hypothesis. Why? (1 point)

8) Attach your response to the questions in the lab manual here. (4 points)

• 1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2 Points),

• 2) Hypothesis: In an If /Then statement highlight the purpose of the experiment.,

• 3) Attach your analysis here including any table chart or plot image. (3 Points),

• 6) In a paragraph between 100 and 150 words explain what you Learn. ,What conclusion can you draw from the results of this lab assignment? (2 points),

• 7) In one sentence, compare the results of the experiment with your Hypothesis. Why? (1 point),

---

Comprehensive Answers (general)

1) Introduction (theory — ~180 words)

This experiment explores the kinematics of free-falling bodies and the determination of gravitational acceleration (g) using measured distances and times. For an object released from rest and falling under uniform gravity (neglecting air resistance), the displacement $s$ after time $t$ follows the kinematic equation

s=ut+12at2s = ut + \tfrac{1}{2} a t^2s=ut+21​at2

where $u$ is initial velocity (here $u=0$), and $a$ is acceleration (for free-fall, $a=g$). Thus s=12gt2s = \tfrac{1}{2} g t^2s=21​gt2. Rearranging gives g=2s/t2g = 2s/t^{2}g=2s/t2. An alternative analysis plots $s$ versus t2t^{2}t2: the slope of that linear plot equals 12g\tfrac{1}{2}g21​g, so $g=2\times (\text{slope})$. Important experimental considerations: measurement uncertainty in distance and time (±∆s, ±∆t), reaction time when using a stopwatch, and air drag which becomes important for low-mass or high-surface-area objects. Percent error is used to compare measured gexpg_\text{exp}gexp​ with the accepted value gtheog_\text{theo}gtheo​ (standard near Earth’s surface ~9.806 m/s²):

% error=∣gexp−gtheogtheo∣×100%.\%\text{ error} = \left|\frac{g_\text{exp}-g_\text{theo}}{g_\text{theo}}\right| \times 100\%.% error=​gtheo​gexp​−gtheo​​​×100%.

References (example): classical kinematics textbooks or lab manual. Define each term when used (s = displacement in m, t = time in s, g = acceleration due to gravity in m/s²).

---

2) Hypothesis (If / Then)

If identical-shape objects of different masses are dropped from the same height in the same environment, then they will hit the ground at (nearly) the same time because gravitational acceleration is independent of mass when air resistance is negligible.

---

3) Analysis (tables, chart/plot, percent error — textual + worked example)

Below is a complete, general analysis you can copy into your report. Replace the sample data with your measured data and attach images of your actual tables/plots where requested.

How to analyze & what to plot

• Collect several trials for each drop height (e.g., 0.5 m, 1.0 m, 1.5 m). For each trial record measured time $t$.

• Compute average time tˉ\bar{t}tˉ and t2t^2t2 for each height.

• Table distance $s$ (m) vs average t2t^2t2 (s²). Fit a straight line; slope = ½ g.

Sample Table 1 — raw data and averages (text)

Linear fit method
Perform linear regression of $s$ (y-axis) vs t2t^2t2 (x-axis). For these sample numbers, slope ≈ 4.90 m/s² (this is 12g \tfrac{1}{2}g21​g ), so measured gexp=2×slope≈9.80 m/s2g_\text{exp} = 2 \times \text{slope} \approx 9.80\ \text{m/s}^2gexp​=2×slope≈9.80 m/s2.

Percent error calculation (Table 1 example)
Let gtheo=9.806 m/s2g_\text{theo}=9.806\ \text{m/s}^2gtheo​=9.806 m/s2, gexp=9.80 m/s2g_\text{exp}=9.80\ \text{m/s}^2gexp​=9.80 m/s2

%error=∣9.80−9.8069.806∣×100%≈0.06%.\%\text{error} = \left|\frac{9.80-9.806}{9.806}\right|\times100\% \approx 0.06\%.%error=​9.8069.80−9.806​​×100%≈0.06%.

Table 2 — alternate method (g from each height)
Compute $g$ per height using g=2s/tˉ2g = 2s/\bar{t}^2g=2s/tˉ2.

Sample calculation (step-by-step)

1. For height 1.00 m, avg time tˉ=0.450\bar{t}=0.450tˉ=0.450 s, tˉ2=0.2025\bar{t}^2 = 0.2025tˉ2=0.2025 s².

2. g=2s/tˉ2=2(1.00)/0.2025=9.8765 m/s2.g = 2s/\bar{t}^2 = 2(1.00)/0.2025 = 9.8765\ \text{m/s}^2.g=2s/tˉ2=2(1.00)/0.2025=9.8765 m/s2.

3. Percent error = $|(9.8765-9.806)/9.806|\times 100\%\approx 0.72\%.$

Chart/plot instructions

• Plot $s$ (vertical axis) vs t2t^2t2 (horizontal axis).

• Add linear trendline and report slope ± uncertainty.

• Compute $g=2\times \text{slope}$ and include uncertainty propagation: if slope uncertainty is $\Delta m$, then $\Delta g=2\Delta m$.

Notes about attachments

• I cannot attach images here; when you prepare the lab file: include (a) a scanned photo of Table 1, (b) the plotted graph (s vs t2t^2t2) with trendline and equation visible, (c) screenshots of calculation steps. Use high-contrast photos and crop tightly so numbers are legible.

---

4) (Requested attachment of image of table/chart) — guidance for your submission

• Save your spreadsheet table as an image (PNG/JPG) or export the plotted chart as PNG.

• Label axes (distance in m, time² in s²), include units and best-fit line equation (e.g., s=(4.90) t2+0.003s = (4.90)\,t^2 + 0.003s=(4.90)t2+0.003).

• Place these image files into your lab report PDF or upload where required.