Galileo

This activity allows students to experimentally determine the value of the acceleration of gravity by analyzing a free fall. It reproduces Galileo's historical approach with modern tools.

In the late 16th century, Galileo Galilei challenged two millennia of Aristotelian physics by demonstrating that all objects fall at the same rate regardless of their weight. According to legend, he dropped balls of different masses from the Leaning Tower of Pisa; in reality, he used inclined planes to slow down the motion enough to measure it with the crude timekeeping devices available. His discovery that the distance fallen is proportional to the square of the elapsed time was revolutionary and laid the groundwork for Newton's laws of motion. Today, the same measurement that occupied Galileo for years can be performed in seconds using a smartphone. By dropping a phone (safely cushioned) from a measured height and recording the accelerometer data during the fall, students can directly observe the transition from rest to free fall and back to rest upon impact. The duration of the free-fall phase, combined with the known drop height, yields a measurement of the acceleration of gravity.

Activity overview:

The student drops their smartphone (protected by a pillow) from a known height and records linear acceleration data during the fall. By identifying the start and end of the fall on the acceleration graph and measuring the elapsed time the student can calculate g using the relationship between height and time in a free fall.

Level:

High school

FizziQ

Author:

Duration (minutes) :

25

What students will do :

- Measure the acceleration of gravity by analyzing the free fall of a smartphone
- Identify the different phases of motion (rest, free fall, impact) on the accelerometer graph
- Apply the kinematic equation h = ½gt² to calculate g from the measured fall time and known height
- Compare the experimental value with the accepted value and evaluate sources of error
- Reproduce Galileo's historical discovery using modern digital tools

Scientific concepts:

- Free fall
- Acceleration of gravity
- Laws of Galilee
- Potential energy conversion
- Interpreting acceleration graphs

Sensors:

- Accelerometer (absolute acceleration or Z-axis component)

Material needed:

- Smartphone with the FizziQ application
- A soft pillow to hold the smartphone
- Tape measure to measure the height of fall
- FizziQ experience notebook

Experimental procedure:

Prepare a thick pillow or cushion on the floor to safely catch the smartphone.
Measure the drop height from the bottom of the smartphone (when held) to the top of the cushion. Use a tape measure and record the value in meters.
Open FizziQ and select the Accelerometer sensor. Choose absolute acceleration and set the sampling rate to maximum.
Place the smartphone in a protective padded sleeve or box (a sock stuffed with soft material works well).
Hold the protected smartphone at the measured height. Ensure the cushion is directly below.
Start recording in FizziQ. Wait 2-3 seconds (to record the initial resting phase), then release the phone cleanly without pushing or spinning it.
After the phone lands on the cushion, wait 2-3 seconds, then stop recording.
Examine the acceleration graph. You should see three distinct phases: a flat region near 9.81 m/s² (rest), a sudden drop to near 0 m/s² (free fall), and a sharp spike (impact).
Identify the start and end of the free-fall phase precisely. The start is where the acceleration drops below 1 m/s², and the end is where the impact spike begins.
Measure the duration of free fall (Δt) from the graph.
Calculate g using the equation: g = 2h / (Δt)², where h is the drop height.
Repeat the measurement 5 times from the same height and calculate the average and standard deviation of your g values.
Try a different drop height and verify that the same value of g is obtained.

Expected results:

For a drop height of 1.0 meter, the free-fall duration should be approximately 0.45 seconds, yielding g ≈ 9.9 m/s². Typical experimental values range from 8.5 to 11 m/s², with the main sources of error being the precise identification of the start and end of the free-fall phase (timing uncertainty of ±0.01-0.02 seconds has a large effect because the fall is so brief) and the measurement of the drop height (±2 cm). Air resistance is negligible for a smartphone-sized object over a 1-meter fall. The impact spike can reach 20-100 m/s² depending on the cushioning. Students should observe that the accelerometer reads near zero during free fall, not 9.81 m/s², which is a direct manifestation of Einstein's equivalence principle.

Scientific questions:

- Why does the accelerometer read approximately zero during free fall instead of 9.81 m/s²?
- How does this observation relate to Einstein's equivalence principle?
- What was Galileo's original experiment, and why did he use inclined planes instead of direct free fall?
- How does the precision of your measurement compare to Galileo's? What modern advantages do you have?
- If you dropped two phones of different masses simultaneously, would they hit the cushion at the same time?
- What is the terminal velocity of a smartphone, and at what drop height would air resistance become significant?

Scientific explanations:

Galileo revolutionized physics in the 17th century by discovering that, contrary to Aristotelian beliefs, all bodies fall with the same acceleration regardless of their mass. For a fall without initial speed, the relationship between height h and time t is given by: h = ½gt².

This equation allows us to calculate g by precisely measuring h and t. The smartphone's accelerometer measures linear acceleration on three axes.

During free fall, in the absence of air resistance, the device should measure zero acceleration on all axes (state of weightlessness), but this value is difficult to observe in practice. To determine g, it is more reliable to identify the start and end of the drop on the graph: the start corresponds to the moment when the acceleration drops suddenly (when the smartphone is dropped), and the end to the moment of an acceleration peak (impact on the pillow).

The time elapsed between these two events corresponds to the fall duration. Knowing the height h and the duration t, we calculate g = 2h/t².

The main sources of error include: air resistance (which becomes significant beyond 1-2 meters of drop), inaccuracy in height measurement, and human reaction time if triggered manually. Carrying out several tests allows you to improve the precision by calculating the average.

This simple experiment reproduces Galileo's conceptual approach with modern tools and perfectly illustrates the transition from a physical observation to a quantitative law.

Extension activities:

Frequently asked questions:

Q: The free-fall duration seems too short to measure accurately. How can I improve precision?
R: Drop from a greater height (1.5-2.0 m) to increase the fall time. Ensure you are reading the graph at maximum time resolution. The start and end of free fall should be identified by the sharp transitions in the acceleration signal.

Q: My value of g is consistently too high (above 10.5 m/s²). What might be wrong?
R: If the measured fall time is too short (perhaps because you are identifying the end of free fall too early, before the impact spike), g will be overestimated. Check that you are measuring to the very beginning of the impact spike. Also verify that you measured the drop height correctly.

Q: Is it safe to drop my smartphone onto a pillow?
R: Yes, modern smartphones are designed to withstand drops from 1-2 meters onto hard surfaces. A cushioned landing produces much lower impact forces than an accidental drop. Use adequate padding to prevent damage.

Q: Why does the acceleration not return to 9.81 m/s² immediately after impact?
R: The phone may bounce or wobble on the cushion, producing oscillating readings for a second or two after impact. This is normal and reflects the elastic response of the cushion.