Free fall: measuring g with a smartphone

Free fall is the motion of a body subject only to the influence of gravity, without air resistance or any other force. The object then accelerates at a constant rate, with an acceleration equal to g, approximately 9.81 m/s² at the Earth’s surface.

Discover FizziQ

How to measure it in class

With the FizziQ app, it is possible to measure the acceleration of gravity by analyzing a free fall.

Steps:

Internal stopwatch method: drop the smartphone from a known height onto a cushion. FizziQ records the fall duration thanks to the accelerometer, which detects the moment of release and the impact.
Video analysis method: film the fall of a ball with FizziQ and use the tracking tool to measure the successive positions in each frame.
From the measured positions, calculate the velocity at each instant and verify that the acceleration is constant. The slope of the velocity-time graph gives g.
Compare the value obtained with 9.81 m/s². Discuss the discrepancies: air resistance, tracking precision, local conditions.

Scientific activities on this topic

Several experiments allow you to study free fall with a smartphone.

Learn more

Galileo’s experiments

Galileo is recognized for his pioneering work on falling bodies in the 16th century. Contrary to the Aristotelian belief that heavy objects fall faster, he demonstrated that all bodies fall with the same acceleration in a vacuum, regardless of their mass. This discovery laid the foundations of classical mechanics.

Newton’s laws

Isaac Newton formalized Galileo’s observations in his three laws of motion. The second law (F = ma) explains why all bodies have the same acceleration in free fall: the gravitational force is proportional to mass, just like inertia.

Air resistance

In air, the fall is not truly “free” because air resistance opposes the motion. This friction force increases with velocity until it balances the weight: the object then reaches its terminal velocity. A sheet of paper and a lead ball do not have the same terminal velocity.

Weightlessness

The astronauts of the ISS are in permanent free fall around the Earth. Although g is still about 8.7 m/s² there, everything falls together, creating a sensation of weightlessness.

School level and curriculum

Grade 10 to Grade 12 - Physics and chemistry

Uniformly accelerated rectilinear motion
Newton’s second law: relationship between force and acceleration
Mechanical energy and conservation
Practical assessment: trajectory analysis by chronophotography

Formula

Equations of motion in free fall (without initial velocity):

Position: y(t) = y₀ - ½ × g × t²

Velocity: v(t) = g × t

Fall time: t = √(2h/g)

Final velocity: v = √(2gh)

Meaning:

y₀: initial height (m)
g: gravitational acceleration (≈ 9.81 m/s²)
t: elapsed time (s)
h: fall height (m)
v: velocity (m/s)

Application examples

A ball dropped from the 3rd floor (10 m) reaches the ground in 1.4 s with a velocity of 14 m/s
A skydiver in free fall accelerates until reaching a terminal velocity of about 200 km/h
On the Moon, where g = 1.62 m/s², a 10 m fall takes 3.5 s instead of 1.4 s
A diver from 10 m enters the water at about 50 km/h
The famous feather and hammer experiment of Apollo 15 verified Galileo’s law on the Moon

FAQ

Q: Why do we say all objects fall at the same speed? A: In a vacuum, all objects have the same acceleration g. The gravitational force and inertia are both proportional to mass, so mass cancels out in the equation of motion.

Q: What distinguishes free fall from a skydiver’s motion? A: In true free fall, only gravity acts. A skydiver also experiences air resistance, which eventually balances their weight, limiting their speed.

Q: How can g be measured precisely with a smartphone? A: The free fall method with FizziQ can achieve a precision of 1 to 2%. Video analysis is often more precise than a manual stopwatch.

Q: Is free fall truly rectilinear? A: Yes, if the object is released without horizontal velocity. Otherwise, the trajectory is parabolic, as for a projectile.

Q: Why does air resistance complicate measurements? A: It creates a force that opposes the motion and increases with velocity. To minimize its effect, dense and compact objects are used over short distances.

Gravitational Acceleration - Law of Gravitation - Parabolic Trajectory (Projectile) - Terminal Velocity - Mechanical Energy - Uniformly Accelerated Linear Motion

Free Fall