Free fall

Free fall refers to the motion of a body under the influence of gravity alone, with no other forces acting upon it, such as air resistance or friction. It is a fundamental concept in classical mechanics that helps to explain the behaviour of objects moving vertically under Earth’s gravitational pull. In a vacuum, all objects, irrespective of their mass, experience the same acceleration due to gravity and thus fall at the same rate. The concept of free fall is essential for understanding not only basic kinematics but also more advanced topics in physics, including projectile motion and orbital dynamics.

Historical Background

The study of free fall dates back to ancient times when philosophers like Aristotle believed that heavier objects fall faster than lighter ones. This view persisted until the 16th and 17th centuries, when experimental science began to challenge these assumptions.
The Italian scientist Galileo Galilei conducted landmark experiments in the early 1600s, reportedly dropping objects of different masses from the Leaning Tower of Pisa. He demonstrated that, in the absence of air resistance, all objects fall with the same uniform acceleration regardless of their mass. Galileo further confirmed this by using inclined planes to study the motion of rolling balls, leading to the discovery that the distance travelled by a freely falling object is proportional to the square of the time taken.
Later, Sir Isaac Newton, in his Principia Mathematica (1687), formulated the law of universal gravitation, establishing that every mass attracts every other mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This provided a theoretical explanation for Galileo’s observations and unified terrestrial and celestial mechanics under a single law.

Concept and Equations of Motion

In free fall, the only force acting on an object is the gravitational force. The acceleration experienced by the object is called the acceleration due to gravity (g). Near the Earth’s surface, its average value is approximately 9.8 m/s² and is directed vertically downwards.
If air resistance is neglected, the motion of a freely falling body can be described by the equations of uniformly accelerated motion:

1. v = u + gt
2. s = ut + ½gt²
3. v² = u² + 2gs

where:

• u = initial velocity,
• v = final velocity after time t,
• s = distance fallen,
• g = acceleration due to gravity.

For an object dropped from rest, u = 0, so the equations simplify to:

• v = gt
• s = ½gt²
• v² = 2gs

These relationships allow the determination of the velocity and displacement of a falling object at any given time.

Acceleration Due to Gravity and Its Variations

Although g is often treated as a constant, it varies slightly with geographical location and altitude due to:

• Shape of the Earth: The Earth is not a perfect sphere but an oblate spheroid, causing g to be slightly higher at the poles and lower at the equator.
• Altitude: The value of g decreases with increasing height above the Earth’s surface.
• Depth: Within the Earth, g also decreases as one moves towards the centre.
• Local Geological Formations: Variations in the density of underlying rocks can cause minor differences in gravitational acceleration.

Free Fall in Vacuum and Air Resistance

In a vacuum, there is no air to resist motion, so all objects fall at the same rate. This was famously demonstrated by astronaut David Scott during the Apollo 15 mission (1971) on the Moon, where he dropped a hammer and a feather simultaneously. Both struck the lunar surface at the same time, proving Galileo’s principle in a real-world vacuum environment.
However, on Earth, air resistance plays a significant role. As an object falls, it encounters friction from air molecules, which opposes its downward motion. The effect of air resistance depends on the object’s shape, surface area, and velocity.
When the upward force of air resistance becomes equal to the downward pull of gravity, the object stops accelerating and continues to fall at a constant speed known as the terminal velocity. For example, a human skydiver typically reaches a terminal velocity of about 55 m/s (200 km/h) when falling in a belly-to-earth position.

Free Fall and Weightlessness

A body in free fall experiences apparent weightlessness, as the only force acting on it is gravity. This is the same condition experienced by astronauts orbiting the Earth in a spacecraft. Although gravity still acts on them, both the spacecraft and the astronauts fall freely around the Earth, creating the sensation of weightlessness.
This phenomenon can also be experienced briefly in drop towers or parabolic flights, where aircraft follow specific trajectories to simulate the effects of microgravity for training and scientific experiments.

Applications of Free Fall

The concept of free fall has wide-ranging applications across various fields:

• Physics Education: It forms the foundation for understanding motion, gravity, and kinematics.
• Astronautics and Space Science: Understanding free fall is crucial for calculating satellite orbits and spacecraft trajectories.
• Engineering and Ballistics: Used in designing parachutes, safety systems, and weapons to predict the motion of falling or projected objects.
• Sports and Recreation: Skydiving, bungee jumping, and base jumping rely on the principles of free fall and terminal velocity.
• Metrology and Geophysics: Measuring variations in gravitational acceleration helps in studying Earth’s internal structure.

Experimental Determination of g

The acceleration due to gravity can be determined through several experimental methods:

• Simple Pendulum Method: Measuring the time period of oscillations of a pendulum using the formula T = 2π√(l/g), where T is the period and l is the length of the pendulum.
• Free Fall Apparatus: Using electronic timing devices to record the time taken for an object to fall a known distance.
• Drop Tower Experiments: Used in laboratories and space research centres to study short-term weightlessness and precise gravitational measurements.