2.3 Free Fall Motion
Free fall motion occurs when an object falls under the sole influence of gravitational force, free from air resistance or other opposing forces. In everyday conditions, falling objects are affected by air resistance, causing objects of different shapes or weights to appear to fall at different rates. However, in a vacuum, all objects fall with the exact same constant gravitational acceleration, regardless of their mass.
Learning Objectives
- Define free fall motion and state its necessary condition.
- Explain the concept of gravitational acceleration, \(g\), and understand why its value varies at different locations on Earth.
- Describe the laboratory experiment using a photogate system to determine Earth's gravitational acceleration.
- Apply linear motion equations to solve numerical problems involving free-falling objects moving vertically upwards and downwards.
Free Fall Motion in Air vs. in a Vacuum and Earth's Gravitational Field
See how air resistance affects falling rates compared to a vacuum, and how the non-spherical shape of Earth causes \(g\) to vary.
Air vs. Vacuum
Earth's Gravitational Field
Short Explanation
What is Free Fall Motion?
Free fall is the motion of an object that is affected only by gravitational force. A free-falling object does not experience any other forces such as air resistance or friction.
Everyday Observation vs. Vacuum
In air, heavy or streamlined objects fall faster than light or broad objects because of air resistance. In a vacuum, all objects fall with the exact same acceleration and reach the floor at the same time.
Gravitational Acceleration, \(g\)
The acceleration of a free-falling object caused by gravitational force is known as gravitational acceleration, \(g\). Near Earth's surface, the average value is \(9.81\text{ m s}^{-2}\).
Historical Integration
Aristotle concluded that falling rate depends on weight, shape and orientation. Galileo Galilei discovered that all objects fall with the same acceleration if air resistance is ignored.
Linear Motion Equations for Free Fall
\(v = u + gt\) \(s = ut + \frac{1}{2}gt^2\) \(v^2 = u^2 + 2gs\)Sign convention: upward is positive, downward is negative. Therefore \(g = -9.81\text{ m s}^{-2}\).
| Location | Distance to Earth's Centre | Value of \(g\) |
|---|---|---|
| Equator | \(6\,372\text{ km}\) | \(9.78\text{ m s}^{-2}\) |
| North / South Poles | \(6\,350\text{ km}\) | \(9.83\text{ m s}^{-2}\) |
| Standard general value | — | \(9.81\text{ m s}^{-2}\) |
Experiment 2.1: Determining Earth's Gravitational Acceleration
A photogate system and electronic timer are used with an electromagnetic release and a steel ball. The ball passes through two photogates separated by height \(h\). The gravitational acceleration is calculated using:
\(g = \dfrac{2h}{t_2^2 - t_1^2}\)
Repeat for \(h = 30.0\text{ cm}\), \(40.0\text{ cm}\), \(50.0\text{ cm}\), \(60.0\text{ cm}\) and \(70.0\text{ cm}\). Ensure the release is purely electromagnetic and the photogates are aligned vertically.
Try to Answer First
Answer in your mind, then press “Check Answer”.
What is the definition of free fall motion?
Check Answer
Why is the value of gravitational acceleration at the equator smaller than at the North Pole?
Check Answer
A stone is released from rest from a height of \(10\text{ m}\). Using \(g = 9.81\text{ m s}^{-2}\) and taking downward displacement as negative, what is the equation used and the time taken to hit the ground?
Check Answer
Common Mistakes
- Forgetting that downward displacement and downward velocity have negative signs when upward is defined as positive.
- Assuming heavier objects inherently accelerate faster due to gravity in a vacuum.
- Substituting a positive value for \(g\) when an object is falling downwards without consistently defining the reference direction.
- Misidentifying the velocity at maximum height as non-zero instead of recognizing that \(v = 0\text{ m s}^{-1}\) instantaneously.
Concept Misunderstandings
A crumpled piece of paper falls faster than a flat sheet because crumpling increases its mass or weight.
The mass remains exactly identical; crumpling reduces the effective surface area, which drastically decreases upward air resistance.
Gravitational acceleration has the same exact value everywhere on the Earth's surface.
The value of \(g\) varies geographically; it is smaller at the equator (\(9.78\text{ m s}^{-2}\)) and larger at the poles (\(9.83\text{ m s}^{-2}\)) because Earth is not a perfect sphere.
Free fall only applies when an object is moving downwards.
An object thrown upwards is also in free fall once released, provided that gravity is the only force acting on it (air resistance ignored).
Summary
- Free fall motion is motion governed strictly by gravitational force alone, in the absence of air resistance or friction.
- In a vacuum, all objects fall with identical gravitational acceleration regardless of shape or mass.
- Gravitational acceleration, \(g\), averages \(9.81\text{ m s}^{-2}\) near Earth's surface (\(9.78\text{ m s}^{-2}\) at the equator and \(9.83\text{ m s}^{-2}\) at the poles).
- The experimental formula using two photogates separated by height \(h\) is \(g = \dfrac{2h}{t_2^2 - t_1^2}\).
- Kinematic equations apply with the sign convention: upward is positive, downward is negative (\(g = -9.81\text{ m s}^{-2}\)).
Short Activity
Objective: Test your understanding of free fall, gravitational acceleration and vertical motion.
A. Objective Quiz
1 Under which of the following conditions does an object undergo true free fall motion?
2 Why does the value of Earth's gravitational acceleration equal \(9.78\text{ m s}^{-2}\) at the equator but \(9.83\text{ m s}^{-2}\) at the poles?
B. Fill in the Blanks
3 In the photogate experiment, the gravitational acceleration \(g\) is calculated using the formula \(g = \frac{2h}{t_2^2 - \text{______}}\).
4 Near the surface of the Earth, the velocity of a freely falling object increases by ______ \(\text{m s}^{-1}\) per second.
C. Matching / Drag and Drop
Match each physical parameter or location to its correct value or condition described in the textbook. If using a phone, tap the answer first, then tap the matching box.
