11.3 Gravitational Acceleration and Free Fall
Every object around us is pulled towards the centre of Earth by Earth's gravitational force. This gravitational force causes objects to fall downwards and experience gravitational acceleration (\(g\)). When an object falls under the influence of gravitational force alone without being affected by air resistance, it is said to undergo free fall.
Learning Objectives
- State the definition of gravitational force and gravitational acceleration (\(g\)).
- Determine the value of gravitational acceleration (\(g\)) using a ticker timer.
- Define free fall and explain the condition required for free fall to occur.
- Compare free fall motion and non-free fall motion in the presence and absence of air resistance.
- Sketch and interpret displacement-time and velocity-time graphs for free falling objects and objects moving against gravitational force.
Comparison of Motion Graphs: Free Fall vs. Moving Against Gravity
The shapes and gradient meanings of displacement-time and velocity-time graphs for downward free fall versus upward vertical throw.
Short Explanation
Gravitational Force and Gravitational Acceleration
Gravitational force is the force that pulls all objects towards the centre of Earth. An object that falls due to Earth's gravitational force experiences gravitational acceleration, denoted by \(g\). The value of gravitational acceleration on the surface of Earth is approximately \(10\text{ m s}^{-2}\).
Gravitational force is the attractive pull exerted by Earth towards its centre. Any object falling freely under Earth's gravity experiences gravitational acceleration, denoted by \(g\), which has a standard value of approximately \(10\text{ m s}^{-2}\) on Earth's surface.
What is Free Fall?
An object undergoes free fall if it falls due to the effects of gravitational force only. In true free fall, no other force acts on the object except gravity; this condition only occurs in a vacuum where there is no air resistance. In a vacuum, all objects—regardless of mass or shape—fall with identical acceleration and hit the ground at the same time.
Free Fall vs. Non-Free Fall
In the presence of air, objects encounter air resistance, causing light or broad objects such as flat paper or feathers to fall more slowly. A falling sheet of paper is affected by air resistance, so it does not fall freely.
Determining \(g\) Using a Ticker Timer
In Experiment 11.1, a ticker timer is used to determine the value of gravitational acceleration. The initial velocity \(u = \dfrac{x_1\text{ cm}}{0.02\text{ s}}\), final velocity \(v = \dfrac{x_2\text{ cm}}{0.02\text{ s}}\), and time interval \(t = 5\text{ ticks} \times 0.02\text{ s} = 0.1\text{ s}\). Gravitational acceleration is then calculated using \(g = \dfrac{v - u}{t}\), converted from \(\text{cm s}^{-2}\) to \(\text{m s}^{-2}\).
Galileo's Discovery
Sometime between 1589 and 1592, Galileo Galilei dropped two spheres of different masses simultaneously from the Leaning Tower of Pisa and discovered that objects of different masses take almost the same time to reach the ground.
Experiment 11.1: Determining the Value of \(g\)
Using a ticker timer to determine gravitational acceleration.
| Item | Details |
|---|---|
| Aim | To determine the value of gravitational acceleration, \(g\), using a ticker timer. |
| Hypothesis | The value of gravitational acceleration, \(g\), is \(10\text{ m s}^{-2}\). |
| Manipulated variable | Mass of weight |
| Responding variable | Value of gravitational acceleration |
| Constant variable | Height of object released |
| Apparatus and materials | Ticker timer, weight (50 g, 100 g, 150 g, 200 g, 250 g), G-clamp, A.C. power supply 12 V, soft board, retort stand and clamp, ticker tape, cellophane tape. |
| Precautionary measure | Place the soft board on the spot where the weight will hit the floor. |
Procedure Summary
- Set up apparatus by clamping the ticker timer vertically on a retort stand placed on the bench.
- Pass a 1 m ticker tape through the ticker timer and attach a 50 g weight to its end.
- Switch on the ticker timer and release the weight.
- Analyse the ticker tape using a 5-tick strip interval.
- Repeat with weights of 100 g, 150 g, 200 g, and 250 g.
Note on Results
Gravitational acceleration is independent of the mass of the weight. Any discrepancy from \(10\text{ m s}^{-2}\) in the laboratory is due to friction between the ticker tape and ticker timer as well as air resistance.
Experiment 11.2: Free Fall and Non-Free Fall Motion
Studying the time taken for an object to fall during free fall and non-free fall motions.
| Item | Details |
|---|---|
| Aim | To study the time taken for an object to fall during free fall and non-free fall motions. |
| Hypothesis | Time taken to reach the ground by a free falling object is shorter than a non-free falling object. |
| Manipulated variable | Presence of air |
| Responding variable | Time taken for the object to fall to the rubber stopper |
| Constant variable | Height of object |
| Apparatus and materials | Transparent cylinder tube, rubber stopper, vacuum pump, pieces of paper. |
Observations
In the presence of air
Pieces of paper take a longer time to fall due to air resistance opposing gravity.
In a vacuum (air pumped out)
Pieces of paper fall much faster and reach the rubber stopper in a shorter time because only gravitational force acts on them.
Try to Answer First
Answer in your mind, then press "Check Answer".
What is the meaning of free fall?
Why do a tennis ball and a chicken feather reach the bottom of a vacuum chamber at the same time when dropped from the same height?
What physical quantity is represented by the gradient of a velocity-time graph for an object undergoing free fall?
Common Mistakes
- Confusing free fall in everyday air with free fall in physics: thinking that skydivers or falling paper are in "free fall," whereas in physics they experience air resistance and are therefore undergoing non-free fall.
- Assuming heavier objects always fall faster in a vacuum: believing mass increases gravitational acceleration, when in fact \(g\) is constant for all masses in a vacuum.
- Misinterpreting the displacement-time graph for free fall as a straight line: drawing a straight line instead of a curve that gets steeper over time due to increasing velocity.
- Forgetting to convert units when calculating \(g\) from ticker tapes: calculating in \(\text{cm s}^{-2}\) and forgetting to divide by 100 to convert to \(\text{m s}^{-2}\).
Concept Misunderstandings
Gravitational force does not exist in a vacuum.
Gravitational force still exists in a vacuum; a vacuum merely removes air and air resistance, allowing gravitational force to act alone.
At maximum height, an object thrown vertically upward has zero acceleration.
At maximum height, only the instantaneous velocity is zero (\(v = 0\text{ m s}^{-1}\)). The gravitational acceleration acting on it is still constant downwards (\(g \approx 10\text{ m s}^{-2}\)).
Summary
- Gravitational force pulls objects toward the centre of Earth.
- Gravitational acceleration (\(g\)) is the acceleration experienced by an object due to Earth's gravitational pull, with an approximate value of \(10\text{ m s}^{-2}\) on Earth's surface.
- Free fall occurs only when gravity is the sole force acting on an object, which strictly happens in a vacuum.
- In a vacuum, objects of different shapes and masses fall with the same gravitational acceleration and reach the ground simultaneously.
- Free fall from rest: \(v-t\) graph has a constant positive gradient (\(g\)); \(s-t\) graph curves upward with increasing gradient. Thrown vertically upwards: \(v-t\) graph has a constant negative gradient (deceleration); \(s-t\) graph curves until the gradient reaches zero at maximum height.
Short Activity
A. Objective Quiz
1 Which of the following conditions is required for an object to experience true free fall?
2 What does the gradient of a velocity-time graph represent for an object falling freely?
B. Fill in the Blanks
3 The value of gravitational acceleration, \(g\), on the surface of Earth is approximately \(\text{m s}^{-2}\).
4 Non-free fall motion of an object falling through the atmosphere is affected by air .
C. Drag and Drop: Match Each Feature to Its Description
Drag each feature to the correct description. On a phone, tap an answer first, then tap a matching box. Tap the Answer Choices area to return a selected item.
C. Match Each Feature to Its Description
Write the correct feature next to each description.
| Description | Feature / Scenario |
|---|---|
| 1. Objects of different masses released from the same height reach the ground simultaneously. | |
| 2. The motion of the falling object is opposed and slowed down by air resistance. | |
| 3. Represents constant gravitational acceleration (\(g\)). | |
| 4. Velocity of the object is momentarily zero before it falls back downwards. |
Answer choices: Free fall in a vacuum • Non-free fall in air • Gradient of free fall \(v-t\) graph • At maximum displacement of upward throw
