Welcome to the World of Free Fall!
Have you ever wondered why a feather and a hammer fall at different speeds on Earth, but hit the ground at the exact same time on the Moon? Or why skydivers don't just keep getting faster and faster forever? In this chapter, we are going to explore the physics of Free Fall. Whether you find Physics a bit intimidating or you're a math whiz, these notes will help you master how things move when gravity takes the lead. Let’s dive in!
1. What is Free Fall?
In Physics, free fall occurs when the only force acting on an object is its weight (the force of gravity). When an object is in true free fall, we ignore things like air resistance or friction.
The Magic Number: \( g \)
Near the surface of the Earth, all objects in free fall accelerate downwards at the same rate, regardless of their mass. This is known as the acceleration of free fall, symbolized by the letter \( g \).
For your H2 Physics syllabus, we take:
\( g \approx 9.81 \text{ m s}^{-2} \)
Wait, doesn't a heavy rock fall faster than a piece of paper?
In everyday life, yes—but that's because of air resistance. If you sucked all the air out of a room (creating a vacuum), a bowling ball and a postage stamp would fall side-by-side! This is because the gravitational field strength is uniform near Earth's surface.
Did you know? In 1971, astronaut David Scott dropped a hammer and a feather on the Moon. Because there is no atmosphere there, they landed at the exact same time, proving Galileo was right!
Quick Review:
• Free fall means gravity is the only force acting.
• Acceleration \( g \) is always \( 9.81 \text{ m s}^{-2} \) (downwards).
• In a vacuum, mass does not affect how fast an object falls.
Key Takeaway: Acceleration due to gravity is constant for all objects near Earth's surface if we ignore air resistance.
2. Weight: The Force of Gravity
Before we calculate motion, we need to understand the force causing it. Weight is the force experienced by a mass when it is placed in a gravitational field.
The Formula
The relationship between weight \( W \), mass \( m \), and gravitational field strength \( g \) is:
\( W = mg \)
Common Mistake to Avoid: Don't confuse mass and weight!
• Mass is the amount of matter in you (measured in kg). It stays the same even if you go to Mars.
• Weight is a force (measured in Newtons, N). It changes depending on the gravity of the planet you are on.
Key Takeaway: Weight is a force (\( W = mg \)) that always acts vertically downwards towards the center of the Earth.
3. Mathematical Free Fall (The SUVAT Equations)
Since the acceleration \( g \) is uniform (constant), we can use our favorite equations of motion to solve problems. Don't worry if these look scary; they are just tools to help us find distance, time, or speed.
The Tools (SUVAT)
\( v = u + at \)
\( s = ut + \frac{1}{2}at^2 \)
\( v^2 = u^2 + 2as \)
\( s = \frac{(u + v)}{2}t \)
How to use them for Free Fall:
When an object is dropped from rest:
1. Initial velocity \( u = 0 \).
2. Acceleration \( a = 9.81 \text{ m s}^{-2} \) (usually taken as positive if you define 'down' as the positive direction).
3. Displacement \( s \) becomes the height \( h \).
Example: If you drop a ball from a tall building, how fast is it going after 2 seconds?
• Use \( v = u + at \)
• \( v = 0 + (9.81)(2) \)
• \( v = 19.6 \text{ m s}^{-1} \)
Memory Aid: Just remember "u-a-t". If you have any three of the variables (s, u, v, a, t), you can always find the other two!
Key Takeaway: Free fall problems are just "Uniformly Accelerated Motion" problems where \( a = 9.81 \text{ m s}^{-2} \).
4. Free Fall with Air Resistance
In the real world, we have air! Air molecules bump into falling objects, creating a force called air resistance (or drag). This force acts opposite to the direction of motion.
The Story of a Skydiver (Step-by-Step)
Imagine a skydiver jumps out of a plane. Here is what happens to their motion:
Step 1: The Start
The moment they jump, their velocity is zero. This means air resistance is zero. The only force is Weight. Their acceleration is exactly \( 9.81 \text{ m s}^{-2} \).
Step 2: Gaining Speed
As they fall faster, they hit more air molecules. Air resistance increases. Since air resistance pushes up and weight pulls down, the resultant (net) force decreases. According to \( F = ma \), if the force decreases, the acceleration decreases. They are still speeding up, but not as quickly as before.
Step 3: Terminal Velocity
Eventually, the skydiver goes so fast that the Air Resistance equals the Weight. The forces are now balanced.
• Resultant Force = \( 0 \)
• Acceleration = \( 0 \)
The skydiver has reached a constant maximum speed called Terminal Velocity.
The Analogy
Think of running into a strong wind. When you stand still, you don't feel much. As you start running faster, the wind pushes against you harder. Eventually, you're running so fast the wind push matches your leg strength, and you can't speed up anymore!
Did you know? A cat’s terminal velocity is lower than a human's because they have a high surface-area-to-weight ratio. This is why cats can sometimes survive falls from high-rise buildings (but please don't test this!).
Common Mistake: Students often think "zero acceleration" means the object has stopped. No! It just means the speed is not changing anymore. The object is still moving very fast!
Key Takeaway: Air resistance increases with speed. Terminal velocity occurs when Air Resistance = Weight, resulting in zero acceleration.
5. Visualizing Motion: Graphs
Being able to sketch and identify graphs is a core skill for H2 Physics.
Velocity-Time (v-t) Graphs
• No Air Resistance: A straight diagonal line starting from the origin. The gradient (slope) is constant and equals \( 9.81 \text{ m s}^{-2} \).
• With Air Resistance: A curve that starts steep but levels off (flattens) as it reaches terminal velocity.
Acceleration-Time (a-t) Graphs
• No Air Resistance: A horizontal line at \( a = 9.81 \text{ m s}^{-2} \).
• With Air Resistance: Starts at \( 9.81 \), but curves down towards zero as the object reaches terminal velocity.
Quick Review Box:
1. Gradient of displacement-time graph = Velocity.
2. Gradient of velocity-time graph = Acceleration.
3. Area under velocity-time graph = Displacement (Distance traveled).
Key Takeaway: Graphs for real-world falling objects always show acceleration decreasing over time until it hits zero at terminal velocity.
Summary Checklist
Before you move on to Projectile Motion, make sure you can:
• Explain that \( g \) is constant (\( 9.81 \text{ m s}^{-2} \)) in a vacuum.
• Use SUVAT equations to calculate fall time or final velocity.
• Describe how air resistance leads to terminal velocity using forces (\( W \) and \( Drag \)).
• Distinguish between the motion of an object with and without air resistance using graphs.
Don't worry if this seems tricky at first! Mechanics is all about practice. Try drawing the force diagrams (Free Body Diagrams) for a falling object at different stages—it really helps the concepts click!