Introduction: Gravity's One-Way Trip
Welcome to the study of Free Fall! This chapter is a crucial part of understanding Projectile Motion. Simply put, free fall is what happens when an object is allowed to move under the influence of gravity alone. Whether you're dropping a pen or watching a cliff diver, the same physical laws are at play. Don't worry if Physics feels a bit heavy sometimes—we’re going to break this down into simple, manageable steps to help you master the mechanics of falling!
1. What exactly is Free Fall?
In Physics, an object is in free fall if the only force acting on it is its weight (the pull of gravity). In the "ideal" version of this world—which we often use to simplify problems—we ignore air resistance.
Quick Review of Prerequisite Terms:
Before we dive in, let’s quickly remember our "SUVAT" variables:
\( s \): Displacement (how far from the start)
\( u \): Initial velocity (starting speed and direction)
\( v \): Final velocity (ending speed and direction)
\( a \): Acceleration (rate of change of velocity)
\( t \): Time
The Acceleration of Free Fall (\( g \))
Near the Earth's surface, all objects fall with the same constant acceleration, regardless of their mass. We call this the acceleration of free fall, represented by the symbol \( g \).
The magic number: For your H1 syllabus, \( g = 9.81 \text{ m s}^{-2} \).
Analogy: Imagine gravity is like a coach constantly yelling "Go faster!" at the same intensity. Every second you fall, you gain exactly \( 9.81 \text{ m s}^{-1} \) of speed.
Key Takeaway: In a vacuum (no air), a bowling ball and a feather will hit the ground at the same time because they share the same acceleration, \( g \).
2. Weight and Gravitational Fields
According to the syllabus, you need to understand weight as a force. Your weight isn't just a number on a scale; it's the result of being in a gravitational field.
The Formula:
\( W = mg \)
Where \( W \) is weight (in Newtons, \( N \)), \( m \) is mass (in \( kg \)), and \( g \) is the gravitational field strength (\( 9.81 \text{ N kg}^{-1} \)).
Did you know?
Numerical-wise, gravitational field strength (\( \text{N kg}^{-1} \)) and acceleration of free fall (\( \text{m s}^{-2} \)) are the same thing near Earth's surface!
3. Solving Problems: The Equations of Motion
When an object falls vertically without air resistance, it is uniformly accelerated motion (the acceleration doesn't change). We use the SUVAT equations you learned in Kinematics:
- \( v = u + at \)
- \( s = ut + \frac{1}{2}at^2 \)
- \( v^2 = u^2 + 2as \)
- \( s = \frac{(u+v)}{2}t \)
Pro-Tip: Choosing your Signs
Physics problems are easier if you pick a direction to be positive (+) right at the start. Usually, we pick "Up" as positive and "Down" as negative.
If "Up" is positive, then \( a = -9.81 \text{ m s}^{-2} \) because gravity pulls down.
Common Mistake to Avoid:
At the very top of a flight (when you throw a ball up), the velocity is zero for a split second, but the acceleration is still \( -9.81 \text{ m s}^{-2} \). Gravity never takes a break!
4. Falling with Style: Air Resistance
In the real world, we have air. Air resistance (also called drag or viscous force) changes how things fall.
How Air Resistance Works:
- It always acts in the opposite direction to the motion.
- It increases as the object's speed increases.
- It depends on the surface area (think of a parachute).
The Journey to Terminal Velocity
When you drop an object in air, three stages happen:
Step 1: The Start
The object just started moving, so speed is low. Air resistance is almost zero. The only force is Weight. The acceleration is roughly \( 9.81 \text{ m s}^{-2} \).
Step 2: Gaining Speed
As the object speeds up, air resistance increases. This force pushes up against the weight. The resultant force downwards gets smaller, so the acceleration decreases (the object is still speeding up, but not as quickly as before).
Step 3: Terminal Velocity
Eventually, the upward air resistance grows until it equals the downward weight. The resultant force is now zero. According to Newton’s First Law, the object stops accelerating and falls at a constant speed. This is called terminal velocity.
Key Takeaway: At terminal velocity, \( \text{Acceleration} = 0 \) because \( \text{Weight} = \text{Air Resistance} \).
5. Graphs of Free Fall
Visualizing motion is key for H1 Physics. Here is how graphs look for free fall without air resistance:
- Displacement-Time (\( s-t \)): A curve (parabola) because the object is covering more distance every second.
- Velocity-Time (\( v-t \)): A straight line with a constant gradient. The gradient of this line equals \( g \) (\( 9.81 \text{ m s}^{-2} \)).
- Acceleration-Time (\( a-t \)): A horizontal flat line at \( 9.81 \text{ m s}^{-2} \).
Quick Review Box:
- Gradient of \( s-t \) graph = Velocity
- Gradient of \( v-t \) graph = Acceleration
- Area under \( v-t \) graph = Displacement
Summary Checklist
Before you move on to projectile motion, make sure you can:
1. State that \( g = 9.81 \text{ m s}^{-2} \) for free fall without air resistance.
2. Use SUVAT equations to calculate height or time of flight.
3. Explain that weight \( W = mg \) is the force in a gravitational field.
4. Describe how an object reaches terminal velocity when air resistance equals weight.
5. Identify that at terminal velocity, acceleration is zero but velocity is constant.
Keep going! You're building the foundation for understanding how everything from footballs to satellites move!