Effects of air resistance

Introduction: When Physics Meets the Real World

Welcome! Up until now, you’ve probably been solving projectile motion problems in a "perfect" world—one where air doesn't exist. We call that motion in a vacuum. But if you’ve ever tried to run against a strong wind or watched a feather drift slowly to the ground, you know that air is very much there! In this chapter, we explore how air resistance changes the way objects fall and move. It’s the difference between a textbook calculation and how things actually work on Earth.

1. What is Air Resistance?

Air resistance (also known as drag) is a type of frictional force or viscous force that acts on an object as it moves through the air.

Think of air as a "fluid" made of tiny molecules. To move through it, an object has to push those molecules out of the way. Those molecules push back! This "push back" is what we call air resistance.

Two Golden Rules of Air Resistance:
1. It always acts in the opposite direction to the object's motion.
2. For most objects, the magnitude of air resistance increases as the speed of the object increases. (The faster you go, the harder the air pushes back!)

Analogy: Think about sticking your hand out of a car window. If the car is moving slowly, you feel a gentle breeze. If the car is moving at highway speeds, the air feels like a solid wall pushing your hand back!

Key Takeaway:

Air resistance is a resistive force that opposes motion and gets stronger as you speed up.

2. The Journey to Terminal Velocity

Don’t worry if the following steps seem a bit repetitive—that’s because motion with air resistance follows a very predictable pattern! Let’s look at a ball dropped from a high building.

Step 1: The Instant of Release (\( t = 0 \))

The moment you let go, the speed \( v \) is zero. Since the speed is zero, the air resistance is also zero. The only force acting on the ball is its weight (\( W = mg \)). At this exact moment, the acceleration is exactly \( 9.81 \, \text{m s}^{-2} \).

Step 2: Speeding Up

As the ball falls, it gets faster. Because it is getting faster, air resistance starts to increase. Now, the weight is pulling down, but air resistance is pushing up.
The resultant force (\( F_{net} = W - \text{Air Resistance} \)) starts to decrease. According to Newton’s Second Law (\( F = ma \)), if the resultant force decreases, the acceleration also decreases.

Step 3: Reaching Terminal Velocity

Eventually, the ball is moving so fast that the air resistance grows until it is exactly equal to the weight of the ball.
At this point:
- The forces are balanced.
- The resultant force is zero.
- The acceleration is zero.
The ball stops speeding up and falls at a constant speed. This maximum constant speed is called terminal velocity.

Quick Review Box:

As an object falls with air resistance:
• Speed (\( v \)) increases until it reaches a limit.
• Air Resistance increases until it equals weight.
• Acceleration (\( a \)) decreases until it reaches zero.

3. Visualizing the Motion: Graphs

When you look at a velocity-time graph for an object falling with air resistance, it isn't a straight line like it is in a vacuum. It is a curve that flattens out.

The Gradient Matters:
In a velocity-time graph, the gradient (slope) represents acceleration.
- At the start, the slope is steep (acceleration is \( g \)).
- As the object falls, the curve becomes less steep (acceleration is decreasing).
- Finally, the curve becomes a horizontal line (gradient is zero, so acceleration is zero). This horizontal line indicates the terminal velocity.

Common Mistake to Avoid:
Many students think "decreasing acceleration" means the object is "slowing down." This is incorrect! As long as acceleration is positive (greater than zero), the object is still speeding up, just not as quickly as before. It only stops speeding up when acceleration hits zero.

4. Energy Perspective

The syllabus requires us to describe this motion in terms of energy as well. This is a favorite topic for exam questions!

In a Vacuum (No Air Resistance):

All Gravitational Potential Energy (GPE) lost is converted directly into Kinetic Energy (KE). Total mechanical energy is conserved.

With Air Resistance:

As the object falls, it does work against air resistance. Some of the GPE lost is converted into KE, but some is converted into Internal Energy (Heat) in the air and the object.
\( \Delta \text{GPE} = \Delta \text{KE} + \text{Work Done against Air Resistance} \)

At Terminal Velocity:

Once terminal velocity is reached, the KE is constant (since speed is constant). This means all the GPE being lost from that point onwards is being converted entirely into Internal Energy. The object doesn't get any faster; it just gets (very slightly) warmer!

5. Summary and Tips

Did you know?
A skydiver’s terminal velocity is roughly \( 55 \, \text{m/s} \) (about \( 200 \, \text{km/h} \))! When they open their parachute, the surface area increases massively, creating much more air resistance. This forces the "balance" to happen at a much lower speed, allowing them to land safely.

Memory Aid: The "V-A-R" Checklist

When describing falling objects, always mention what is happening to these three things in order:
1. Velocity (Increases)
2. Air Resistance (Increases because Velocity increases)
3. Resultant Force/Acceleration (Decreases because Weight stays same but Air Resistance grows)

Final Encouragement:
Projectile motion with air resistance is all about a "tug-of-war" between gravity pulling down and air pushing up. If you can describe how that tug-of-war changes as the object gets faster, you’ve mastered this chapter!