Newton’s third law

Welcome to Newton’s Third Law!

In this chapter, we are looking at the final piece of the puzzle in Newton’s Laws of Motion. While the first two laws tell us what happens to a single object, the Third Law is all about how two objects interact. It’s often called the "it takes two to tango" law of physics! Don't worry if it feels a bit abstract at first; once you see the patterns, it becomes one of the most logical parts of Mechanics.

1. What is Newton’s Third Law?

The official syllabus definition states: "Every action has an equal and opposite reaction."

In simpler terms: If Object A exerts a force on Object B, then Object B exerts a force of the same size but in the opposite direction back on Object A.

Key Characteristics of a Newton's Third Law Pair:

• They are the same size (magnitude).
• They act in opposite directions.
• They are the same type of force (e.g., both are gravitational, or both are contact forces).
• They act on different objects (this is the most important part to remember!).

Real-World Analogy: Imagine you are wearing roller skates and you push against a wall. You move backwards! Why? Because as you push the wall (Action), the wall pushes you back with the exact same amount of force (Reaction).

Memory Aid: The "S.O.D.A." Rule
Forces in a pair are:
S – Same size
O – Opposite direction
D – Different objects
A – Alike in type

Key Takeaway: You can never have just one force. Forces always come in pairs!

2. Normal Reaction Force \( (R) \)

Have you ever wondered why you don't fall through the floor? This is thanks to the Normal Reaction Force. When an object rests on a surface, the surface pushes back up.

• "Normal" in maths means "perpendicular." The reaction force always acts at 90 degrees to the surface.
• For an object resting on a flat, horizontal surface, the Normal Reaction \( R \) is equal and opposite to the Weight \( W \).
• Formula: \( R = mg \)

Important: Loss of Contact

In exam questions, they might ask when an object "leaves the surface" or "loses contact."
Quick Review: Contact is lost when the Normal Reaction force becomes zero \( (R = 0) \).

Did you know? Your "weight" that you feel is actually the floor pushing up on you (\( R \)), not gravity pulling you down. This is why you feel "weightless" on a fast-dropping roller coaster—the seat isn't pushing against you as hard, so \( R \) decreases!

3. Modelling Systems as a Single Particle

Sometimes we have two objects moving together, like a car towing a caravan. The syllabus says that if there is no relative motion between components (they are moving at the same speed and acceleration), we can model the whole thing as a single particle.

Example: A car of mass 1000 kg pulling a trailer of mass 500 kg.
Instead of doing two separate equations, you can treat them as one big object of mass 1500 kg to find the overall acceleration.

Step-by-Step for Combined Systems:
1. Add the masses together to get a "Total Mass."
2. Identify the external driving force (e.g., the car's engine).
3. Identify external resistances (e.g., air resistance on both vehicles).
4. Use \( F = ma \) where \( F \) is the total resultant force.

4. Connected Particles (Trains and Pulleys)

When objects are connected by a light inextensible string or a tow-bar, they share the same Tension \( (T) \) and the same Acceleration \( (a) \).

The "Smooth" Model:

The syllabus mentions "smooth" contact or "smooth" pulleys. This is a simplification that means:
• There is no friction.
• For pulleys, the Tension is the same on both sides of the string.

Solving Connected Particle Problems:

Don't panic if the diagram looks messy! Follow these steps:
1. Separate the objects: Draw a force diagram for each object individually.
2. Apply Newton’s Second Law \( (F = ma) \): Write one equation for Object A and one for Object B.
3. Solve simultaneously: Usually, you can add the two equations together to make the Tension \( T \) cancel out, allowing you to find acceleration \( a \).

Common Mistake to Avoid: Forgetting that the Tension acts in different directions for each object. On the car, Tension pulls backward. On the trailer, Tension pulls forward!

5. Equilibrium in Two Dimensions

As you move into Stage 2 of the syllabus, you will look at forces that aren't just in a straight line. An object is in Equilibrium if the resultant force is zero.

• To solve these, we resolve forces into horizontal and vertical components (using \( \cos\theta \) and \( \sin\theta \)).
• For equilibrium: Total Up Force = Total Down Force AND Total Left Force = Total Right Force.
• You can also use Vectors. If the forces are \( \mathbf{F_1, F_2, F_3} \), then in equilibrium: \( \mathbf{F_1 + F_2 + F_3} = 0 \).

Quick Review Box:
• Equilibrium: \( a = 0 \), Resultant Force = 0.
• Newton's 3rd Law: Always true, whether moving or still.
• Inextensible string: Means acceleration is the same for both connected objects.

Final Summary Takeaways

• Newton's Third Law is about pairs of forces acting on different objects.
• Normal Reaction \( R \) is the "push back" from a surface. It disappears \( (R = 0) \) when contact is lost.
• Connected particles move as one. Use separate \( F = ma \) equations for each part to find Tension.
• Smooth means we ignore friction to keep calculations simple.

Great job getting through these notes! Mechanics takes practice, so try drawing a few force diagrams for a car and trailer to see these pairs in action. You've got this!