Welcome to Newton’s Third Law!

In this chapter, we are going to explore one of the most famous rules in physics. You’ve probably heard it before: "For every action, there is an equal and opposite reaction." But what does that actually mean for your Mechanics exam? We are going to break down how objects push back, how they stay connected, and how to solve those "tricky" pulley problems with ease.

1. The Core Principle: Action and Reaction

Newton’s Third Law tells us that forces never happen in isolation; they always come in pairs. If Object A exerts a force on Object B, then Object B must exert a force of the same size back on Object A, but in the opposite direction.

Key Rules for Third Law Pairs:

  • They are the same size (magnitude).
  • They act in opposite directions.
  • They act on different objects.
  • They are the same type of force (e.g., both are gravitational or both are contact forces).

Example: Imagine you are standing on a skateboard and you push against a wall. You push the wall (Action), and the wall pushes you back (Reaction). This reaction force is what actually makes you roll away!

Quick Summary: You can't touch something without it touching you back just as hard!

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

When an object rests on a surface (like a book on a table), why doesn't it fall through? It’s because the surface pushes back up. This is called the Normal Reaction Force (or sometimes the Normal Contact Force).

Important Points:

  • Normal means "perpendicular." This force always acts at 90 degrees to the surface.
  • If an object is resting on a horizontal surface and is not moving up or down, the Normal Reaction (\(R\)) is equal and opposite to the weight (\(W\)).
  • Formula for weight: \( W = mg \) (where \(m\) is mass and \(g\) is 9.8 \(m s^{-2}\)).
  • Therefore, on a flat floor: \( R = mg \).

Did you know? If you are in a lift that starts accelerating upwards, the floor has to push you harder to move you up. This is why you feel "heavier"—the Normal Reaction (\(R\)) has increased!

Losing Contact: In some exam questions, an object might be lifted or jump. If the object loses contact with the surface, the Normal Reaction force becomes \( R = 0 \).

3. Connected Particles: Trains, Carriages, and Strings

The syllabus (3.03h) mentions that if a system has no relative motion (parts aren't moving differently from each other), we can treat the whole thing as a single particle. This is a huge time-saver!

Example: A car (mass \(1000 kg\)) towing a trailer (mass \(500 kg\)).

  • You can look at the car and trailer as one big object with a total mass of \(1500 kg\).
  • This is great for finding the acceleration of the whole system using \( F = ma \).

Tension (\(T\))

When objects are connected by a string or a tow-bar, we deal with Tension. According to Newton's Third Law, if a car pulls a trailer, the trailer also pulls back on the car with an equal force. We represent this as \(T\) acting in opposite directions at each end of the string or bar.

Don't worry if this seems tricky! Just remember that Tension always "pulls" away from the objects it is attached to.

4. Smooth Pulleys and Pegs

Pulley questions are a classic part of OCR AS Mathematics. Usually, the syllabus refers to a "smooth" pulley or peg.

What does "Smooth" mean?

  • It means there is no friction.
  • Crucially, it means the Tension (\(T\)) is the same on both sides of the pulley.

Step-by-Step for Pulleys:

  1. Draw a clear diagram.
  2. Mark the weights acting downwards (\(mg\)).
  3. Mark the Tension (\(T\)) pulling away from the masses, up toward the pulley.
  4. Choose a direction of motion (usually the side with the heavier mass goes down).
  5. Write a separate \( F = ma \) equation for each mass.
  6. Solve the equations simultaneously to find \(a\) or \(T\).

Key Takeaway: Because the pulley is smooth, the rope just "transfers" the force, so \(T\) stays constant throughout the string.

5. Equilibrium in Two Dimensions

Sometimes forces aren't just up and down; they might be given as vectors (like \( \mathbf{F} = 3\mathbf{i} - 2\mathbf{j} \)).

If a particle is in equilibrium, it means it is either stationary or moving at a constant velocity. In this state:

  • The Resultant Force is Zero.
  • The sum of all \( \mathbf{i} \) components = 0.
  • The sum of all \( \mathbf{j} \) components = 0.

Common Mistake to Avoid: Forgetting to include the Reaction force or Weight when summing your vectors. Always double-check your force diagram!

6. Summary and Quick Review

Newton's Third Law is the backbone of "connected" mechanics. Here is a quick checklist for your revision:

  • Force Pairs: Equal in size, opposite in direction, acting on different bodies.
  • Normal Reaction (\(R\)): The "push back" from a surface. It is 0 if contact is lost.
  • Connected Particles: Use a "whole system" approach to find acceleration, then "individual parts" to find Tension.
  • Pulleys: If it's smooth and the string is light, the Tension is the same everywhere.
  • Equilibrium: All forces must balance out to zero.

Memory Aid: Think of the 3rd Law as a Mirror. Whatever force you put into a surface, you see an identical (but opposite) force reflected back at you!