Introduction to Forces

In our previous studies of motion (kinematics), we looked at how objects move—their displacement, velocity, and acceleration. Now, we are diving into the "why." In this chapter, we explore Dynamics: the study of forces and how they change the motion of objects. Understanding these laws is like learning the rules of the universe's engine. Whether you are aiming to be an engineer or just want to understand why you don't float away into space, Newton's Laws are the foundation you need!

1. Weight and Gravitational Field Strength

Before we look at how things move, we need to understand the most common force we experience: Weight. It is very common to confuse "mass" and "weight" in everyday speech, but in Physics, they are quite different.

Mass (\(m\)) is a measure of the amount of matter in an object, measured in kilograms (\(\text{kg}\)). It stays the same no matter where you are in the universe.

Weight (\(W\)) is a force caused by gravity acting on that mass. Because it is a force, it is measured in Newtons (\(\text{N}\)).

The relationship between them is given by the formula:
\(W = mg\)

In this equation, \(g\) is the gravitational field strength. On Earth, we use the value:
\(g = 9.81 \, \text{N kg}^{-1}\)

Quick Tip: You can also think of \(g\) as the acceleration of free fall (\(9.81 \, \text{m s}^{-2}\)). The syllabus treats these as equivalent near the Earth's surface. If you know the force and the mass, you can rearrange the formula to find \(g\):
\(g = \frac{F}{m}\)

2. Free-Body Force Diagrams

A free-body force diagram is a essential tool. It is a simplified sketch that shows only the forces acting on a single object. We represent the object as a point or a simple box to keep things clear.

How to draw them correctly:
  • Identify the object: Only draw forces acting on that specific object, not forces the object exerts on its surroundings.
  • The Centre of Gravity: All weight vectors should be drawn starting from the object's centre of gravity (the point where the entire weight of the object appears to act).
  • Use Arrows: The direction of the arrow shows the direction of the force. The length of the arrow should represent the relative magnitude (size) of the force.
  • Label clearly: Use names like Weight, Normal Contact Force (or Reaction), Drag, and Thrust.

Example: For a book resting on a table, you would draw an arrow pointing down from the centre of gravity labeled "Weight" and an equal-length arrow pointing up from the base of the book labeled "Normal Contact Force."

3. Newton’s First Law of Motion

Newton’s First Law tells us what happens when forces are balanced. It states that an object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant force.

What is a Resultant Force?
The resultant force (\(\sum F\)) is the single force that has the same effect as all the individual forces acting on an object added together. If the forces in all directions cancel each other out, the resultant force is zero.

Key Scenarios:
  • If \(\sum F = 0\) and the object is stationary, it stays stationary.
  • If \(\sum F = 0\) and the object is already moving, it keeps moving at the exact same speed and in the exact same direction.

Did you know? This is why you feel a jolt when a car suddenly stops. Your body wants to keep moving at a constant velocity (Newton's First Law), but the seatbelt provides the resultant force to stop you!

4. Newton’s Second Law of Motion

Newton's Second Law explains what happens when there is a resultant force. It states that the acceleration of an object is directly proportional to the resultant force and acts in the same direction.

For an object with constant mass, the formula is:
\(\sum F = ma\)

Where:
\(\sum F\) = Resultant force (Newtons, \(\text{N}\))
\(m\) = Mass (Kilograms, \(\text{kg}\))
\(a\) = Acceleration (Metres per second squared, \(\text{m s}^{-2}\))

Important Note: Newton's First Law is actually just a "special case" of the Second Law. If the resultant force (\(F\)) is zero, then the acceleration (\(a\)) must also be zero!

Steps for Calculation Questions:
  1. Draw a free-body diagram.
  2. Calculate the resultant force by subtracting forces in opposite directions (e.g., \(Thrust - Drag\)).
  3. Plug the resultant force and the mass into \(\sum F = ma\) to find the acceleration.

5. Terminal Velocity

When an object falls through a fluid (like air or water), it experiences Drag (air resistance). As the object speeds up, the drag force increases. Eventually, the drag force becomes equal to the weight of the object.

At this point:
1. The forces are balanced (\(\sum F = 0\)).
2. According to Newton's First Law, the acceleration becomes zero.
3. The object continues to fall at a steady speed called terminal velocity.

Quick Review: At the start of a fall, \(Weight > Drag\), so the object accelerates. At terminal velocity, \(Weight = Drag\), so acceleration is zero.

6. Newton’s Third Law of Motion

This law is often stated as "every action has an equal and opposite reaction," but this can be confusing. It is better to think about Force Pairs.

Newton's Third Law states: If Object A exerts a force on Object B, then Object B exerts an equal and opposite force of the same type on Object A.

How to identify a Newton's Third Law Pair:

A true Third Law pair must meet these four criteria:

  • The forces are equal in magnitude.
  • The forces act in opposite directions.
  • The forces act on different objects (Object A on B, and B on A).
  • The forces are of the same type (e.g., both are gravitational, or both are contact forces).

Common Mistake Alert! Many students think the Weight of a book and the Normal Contact Force from the table are a Third Law pair because they are equal and opposite. This is wrong! They act on the same object (the book) and are different types of forces (gravitational vs. electrostatic contact force). These are balanced forces due to the First Law, not a Third Law pair.

The real Third Law pair for Weight: If the Earth pulls down on a book (Weight), the book pulls up on the Earth with an equal gravitational force!

Summary Key Takeaways

1. Mass vs Weight: \(W = mg\). Weight is a force, mass is matter.
2. FBDs: Always draw forces from the centre of gravity and only show forces acting on the object.
3. Newton 1: No resultant force means no change in velocity (equilibrium).
4. Newton 2: Resultant force causes acceleration (\(F = ma\)).
5. Terminal Velocity: Occurs when drag equals weight, resulting in zero acceleration.
6. Newton 3: Force pairs act on different objects and must be the same type of force.