Forces: What Makes Things Move, Stop, or Bend? (IGCSE Physics 0625)

Hello Physics learners! This chapter, "Forces," is absolutely crucial. Why? Because forces are the invisible hands of the universe—they cause motion, stop motion, and change shapes. Everything you see, from kicking a football to building a stable tower, relies on the principles of force.

In these notes, we'll break down how forces affect objects, how they cause things to turn, and why some objects are more stable than others. Ready to explore the power of push and pull? Let's dive in!

1.5.1 Effects of Forces

What is a Force?

A force is simply a push or a pull. Since a force has both magnitude (size) and direction, it is a vector quantity.

The standard unit for force is the newton (N).

Forces can cause three main changes (Core 1, 5):
  1. Change the object's speed (accelerate or decelerate).
  2. Change the object's direction of motion. (If you change speed OR direction, you change velocity!)
  3. Change the object's size or shape (deformation).

A. Deformation and Hooke's Law

When you squeeze a sponge or stretch a spring, you are applying a force to change its shape.

Load-Extension Graphs and Elasticity (Core 2, Supplement 10)

When you hang a mass (the load) on a spring, the spring stretches (the extension). If you plot a graph of load (Force, \(F\)) against extension (\(x\)):

  • For many materials, especially springs, the graph starts as a straight line passing through the origin.
  • This linear relationship shows that Force is directly proportional to Extension. This is known as Hooke's Law.

$$F \propto x$$

Important Term: Limit of Proportionality

This is the point beyond which the graph stops being a perfectly straight line. If the force is removed before this limit, the object will return to its original length (it is elastically deformed). If the force goes beyond this point, the object may be plastically deformed (permanently stretched).

The Spring Constant \(k\) (Supplement 9)

If \(F \propto x\), we can write an equation:

$$F = kx$$

Where \(k\) is the spring constant (or stiffness constant).

$$k = \frac{F}{x}$$

  • Definition: The spring constant (\(k\)) is the force required per unit extension.
  • Unit: Newtons per metre (N/m) or Newtons per centimetre (N/cm).
  • A higher \(k\) means a stiffer spring.
Did You Know? Hooke's Law is crucial in engineering, ensuring structures like bridges and plane wings flex appropriately without suffering permanent damage.

B. Resultant Force and Equilibrium

Finding the Resultant Force (Core 3)

The resultant force is the single force that has the same effect as all the forces acting on the object combined.

  • Forces in the Same Direction: Add them up. (Example: Two people pushing a car together.)
  • Forces in Opposite Directions: Subtract the smaller force from the larger one. The direction of the resultant is the direction of the larger force. (Example: A tug-of-war where one team is stronger.)
Resultant Force and Motion (Core 4)

This links directly to Newton’s First Law of Motion (the Law of Inertia):

An object will remain at rest or continue to move in a straight line at a constant speed (constant velocity) unless acted upon by a resultant force.

When an object is in this state (zero resultant force and zero resultant moment—see next section), we say it is in equilibrium.

C. Newton's Second Law: F = ma (Supplement 11)

When a resultant force acts on an object, it causes the object to accelerate.

$$F = ma$$

  • \(F\) = Resultant force (N)
  • \(m\) = Mass of the object (kg)
  • \(a\) = Acceleration (m/s²)

Crucial Point: The force (\(F\)) and the acceleration (\(a\)) are always in the same direction. If you push something to the right, it accelerates to the right.

Quick Tip: If you need to calculate acceleration (\(a\)) and you have multiple forces, always calculate the resultant force first before using \(F=ma\).

D. Friction and Resistance (Core 6, 7, 8)

Friction is the force that opposes motion. It always acts in the opposite direction to the movement or the tendency of movement.

Types of Friction:
  1. Solid Friction: The force acting between two solid surfaces sliding past each other. This impedes motion and produces heating (think of rubbing your hands together).
  2. Drag (Fluid Resistance): The friction that acts on an object moving through a fluid (a liquid or a gas). Examples include: air resistance on a falling object or water resistance on a boat.
Terminal Velocity (Related Concept - 1.2 Motion)

When an object falls, gravity pulls it down, and air resistance (drag) pushes up. As the object speeds up, the air resistance increases.

The object reaches terminal velocity when the downward force (weight) is equal to the upward force (air resistance). At this point, the resultant force is zero, and the object stops accelerating (it moves at a constant maximum speed).

E. Circular Motion (Supplement 12)

Objects moving in a circle, even at a constant speed, are constantly changing direction. Since velocity is changing, they must be accelerating, and therefore, a resultant force must be acting on them.

  • This force is called the centripetal force.
  • The centripetal force always acts towards the centre of the circle and is perpendicular to the direction of motion.

Analogy: Imagine swinging a ball on a string. The centripetal force is the tension in the string pulling the ball inwards. If you cut the string, the force disappears, and the ball flies off in a straight line (tangential to the circle).

Qualitatively, we know that to keep the radius and speed constant, if we increase the mass, we need a larger centripetal force.

Key Takeaway: Effects of Forces

Forces change velocity or shape. If \(F_{\text{resultant}} = 0\), the object is in equilibrium (not accelerating). If \(F_{\text{resultant}} \neq 0\), the object accelerates according to \(F = ma\).

1.5.2 Turning Effect of Forces (Moments)

Not all forces cause linear movement; some cause rotation or turning!

A. Defining the Moment (Core 1, 2)

The moment of a force is a measure of its turning effect.

To calculate a moment, you need the force and the perpendicular distance from the pivot (the point of rotation).

$$\text{Moment} = \text{Force} \times \text{Perpendicular distance from the pivot}$$

$$M = F \times d$$

  • Unit of Moment: Newton metres (Nm).

Example: Opening a door. You push the handle (Force) far away from the hinges (Pivot). If you try to push near the hinges, the distance \(d\) is small, so you need a much larger force to get the same turning effect!

B. Principle of Moments and Equilibrium (Core 3, 4, Supplement 5, 6)

The Principle of Moments states that for an object to be in rotational equilibrium (perfectly balanced):

The total clockwise moment about any pivot must be equal to the total anticlockwise moment about the same pivot.

$$\text{Total Clockwise Moments} = \text{Total Anticlockwise Moments}$$

Conditions for Complete Equilibrium

An object is in complete equilibrium if two conditions are met (Core 4):

  1. There is no resultant force (the object isn't moving linearly or accelerating).
  2. There is no resultant moment (the object isn't rotating or accelerating angularly).

Step-by-step application (Balancing a Beam):

  1. Identify the pivot (fulcrum).
  2. Identify all forces trying to turn the object clockwise (CW).
  3. Calculate the total CW Moment (\(M_{CW} = F_1 d_1 + F_2 d_2 + ...\)).
  4. Identify all forces trying to turn the object anticlockwise (ACW).
  5. Calculate the total ACW Moment (\(M_{ACW} = F_a d_a + F_b d_b + ...\)).
  6. For balance (equilibrium), set \(M_{CW} = M_{ACW}\) and solve for the unknown quantity.

Key Takeaway: Moments

Moments measure turning effect: \(M = F \times d_{\text{perp}}\). For balance, the Principle of Moments applies: Clockwise moments must equal Anticlockwise moments.

1.5.3 Centre of Gravity

A. What is the Centre of Gravity (CoG)? (Core 1)

The centre of gravity (CoG) of an object is the single point where the entire weight of the object appears to act.

  • For uniformly shaped objects (like a metre rule or a cube), the CoG is exactly at the geometric centre.
  • For irregular objects, it must be determined experimentally.

B. Experiment to Find the CoG (Core 2)

We usually determine the CoG for a flat, irregularly shaped sheet of material (a lamina) using the method of suspension:

  1. Hang the lamina freely from a pin through a hole near its edge (Point A).
  2. Hang a plumb line (a string with a mass/bob) from the same pin.
  3. Once the lamina stops swinging, draw a straight line down the lamina following the plumb line. The CoG must lie somewhere along this line.
  4. Repeat the process, hanging the lamina from a different point (Point B). Draw the second line.
  5. The point where the two lines intersect is the Centre of Gravity (CoG).

C. Stability and the CoG (Core 3)

The position of the CoG determines how stable an object is. Stability is an object's ability to resist toppling over.

To increase stability, you want:
  1. A low centre of gravity.
  2. A wide base area.

Example: Racing cars are designed to be very stable—they are built low to the ground (low CoG) and have wide wheelbases (wide base area). A tall double-decker bus, conversely, has a higher CoG and needs careful driving to avoid toppling.

An object only topples over when the vertical line drawn downwards from its centre of gravity falls outside its base area.

Key Takeaway: Centre of Gravity

The CoG is the point where weight acts. Stability is maximized by keeping the CoG low and having a wide base.