Forces

Level 1

Discovering the concept of force

In everyday life, many actions on objects are described by the word force: you push a door, the wind pushes a leaf, the Earth attracts an apple. In physics, we use the model of force to represent and analyze these actions.

A force is like an identity card for an action: it does not show the "real" action, but gives all the information needed to describe and compare it.

The four characteristics of a force

  • Point of application

    The precise location where the force acts on the object

  • Line of action

    The line of action (vertical, horizontal, or inclined)

  • Magnitude

    The length of the arrow represents the magnitude in newtons (N)

  • Direction

    The arrowhead indicates where the force is directed

  Example : the weight of a 10 kg object

  • Point of application: center of gravity of the object.
  • Line of action: vertical line passing through the object and the center of the Earth.
  • Direction: downwards (towards the center of the Earth).
  • Magnitude: calculated using the formula $P = m \times g$, with $g \approx 9.81\ \text{N/kg}$ (often rounded to $10\ \text{N/kg}$, unit also written m/s²), so $P = 10 \times 9.81 \approx 98.1\ \text{N}$
Modèles Poids

Representing a force with a diagram

In physics, each force is represented by an arrow. Each property of the arrow corresponds to a characteristic of the force:

The point of application corresponds to the place where the arrow begins.
Direction and sense are represented by the arrow itself
The magnitude is represented by the length of the arrow.

Method for drawing a force

  1. Identify the 4 characteristics of the force.
  2. Choose a scale (e.g.: 1 cm = 10 N).
  3. Place the point of application on the drawing of the object.
  4. Draw the arrow along the direction and sense.
  5. The length of the arrow corresponds to the magnitude of the force. (e.g.: the force is 50 N. According to the scale, the arrow will be 5 cm)

Important rules: use the same scale for all forces in the same diagram, name each force (P, R, F, ...), indicate the value if it is known, and be precise about the point of application.

Forces in situations and equilibrium

Souvent plusieurs forces agissent simultanément sur un même objet. Pour savoir ce qui arrive à l’objet, on considère la resultant force (somme vectorielle des forces). 

  • If the resultant is zero then there is no change in the motion of the object.
  • Otherwise there is a change in the motion (speeding up or slowing down depending on the direction of the resultant).

Equilibrium and imbalance

  • Equilibrium: the forces balance each other out, so the resultant is zero, so the object is stationary or at constant speed.
  • Imbalance: the forces do not balance each other out, the resultant is not zero, so the object speeds up or slows down.

  Examples of analysis

1) Book placed on a table:

  • Forces:
    • weight P (downwards, at the centre of the book),
    • reaction of the table R (upwards, at the point of contact).
  • If P = R then
  • the object is in equilibrium (does not move).

2) Crate pulled at constant speed:

  • Horizontal forces:
    • pull forwards
    • friction backwards.
  • If pull = friction then constant speed.
livre
⚖️ Equilibrium F res. = 0 N
Caisse
⚖️ Equilibrium F res. = 0 N
Velo
⚠️ Imbalance F res. = — N

To go further: Newton's Laws

Isaac Newton (1643-1727) formulated three simple but powerful laws to describe the motion of bodies. These laws are still used today to understand mechanics.

1. First law: principle of inertia

Without a net force, a stationary object remains stationary and an object in motion keeps its speed constant (same direction, same sense).

Example: if a marble rolls on a perfectly smooth and horizontal table, it would continue indefinitely if nothing slowed it down.

2. Second law: relationship between force and motion

The net force $\vec{F}$ acting on an object is proportional to its mass $m$ and its acceleration $\vec{a}$:

$$\vec{F} = m \times \vec{a}$$

This means that with the same force, a light object accelerates more than a heavy object.

3. Third law: action and reaction

If an object A exerts a force on an object B, then B exerts a force of the same current but in the opposite direction on A.

  Example: when you push a wall, the wall "pushes back" on you with an equal force in the opposite direction, even if it does not move.