Forces
Newton's laws of motion
Newton's First Law
Newton's First Law: An object remains at rest or continues to move at constant velocity unless acted on by a resultant (net) force.
Equivalently: if the resultant force on an object is zero, its velocity does not change — it is in equilibrium.
Equivalently: if the resultant force on an object is zero, its velocity does not change — it is in equilibrium.
What this means in practice:
- A stationary book stays still because normal reaction and weight cancel (resultant = 0).
- A car moving at constant speed on a motorway has driving force = friction + air resistance (resultant = 0).
- If the resultant force is non-zero, the object accelerates (speeds up, slows down, or changes direction).
Inertia is the tendency of an object to resist changes in its state of motion. A large mass has more inertia — it is harder to start moving, stop, or change direction.
Newton's Second Law
The resultant force acting on an object is directly proportional to its acceleration and acts in the same direction as the acceleration.
\[ F = ma \]
| Symbol | Quantity | Unit |
|---|---|---|
| \( F \) | Resultant force | newton, N |
| \( m \) | Mass | kilogram, kg |
| \( a \) | Acceleration | m/s² |
Rearrangements:
\[ a = \frac{F}{m} \qquad m = \frac{F}{a} \]
- For a fixed force, a larger mass means a smaller acceleration.
- For a fixed mass, a larger force means a larger acceleration.
- A resultant force of 1 N gives a mass of 1 kg an acceleration of 1 m/s² — this defines the newton.
Example 1 — find acceleration
A resultant force of 360 N acts on a car of mass 900 kg. Find the acceleration.
\( a = \dfrac{F}{m} = \dfrac{360}{900} = 0.40\,\text{m/s}^2 \)
Example 2 — find resultant force (with friction)
A 1200 kg car has a driving force of 2400 N and a total friction/drag force of 800 N. Find the acceleration.
Resultant force: \( F = 2400 - 800 = 1600\,\text{N} \) (forward).
\( a = \dfrac{F}{m} = \dfrac{1600}{1200} = 1.33\,\text{m/s}^2 \)
Always use the resultant (net) force in \( F = ma \) — not just one of the forces acting. Subtract opposing forces (friction, air resistance) from the driving force first.
Newton's Third Law
Newton's Third Law: If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
The two forces in a Newton's Third Law pair are:
The two forces in a Newton's Third Law pair are:
- Equal in magnitude
- Opposite in direction
- The same type of force (both gravitational, both contact, etc.)
- Acting on different objects
| Situation | Force A exerts on B | Force B exerts on A |
|---|---|---|
| Book resting on table | Weight of book pushes down on table | Table pushes up on book (normal reaction) |
| Rocket engine | Rocket pushes exhaust gases backward | Exhaust gases push rocket forward (thrust) |
| Earth and Moon | Earth's gravity pulls Moon toward Earth | Moon's gravity pulls Earth toward Moon |
| Swimmer pushing wall | Swimmer pushes backward on wall | Wall pushes swimmer forward |
Newton's Third Law pairs do not cancel each other — they act on different objects. The weight of a book and the table's normal reaction on the book are not a Newton's Third Law pair (they are balanced forces on the same object). The N3L pair of "Earth pulls book down" is "book pulls Earth up."
Identifying a Newton's Third Law pair
A horse pulls a cart with a force of 500 N. Identify the Newton's Third Law pair.
Force 1: Horse exerts 500 N forward force on cart (tension in rope).
Force 2: Cart exerts 500 N backward force on horse.
Same magnitude (500 N), opposite direction, same type (tension), on different objects (horse and cart). ✓
To check if two forces are a Newton's Third Law pair, ask: (1) same type of force? (2) equal magnitude? (3) opposite direction? (4) on different objects? All four must be yes.