Motion & Forces
Investigate Newton’s three laws of motion in detail, and explore how momentum and impulse explain everyday collisions and crashes.
Newton's Three Laws of Motion
First Law: Law of Inertia
"An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force."
Inertia is the tendency of an object to resist changes in its motion. Greater mass means greater inertia. Example: When a car brakes suddenly, passengers lurch forward because their bodies continue moving at the original speed — this is why seatbelts are essential on Australian roads.
Second Law: F = ma
"The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass."
F = m × a
F = net force (N) | m = mass (kg) | a = acceleration (m/s²)
Example: A rugby player of mass 100 kg accelerates at 3 m/s². The net force on the player is F = 100 × 3 = 300 N.
Third Law: Action & Reaction
"For every action, there is an equal and opposite reaction."
Forces always occur in pairs acting on different objects. The action and reaction forces are equal in magnitude but opposite in direction. Example: When you jump from a surfboard, you push backward on the board (action), and the board pushes you forward (reaction). The board moves backward due to the force you exerted on it.
Momentum
Momentum (symbol: p) is a measure of how hard it is to stop a moving object. It depends on both mass and velocity:
p = m × v
p = momentum (kg·m/s) | m = mass (kg) | v = velocity (m/s)
Conservation of Momentum
In a closed system (no external forces), the total momentum before a collision equals the total momentum after. This is the law of conservation of momentum.
pbefore = pafter
Momentum is a vector
Momentum has both magnitude and direction. When calculating momentum for collisions, choose a positive direction. Objects moving in the opposite direction have negative momentum.
Impulse
Impulse is the change in momentum of an object. It equals the product of the force applied and the time for which it acts:
J = F × Δt = Δp
J = impulse (N·s) | F = force (N) | Δt = time interval (s) | Δp = change in momentum (kg·m/s)
Impulse and Safety Design
Increasing the time over which a force acts reduces the peak force for the same change in momentum. This principle explains:
- Crumple zones in cars: extend collision time, reducing force on occupants
- Crash mats in gymnastics: extend landing time, reducing impact force
- Airbags: increase time of head contact, reducing force on skull
- Catching a cricket ball: pulling your hands back increases time, reducing sting
Key Vocabulary
| Term | Definition |
|---|---|
| Inertia | The tendency of an object to resist changes in its state of motion; proportional to mass. |
| Net force | The overall (resultant) force acting on an object, found by combining all individual forces. |
| Momentum | The product of an object's mass and velocity (p = mv); a vector quantity measured in kg·m/s. |
| Impulse | The product of force and time interval; equal to the change in momentum of an object. |
Worked Examples
Using Newton's Second Law to find acceleration.
Given: A car of mass 1 200 kg experiences a net force of 3 600 N.
Step 1: Write the formula: F = m × a → a = F ÷ m
Step 2: Substitute values: a = 3 600 ÷ 1 200
Answer: a = 3 m/s²
Calculating momentum of a sprinter.
Given: An athlete of mass 70 kg is running at 9 m/s.
Step 1: p = m × v
Step 2: p = 70 × 9
Answer: p = 630 kg·m/s in the direction of motion.
Applying the impulse-momentum theorem.
Given: A 0.5 kg ball hits a wall at 10 m/s and bounces back at 8 m/s. The collision lasts 0.02 s.
Step 1: Taking towards the wall as positive, initial p = 0.5 × 10 = +5 kg·m/s; final p = 0.5 × (−8) = −4 kg·m/s.
Step 2: Δp = −4 − 5 = −9 kg·m/s (impulse on ball is 9 N·s away from wall).
Step 3: F = Δp ÷ Δt = 9 ÷ 0.02 = 450 N (force exerted by wall on ball).
Knowledge Check
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Key Concepts Summary
- •Newton’s 1st Law: objects maintain their motion unless a net force acts on them (inertia).
- •Newton’s 2nd Law: F = ma; acceleration is directly proportional to net force and inversely proportional to mass.
- •Newton’s 3rd Law: every action has an equal and opposite reaction acting on a different object.
- •Momentum (p = mv) is conserved in closed systems; it is a vector quantity.
- •Impulse (J = FΔt = Δp); increasing collision time reduces the peak force — the basis of safety design.