What you'll learn
This topic combines Newton's laws of motion with fundamental conservation principles that govern how objects move and interact. Understanding momentum transfer, energy conservation, and force calculations is essential for both Foundation and Higher tier papers, typically appearing in questions worth 4-9 marks that require extended calculations and explanations.
Key terms and definitions
Momentum — the product of an object's mass and velocity, measured in kg m/s (kilogram metres per second). Momentum = mass × velocity.
Conservation of momentum — in a closed system, the total momentum before an event equals the total momentum after the event, provided no external forces act.
Newton's First Law — an object remains at rest or continues moving at constant velocity unless acted upon by a resultant force.
Newton's Second Law — the acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass. F = ma.
Newton's Third Law — when two objects interact, they exert equal and opposite forces on each other.
Resultant force — the single force that has the same effect as all the forces acting on an object combined.
Conservation of energy — energy cannot be created or destroyed, only transferred from one store to another or between different forms.
Work done — energy transferred when a force moves an object through a distance. Work done (J) = force (N) × distance moved in direction of force (m).
Core concepts
Newton's Laws and Force Calculations
Newton's First Law explains why seatbelts are essential in cars. When a car brakes suddenly, passengers continue moving forward at the original velocity until a force (the seatbelt) acts to slow them down. This law describes inertia — the tendency of objects to resist changes in motion.
Newton's Second Law provides the mathematical relationship: F = ma, where F is resultant force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²). Rearrangements you must know:
- a = F/m (acceleration equals force divided by mass)
- m = F/a (mass equals force divided by acceleration)
Edexcel GCSE Physics papers frequently test whether you can identify the resultant force from multiple forces acting on an object. For a car experiencing 5000 N forward thrust and 1200 N air resistance, the resultant force is 5000 - 1200 = 3800 N forwards.
Newton's Third Law applies to all interactions. When a swimmer pushes backwards against the water, the water pushes the swimmer forwards with an equal force. These force pairs always:
- Act on different objects
- Are equal in magnitude
- Are opposite in direction
- Are the same type of force (both contact, both gravitational, etc.)
Momentum and Its Conservation
Momentum is a vector quantity — direction matters. An object with mass 50 kg moving at 3 m/s to the right has momentum = 50 × 3 = 150 kg m/s to the right.
The principle of conservation of momentum states:
Total momentum before collision = Total momentum after collision
This applies to:
- Elastic collisions where objects bounce apart
- Inelastic collisions where objects stick together
- Explosions where objects push apart from rest
For calculations involving two objects: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where:
- m₁ and m₂ are the masses
- u₁ and u₂ are initial velocities
- v₁ and v₂ are final velocities
When objects move in opposite directions, assign one direction as positive and the other as negative. Consistency is crucial for correct answers on exam papers.
Forces and Motion Relationships
The relationship between force and motion depends on whether forces are balanced or unbalanced:
Balanced forces (resultant force = 0):
- Object at rest stays at rest
- Moving object continues at constant velocity
- Acceleration = 0 m/s²
Unbalanced forces (resultant force ≠ 0):
- Object accelerates in the direction of resultant force
- Acceleration proportional to force (F = ma)
- Velocity changes
Edexcel papers test whether you can calculate acceleration from force and mass, then use kinematic equations to find velocity or distance. You must connect F = ma with equations like v = u + at and v² = u² + 2as.
Energy Conservation in Motion
The principle of conservation of energy means the total energy in a closed system remains constant. For moving objects, energy transfers between stores:
Kinetic energy store: KE = ½mv²
- m = mass (kg)
- v = velocity (m/s)
- KE measured in joules (J)
Gravitational potential energy store: GPE = mgh
- m = mass (kg)
- g = gravitational field strength (9.8 N/kg on Earth)
- h = height (m)
Elastic potential energy store: energy stored in stretched or compressed elastic objects.
When a ball falls, GPE transfers to KE. At maximum height, KE = 0 and GPE is maximum. Just before hitting the ground, GPE = 0 and KE is maximum. The sum remains constant (ignoring air resistance).
Work done transfers energy. When a force moves an object:
Work done = force × distance moved in direction of force W = Fs
This links to energy: work done = energy transferred. Lifting a 2 kg book 1.5 m requires work done = mgh = 2 × 9.8 × 1.5 = 29.4 J.
Stopping Distances and Force
The thinking distance is how far a vehicle travels during the driver's reaction time. The braking distance is how far the vehicle travels while braking.
Stopping distance = thinking distance + braking distance
Factors affecting thinking distance:
- Speed of the vehicle (higher speed = greater distance)
- Driver's reaction time (increased by tiredness, alcohol, drugs, distractions)
Factors affecting braking distance:
- Speed of the vehicle (doubling speed roughly quadruples braking distance due to KE = ½mv²)
- Vehicle mass (heavier vehicles require more force to stop)
- Brake condition (worn brakes reduce braking force)
- Road surface (wet, icy, or poor surfaces reduce friction)
- Tyre condition (worn tyres reduce grip)
The braking force does work against the kinetic energy of the vehicle: Work done by brakes = loss in KE = ½mv². Edexcel questions often ask you to calculate braking forces using this relationship or estimate stopping distances under different conditions.
Momentum and Safety Features
Vehicle safety features increase collision time to reduce force. Since momentum change is constant (determined by the vehicle's initial momentum), increasing the time reduces the force:
Force = change in momentum ÷ time
Safety features that work on this principle:
- Crumple zones: deform in collisions, increasing collision time
- Airbags: inflate to cushion occupants, increasing stopping time
- Seatbelts: stretch slightly to increase stopping time
- Crash barriers: deform on impact, increasing collision time for vehicles
Higher tier papers may ask you to calculate forces with and without safety features, demonstrating how a longer collision time reduces peak force experienced.
Worked examples
Example 1: Conservation of Momentum (Foundation/Higher, 4 marks)
A trolley of mass 2 kg moving at 4 m/s collides with a stationary trolley of mass 3 kg. After collision, they move together. Calculate their combined velocity.
Solution:
Step 1: Calculate total momentum before collision Momentum = m₁u₁ + m₂u₂ Momentum = (2 × 4) + (3 × 0) = 8 + 0 = 8 kg m/s ✓
Step 2: Apply conservation of momentum Total momentum after = Total momentum before = 8 kg m/s ✓
Step 3: Calculate combined velocity Combined mass = 2 + 3 = 5 kg Momentum = mass × velocity 8 = 5 × v ✓ v = 8 ÷ 5 = 1.6 m/s ✓
Example 2: Newton's Second Law and Kinematics (Higher, 5 marks)
A car of mass 1200 kg accelerates from rest under a resultant force of 3600 N for 5 seconds. Calculate the final velocity.
Solution:
Step 1: Calculate acceleration using F = ma 3600 = 1200 × a ✓ a = 3600 ÷ 1200 = 3 m/s² ✓
Step 2: Calculate final velocity using v = u + at u = 0 m/s (starts from rest) v = 0 + (3 × 5) ✓ v = 15 m/s ✓✓ (additional mark for correct unit)
Example 3: Energy Conservation and Braking (Higher, 6 marks)
A vehicle of mass 800 kg travelling at 25 m/s brakes and stops in 50 m. Calculate the braking force.
Solution:
Step 1: Calculate initial kinetic energy KE = ½mv² KE = ½ × 800 × 25² ✓ KE = 400 × 625 = 250,000 J ✓
Step 2: Apply work done = energy transferred Work done by brakes = loss in kinetic energy = 250,000 J ✓
Step 3: Calculate braking force W = Fs 250,000 = F × 50 ✓ F = 250,000 ÷ 50 ✓ F = 5000 N ✓
Common mistakes and how to avoid them
• Confusing mass and weight in momentum calculations — momentum uses mass (kg), not weight (N). Always use p = mv, never p = wv. Weight = mg is only needed when converting between mass and gravitational force.
• Forgetting direction in momentum problems — momentum is a vector. In collision questions, assign one direction as positive (usually right or forward), then opposite direction velocities are negative. A common error is adding all values as positive and getting incorrect final directions.
• Misapplying Newton's Third Law — the equal and opposite forces act on different objects, not the same object. When a book sits on a table, the book's weight (downward) and the table's normal contact force (upward) are NOT a Third Law pair because they both act on the book.
• Using wrong units in F = ma — force must be in newtons (N), mass in kilograms (kg), acceleration in metres per second squared (m/s²). If mass is given in grams, convert to kilograms first by dividing by 1000.
• Forgetting that KE depends on v² — doubling speed quadruples kinetic energy (2² = 4). This explains why braking distance increases dramatically with speed. Students often incorrectly assume KE doubles when speed doubles.
• Mixing up thinking and braking distance factors — reaction time affects thinking distance only. Road conditions and brake quality affect braking distance only. Speed affects both. Exam questions specifically test whether you can categorise factors correctly.
Exam technique for Motion Forces and Conservation Laws
• Command words matter: "Calculate" requires a numerical answer with working and units (typically 3-4 marks). "Explain" requires reasons using physics principles, not just descriptions. "State" needs a brief factual answer without explanation.
• Show all working in momentum calculations — even if your final answer is wrong, you gain method marks for correct equations and substitutions. Write p = mv, substitute values, then calculate. Each step typically earns one mark.
• Use equation triangles carefully — Edexcel mark schemes award marks for rearrangement. Write the equation (F = ma), then show the rearranged form (a = F/m) before substituting numbers.
• Extended response questions on stopping distances or safety features require structured answers. Identify the physics principle (conservation of momentum or energy), explain how the feature applies it (increases time/distance), and state the result (reduced force). Aim for 4-6 sentences covering cause → mechanism → effect for full marks.
Quick revision summary
Newton's laws govern how forces affect motion: objects continue at constant velocity unless a resultant force acts (First Law), F = ma relates force to acceleration (Second Law), and interactions produce equal opposite forces on different objects (Third Law). Momentum (p = mv) is conserved in collisions and explosions. Energy conservation links GPE, KE, and work done (W = Fs). Safety features reduce impact forces by increasing collision time. Stopping distance combines thinking distance (affected by reaction time and speed) and braking distance (affected by speed, mass, road conditions, and vehicle condition). Always show working, include units, and consider vector directions in calculations.