What you'll learn
This topic covers how forces affect the motion and shape of objects, including contact and non-contact forces, free-body diagrams, Newton's laws of motion, and calculations involving force, mass, and acceleration. You'll learn to identify forces in real situations, calculate resultant forces, and apply Newton's laws to solve problems involving moving objects.
Key terms and definitions
Force — a push or pull acting on an object due to interaction with another object, measured in newtons (N)
Vector quantity — a physical quantity with both magnitude and direction (e.g. force, velocity, acceleration)
Scalar quantity — a physical quantity with magnitude only (e.g. mass, speed, distance, energy)
Resultant force — the single force that has the same effect as all the individual forces acting on an object combined
Friction — a contact force that opposes motion between two surfaces sliding past each other
Terminal velocity — the constant maximum speed reached by a falling object when the drag force equals the weight
Inertia — the tendency of an object to remain at rest or continue moving at constant velocity unless acted upon by a resultant force
Free-body diagram — a diagram showing all forces acting on an isolated object, represented by arrows indicating direction and magnitude
Core concepts
Contact and non-contact forces
Forces can be classified into two categories based on whether objects need to be touching.
Contact forces require physical contact between objects:
- Friction — opposes relative motion between surfaces
- Air resistance (drag) — opposes motion through air
- Tension — pulling force transmitted through a rope, cable, or string
- Normal contact force — reaction force perpendicular to a surface supporting an object
- Upthrust — upward buoyant force exerted by a fluid
Non-contact forces act at a distance without physical contact:
- Gravitational force — attractive force between masses
- Electrostatic force — force between charged objects
- Magnetic force — force between magnets or magnetic materials
All forces are interactions between pairs of objects. When object A exerts a force on object B, object B exerts an equal and opposite force on object A (Newton's third law).
Vector diagrams and resultant forces
Forces are vectors, so they must be represented with both magnitude and direction. In diagrams, arrows show:
- Direction of force (arrow direction)
- Magnitude of force (arrow length, to scale)
Free-body diagrams show all forces acting on a single object. The object is represented as a point or simple shape, with force arrows starting from the object.
To find the resultant force:
For forces in the same line:
- Add forces in the same direction
- Subtract forces in opposite directions
- The resultant has the direction of the larger force
Example: A car experiences 5000 N driving force forward and 1200 N air resistance backward. Resultant force = 5000 N - 1200 N = 3800 N forward
For forces at right angles:
- Use Pythagoras' theorem: F = √(F₁² + F₂²)
- Can also use scale drawings with ruler and protractor
When the resultant force is zero, forces are balanced and the object is in equilibrium.
Newton's First Law of Motion
Newton's First Law states: An object will remain at rest or continue moving at constant velocity unless acted upon by a resultant force.
This law describes inertia — the natural tendency of objects to resist changes in motion.
Applications:
- A book resting on a table stays at rest (balanced forces: weight downward, normal contact force upward)
- A spacecraft in deep space continues at constant velocity with engines off (no air resistance)
- A passenger in a braking car continues forward (inertia) until the seatbelt applies a force
Key points:
- If resultant force = 0 N, then acceleration = 0 m/s²
- Zero acceleration means constant velocity (which includes zero velocity/at rest)
- Velocity is constant when both speed AND direction are constant
Newton's Second Law of Motion
Newton's Second Law states: The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass.
Equation: F = ma
Where:
- F = resultant force (N)
- m = mass (kg)
- a = acceleration (m/s²)
Rearranged forms:
- a = F/m
- m = F/a
Key relationships:
- Doubling the force doubles the acceleration (if mass stays constant)
- Doubling the mass halves the acceleration (if force stays constant)
- More massive objects are harder to accelerate (greater inertia)
Inertial mass is defined as the ratio of force to acceleration: m = F/a. This measures how difficult it is to change an object's velocity.
Newton's Third Law of Motion
Newton's Third Law states: When two objects interact, they exert equal and opposite forces on each other.
These force pairs:
- Are equal in magnitude
- Act in opposite directions
- Act on different objects (crucial!)
- Are the same type of force
Examples:
Book on a table:
- Book exerts gravitational force downward on Earth
- Earth exerts gravitational force upward on book (the book's weight) These are Newton's third law pairs.
Note: The normal contact force from the table on the book is NOT the third law pair to the book's weight — they're both acting on the book.
Rocket propulsion:
- Rocket exerts force on exhaust gases (pushing them backward)
- Exhaust gases exert force on rocket (pushing it forward)
Walking:
- Foot pushes backward on ground (friction)
- Ground pushes forward on foot (friction) — this accelerates you forward
Weight, mass, and gravitational field strength
Mass is the amount of matter in an object, measured in kilograms (kg). Mass is a scalar quantity and doesn't change with location.
Weight is the force of gravity acting on an object's mass, measured in newtons (N). Weight is a vector quantity acting toward the centre of the gravitational field (downward on Earth).
Equation: W = mg
Where:
- W = weight (N)
- m = mass (kg)
- g = gravitational field strength (N/kg)
On Earth's surface: g ≈ 9.8 N/kg (often approximated as 10 N/kg in calculations)
The gravitational field strength varies:
- Earth surface: 9.8 N/kg
- Moon surface: 1.6 N/kg
- Jupiter surface: 25 N/kg
An object's mass remains constant everywhere, but its weight changes depending on gravitational field strength.
The centre of mass is the point where the entire weight of an object appears to act. For uniform, symmetrical objects, it's at the geometric centre.
Forces and motion: terminal velocity
When an object falls through a fluid (liquid or gas), it experiences:
- Weight — constant downward force (mg)
- Drag force (air resistance) — upward force that increases with speed
Sequence of motion:
Initially: Object accelerates downward
- Weight > drag
- Resultant force downward
- Acceleration = (W - drag)/m
As speed increases: Drag increases (depends on speed²)
- Resultant force decreases
- Acceleration decreases
Terminal velocity reached: Speed becomes constant
- Weight = drag
- Resultant force = 0 N
- Acceleration = 0 m/s²
Factors affecting terminal velocity:
- Surface area — larger area = greater drag = lower terminal velocity (parachute effect)
- Shape — streamlined shapes reduce drag = higher terminal velocity
- Mass — greater mass = higher weight = higher terminal velocity needed to balance forces
A skydiver demonstrates terminal velocity:
- Falls with increasing speed until reaching terminal velocity (~120 mph)
- Opens parachute: drag suddenly increases massively
- Speed decreases until new, much lower terminal velocity is reached (~15 mph)
Stopping distances
The stopping distance of a vehicle is the total distance travelled from when the driver sees a hazard until the vehicle stops.
Stopping distance = thinking distance + braking distance
Thinking distance — distance travelled during the driver's reaction time (before brakes applied)
- Depends on: speed, reaction time
- Increased by: distractions, tiredness, alcohol, drugs
Braking distance — distance travelled while braking (after brakes applied)
- Depends on: speed, mass, brake condition, road condition, tyre condition
- Increased by: higher speed (squared relationship), wet/icy roads, worn brakes/tyres, greater vehicle mass
Speed relationship:
- If speed doubles, thinking distance doubles
- If speed doubles, braking distance quadruples
- If speed doubles, stopping distance more than doubles
Typical values at 30 mph (13 m/s):
- Thinking distance: 9 m
- Braking distance: 14 m
- Total stopping distance: 23 m
Worked examples
Example 1: Calculating resultant force and acceleration
Question: A cyclist and bicycle have a combined mass of 85 kg. The cyclist applies a forward force of 250 N. Friction and air resistance provide a total resistive force of 80 N.
(a) Calculate the resultant force on the cyclist. [2 marks] (b) Calculate the acceleration of the cyclist. [3 marks]
Solution:
(a) Resultant force = forward force - resistive force [1] Resultant force = 250 N - 80 N = 170 N [1]
(b) F = ma, so a = F/m [1] a = 170/85 [1] a = 2.0 m/s² [1]
Example 2: Weight on different planets
Question: An astronaut has a mass of 72 kg.
(a) Calculate the astronaut's weight on Earth, where g = 9.8 N/kg. [2 marks] (b) The astronaut's weight on Mars is 270 N. Calculate the gravitational field strength on Mars. [3 marks]
Solution:
(a) W = mg [1] W = 72 × 9.8 = 706 N (or 705.6 N) [1]
(b) W = mg, so g = W/m [1] g = 270/72 [1] g = 3.75 N/kg [1]
Example 3: Terminal velocity
Question: A ball bearing is dropped into a tall cylinder of oil.
(a) Explain why the ball bearing initially accelerates. [2 marks] (b) Explain what happens to the ball bearing's motion as it continues to fall. [4 marks]
Solution:
(a) The weight (downward force) is greater than the drag/upward force [1] So there is a resultant force downward/in the direction of motion [1]
(b) As the speed increases, the drag force increases [1] This reduces the resultant force [1] So acceleration decreases [1] Eventually drag equals weight, resultant force becomes zero, and the ball reaches constant speed/terminal velocity [1]
Common mistakes and how to avoid them
Confusing mass and weight — mass is measured in kg and doesn't change; weight is measured in N and depends on gravitational field strength. Always use W = mg to convert between them.
Forgetting direction in force calculations — forces are vectors. When calculating resultant forces, subtract forces in opposite directions, don't add them. A 100 N force forward and 30 N friction backward gives 70 N forward, not 130 N.
Misidentifying Newton's third law pairs — the two forces must act on different objects and be the same type. The weight of a book and the normal contact force from the table are NOT third law pairs (both act on the book).
Thinking terminal velocity requires upward motion — terminal velocity occurs when drag equals weight and acceleration is zero. The object continues moving downward at constant speed, not upward.
Using the wrong units — ensure mass is in kg (not g), force in N, and acceleration in m/s². Convert before calculating: 500 g = 0.5 kg.
Assuming balanced forces mean stationary — balanced forces (zero resultant) mean zero acceleration, which includes moving at constant velocity. An object can be moving and have balanced forces.
Exam technique for "Forces and their effects"
Command word precision — "Calculate" requires working and a numerical answer with units. "Explain" needs reasons using physics principles (e.g., "because the resultant force is zero"). "Describe" wants what happens without detailed explanation.
Free-body diagrams — always draw arrows from the object, label each force clearly, and ensure arrow lengths represent relative magnitudes. Include all relevant forces (weight, normal contact, friction, thrust, drag, tension).
Show working for calculations — write the equation, substitute values with units, then give the answer. This gains method marks even if the final answer is incorrect. For 3-mark calculations: 1 mark for correct equation, 1 mark for substitution, 1 mark for answer.
Link force changes to motion — exam questions often ask you to connect forces to acceleration or velocity. Use Newton's second law: resultant force → acceleration → velocity change. State the sequence clearly.
Quick revision summary
Forces are pushes or pulls measured in newtons. Contact forces require touching; non-contact forces act at a distance. The resultant force determines acceleration via F = ma. Newton's First Law: objects maintain constant velocity without a resultant force. Newton's Second Law: F = ma. Newton's Third Law: interaction forces are equal and opposite on different objects. Weight (W = mg) depends on gravitational field strength; mass doesn't. Terminal velocity occurs when drag equals weight. Stopping distance equals thinking distance plus braking distance, both increasing with speed.