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Forces & Momentum

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Edexcel IAL Physics · Unit 1

Forces & Momentum

Big Idea: Forces change how things move — and no matter how messy a collision looks, the total "oomph" (momentum) in the system never disappears.

Chapter Summary

This chapter is really two connected stories. Story one is about why things speed up, slow down, or stay still — that's Newton's Laws. Story two is about what happens when things collide or push apart — that's momentum. Here's the whole chapter at a glance:

Newton's First Law

No resultant force = no change in velocity. Balanced forces mean constant speed (or rest).

Newton's Second Law

Resultant force causes acceleration: ΣF = ma. Bigger force or smaller mass = bigger acceleration.

Terminal Velocity

Drag force grows until it balances the driving force — then acceleration becomes zero.

Mass, Weight & g

Mass is fixed; weight (W = mg) depends on gravitational field strength.

Core Practical 1

Three ways to measure g experimentally: electromagnet drop, light gates, and ramp & trolley.

Newton's Third Law

Every force has an equal, opposite, same-type reaction force on a different object.

Momentum

p = mv. A vector — direction matters, so momentum can be negative.

Conservation of Momentum

In a closed system, total momentum before a collision = total momentum after.

1. Force & Acceleration

Newton's First Law of Motion

Here's the core idea, and it trips people up because it feels wrong at first: objects don't need a force to keep moving. Your instinct says "if nothing's pushing it, it should stop" — but that's only because in real life, friction is almost always secretly pushing back. Newton's First Law says that if the forces on an object are perfectly balanced (including zero forces at all), the object just keeps doing whatever it was already doing — staying still, or cruising at constant velocity in a straight line.

Newton's First Law — in words

A body remains at rest or moves at constant velocity unless acted on by a resultant force.

Translation: no net push = no change in speed or direction.

"Resultant force" just means the overall force left over once you've added up everything acting on the object (accounting for direction). If forces-left = forces-right AND forces-up = forces-down, the resultant is zero, and the object's velocity is locked in — whatever it was.

Worked Example

A car moves at constant velocity. The driving force from the engine is 6 kN. What is the frictional force F?

Step 1 — spot the clue word: "constant velocity" means forces are balanced.

Step 2 — apply ΣF = 0: so F (friction) = D (driving force).

Step 3 — answer with units: F = 6 kN.

Practice Question

A book sits still on a table. Explain, using Newton's First Law, why the book doesn't accelerate even though gravity is pulling down on it.

Newton's Second Law of Motion

First Law tells you what happens when forces are balanced. Second Law tells you what happens when they're not — when there's a leftover, resultant force. The rule is beautifully simple: the bigger the resultant force, the bigger the acceleration; the bigger the mass, the smaller the acceleration for the same force. Push a shopping trolley and a truck with the same force, and the trolley shoots off while the truck barely budges — same force, wildly different mass, wildly different acceleration.

Newton's Second Law

ΣF = ma

The Σ (sigma) is important — it means "the sum of all forces," not just one force acting alone. Always find the resultant force first.

If the resultant force points along the direction of travel, the object speeds up or slows down. If it points at an angle to the direction of travel, the object changes direction instead (this is how circular motion works, which you'll meet later).

Worked Example

An object with mass 750 g accelerates in a straight line at 11 m s⁻². Find the resultant force.

Step 1 — convert units: m = 750 g = 0.750 kg (always convert to kg before using ΣF = ma).

Step 2 — substitute: ΣF = ma = 0.75 × 11 = 8.25

Step 3 — round sensibly and add units: ΣF = 8.3 N

Practice Question

A resultant force of 15 N acts on a trolley of mass 2.5 kg. Calculate its acceleration.

Terminal Velocity

This is one of the most satisfying applications of the two laws combined. Picture a skydiver jumping out of a plane. At the moment they jump, the only significant force is their weight pulling them down — air resistance is almost zero because they're barely moving. So there's a big resultant force, and by Newton's Second Law, they accelerate downward.

But as their speed increases, air resistance (drag) increases too — drag always opposes motion, and it grows with speed. So the resultant force (weight minus drag) gets smaller as they fall, which means their acceleration gets smaller too — they're still speeding up, just less and less quickly. Eventually, drag grows until it exactly equals weight. At that point the resultant force is zero, so by Newton's First Law, the velocity stops changing. This constant maximum speed is called terminal velocity.

Analogy

Think of terminal velocity like running against an increasingly strong headwind while sprinting downhill. At first you accelerate easily. But the faster you go, the harder the wind pushes back, until eventually the wind's push exactly cancels your effort — you stop accelerating and just cruise at a fixed top speed.

Stage A: Weight > Drag → accelerating (fast) Stage B: Weight > Drag → accelerating (slower, drag catching up) Stage C: Weight = Drag → ZERO acceleration = TERMINAL VELOCITY

Worked Example

Suggest two ways a car designer could increase the car's maximum (terminal) velocity.

Step 1 — identify what "maximum velocity" means: it's reached when all forces are balanced, so to raise it you must either increase the forwards force or decrease the backwards (opposing) forces.

Step 2 — list the forces: Forward = engine thrust. Backward = tyre friction, air resistance, engine friction, wheel-bearing friction.

Step 3 — suggest changes: Increase engine power (more forward thrust); OR make the car body more streamlined (less air resistance); OR use better lubricant in the engine and bearings (less internal friction).

Practice Question

Explain why a skydiver's acceleration decreases as they fall, even before they reach terminal velocity.

2. Mass, Weight & Gravitational Field Strength

These three get mixed up constantly, so let's nail the distinction once and for all.

Mass is the amount of "stuff" (matter) in an object, measured in kilograms. It's a measure of how much an object resists a change in motion — more mass, harder to accelerate. Crucially, mass doesn't change depending on where you are in the universe.
Weight is a force — the pull of gravity on that mass — measured in newtons. Because it's a force caused by a gravitational field, weight does change depending on where you are (your weight on the Moon is about 1/6 of your weight on Earth, even though your mass is identical).
Gravitational field strength (g) is the force per kilogram acting on any object in that field, measured in N kg⁻¹. On Earth's surface, the average value is 9.81 N kg⁻¹.

Weight

W = mg

Weight (N) = mass (kg) × gravitational field strength (N kg⁻¹)

Gravitational Field Strength

g = F / m

Force per kilogram acting on an object — same equation as weight, just rearranged.

Constant Acceleration in Freefall

"Freefall" describes an object falling where the only force acting is its weight — we deliberately ignore drag. Here's the elegant bit: because weight = mg, and Newton's Second Law says ΣF = ma, in freefall these are the same force. So:

Why all objects fall at the same rate

ma = mg → a = g

The mass cancels out completely! That means a bowling ball and a feather accelerate at exactly the same rate in a vacuum (9.81 m s⁻²), regardless of their mass or weight — it's only air resistance in real life that makes feathers fall slower.

Why this feels surprising

It seems like heavier objects should fall faster because they have more weight (bigger force). But they also have more mass (more resistance to acceleration) — and those two effects cancel out exactly. Galileo famously demonstrated this by dropping objects of different mass from the Leaning Tower of Pisa.

Practice Question

An astronaut has a mass of 80 kg. On the Moon, g = 1.6 N kg⁻¹. Calculate the astronaut's weight on the Moon, and explain why their mass is unchanged.

3. Core Practical 1 — Investigating the Acceleration of Freefall

You need to know three different experimental setups for measuring g. Examiners love asking about the method, the graph you'd plot, and the sources of error — so understand the logic behind each rather than memorising word-for-word.

Method 1: Electromagnet & Trapdoor

Idea: A steel ball is held by an electromagnet at a measured height, h, above a trapdoor. When the current is switched off, the ball drops and simultaneously starts a timer; when it hits the trapdoor, the timer stops — giving the fall time, t.

Which SUVAT equation, and why

h = ½gt²

You know s (=h), u (=0, dropped from rest), and a (=g); you measure t. Rearranged into y = mx + c form: plot h (y-axis) against t² (x-axis) → gradient = ½g.

Method summary: Measure h with a metre ruler → drop the ball → record t → repeat 3 times per height and average → repeat for 5–10 different heights → plot h vs t² → gradient = ½g.

Method 2: Card & Single Light Gate

Idea: A weighted card of known length falls through a clear tube and passes through a single light gate, which uses the card's length and how long it blocks the beam to calculate a final velocity, v, at that point.

Which SUVAT equation, and why

v² = 2gh

You know u (=0), a (=g), s (=h); you measure v. Rearranged: plot v² (y-axis) against 2h (x-axis) → gradient = g directly.

Method 3: Ball Bearing & Two Light Gates

Idea: Same principle as Method 1, but instead of a manual trapdoor timer, two light gates positioned a known distance h apart start and stop the timer automatically as the ball passes through each one — more precise than reaction-time-dependent methods.

The algebra (rearranged straight-line form)

2h/t = gt + 2u

Plot 2h/t (y-axis) against t (x-axis) → gradient = g, y-intercept = 2u.

Method 4: Ramp & Trolley (Galileo's method)

Idea: Instead of dropping something straight down, a trolley with a card attached rolls down an inclined ramp, passing through a light gate that records its velocity. This "dilutes" gravity so it's easier to measure accurately — same physics, gentler motion.

Which SUVAT equation, and why

v = u + at

u = 0 (starts from rest), a = the acceleration provided by gravity component along the ramp. Plot v (y-axis) against t (x-axis) → gradient = acceleration = g (for this setup).

Common Errors Across All Methods

Systematic error: residual magnetism in the electromagnet can delay release, making t recorded as longer than it should be — this would make your calculated g too small.
Random error: a 1 mm precision ruler gives a large percentage uncertainty for small heights — always measure the biggest height/distance practical.
Random error: parallax error when reading a ruler — always read at eye level.
Repeat each measurement 3–5 times and average to reduce the effect of random error.

Safety

Electromagnets need current — keep water away and only switch on once fully set up. Use a cushion to catch falling ball bearings. Clamp stands must be secured with a G-clamp so they don't tip.

Practice Question

In the electromagnet method, a graph of h against t² is plotted. Explain how you would use this graph to determine g, and state the gradient in terms of g.

4. Newton's Third Law of Motion

This is the law students confuse most often with the First Law — so let's be really precise. Newton's Third Law is about what happens whenever two separate objects interact.

Newton's Third Law — in words

Whenever two bodies interact, the forces they exert on each other are equal in size, opposite in direction, and of the same type.

"Same type" matters: if object A pulls B with a gravitational force, B pulls A back with a gravitational force too — not a different kind of force.

FOOT GROUND ┌──────┐ F (foot pushes ground back) │ shoe │ ─────────────────────────────► └──────┘ ◄───────────────────────────────── F (ground pushes foot forward) Foot pushes the ground BACKWARDS. Ground pushes the foot FORWARDS with an equal, opposite force. → This is how walking works!

The Golden Test — First Law vs Third Law

Ask yourself: how many objects are the two forces acting on?

Forces acting on one object that happen to be balanced → First Law scenario.
A pair of equal-and-opposite forces acting on two different objects → Third Law pair.

Worked Example (the classic exam trap)

A physics textbook rests on a table. Someone claims the "weight down / normal force up" pair shown on a free-body diagram of the book is an example of Newton's Third Law. Is this correct?

Step 1 — check how many objects are involved: Both forces (weight and normal reaction) act on the same object — the book.

Step 2 — check the force types: Weight is gravitational; the normal reaction is a contact force. Different types, acting on one object.

Step 3 — conclusion: This is not a Third Law pair — it's a First Law situation (balanced forces on one stationary object). The true Third Law pairs here would be: (1) Earth pulls book down / book pulls Earth up (gravitational pair), and (2) table pushes book up / book pushes table down (contact force pair) — each pair acts on two different objects.

Practice Question

A rocket expels gas downwards to launch upwards. Use Newton's Third Law to explain why this makes the rocket accelerate upward.

5. Momentum

Momentum is basically a measure of "how hard it would be to stop something." A slow-moving truck and a fast-moving tennis ball can have very different masses but end up with surprisingly similar momentum — that's exactly why the concept is useful.

Linear Momentum

p = mv

Momentum (kg m s⁻¹) = mass (kg) × velocity (m s⁻¹)

The crucial thing to remember: momentum is a vector. It has both size and direction, which means it can be positive or negative depending on which way the object is moving. If you define "rightward" as positive, an object moving left has negative momentum — even if its speed (and mass) is identical to something moving right.

Worked Example

Which has more momentum: a 60 g tennis ball moving at 75 m s⁻¹, or a 3 kg brick moving at 1.5 m s⁻¹?

Ball: p = mv = 0.06 kg × 75 m s⁻¹ = 4.5 kg m s⁻¹

Brick: p = mv = 3 kg × 1.5 m s⁻¹ = 4.5 kg m s⁻¹

Conclusion: They're exactly equal! Even though the brick is 50× heavier, the ball is 50× faster — momentum balances mass against velocity. On impact, both would exert a similar force (depending on how quickly each comes to rest).

Unit Traps

Mass given in grams? Divide by 1000 to convert to kg before using p = mv.
Velocity given in km s⁻¹? Multiply by 1000 to convert to m s⁻¹.
Always sketch a quick diagram with a defined positive direction and arrows — it prevents sign errors.

Practice Question

A 1200 kg car travels east at 20 m s⁻¹. Calculate its momentum, stating a direction convention.

6. Conservation of Linear Momentum

This is the payoff of the whole chapter, and it's genuinely one of the most powerful ideas in physics: in any closed system (no external forces), the total momentum before an event exactly equals the total momentum after it — no matter how violent or messy the collision looks.

The Principle of Conservation of Momentum

Total momentum before = Total momentum after

This only holds true if no external (outside) forces act on the system during the event.

Because momentum is a vector, objects moving toward each other from opposite directions can have momenta that partly (or fully) cancel out — the total can even be zero, even though both objects are clearly moving.

BEFORE collision: m ──u──► M (stationary) momentum = m × u + M × 0 = m × u AFTER collision (m bounces back, M moves forward): ◄──v── m M ──V──► momentum = M × V + m × (−v) = M×V − m×v Conservation: m × u = M×V − m×v

Worked Example (perfectly inelastic collision)

Trolley A (mass 0.80 kg) collides head-on with stationary trolley B, travelling at 3.0 m s⁻¹. B has twice the mass of A. They stick together on impact. Find their common velocity afterwards.

Step 1 — find B's mass: M_B = 2 × 0.80 = 1.60 kg

Step 2 — momentum before: (M_A × V_A) + (M_B × V_B) = (0.8 × 3.0) + (1.6 × 0) = 2.4 kg m s⁻¹

Step 3 — momentum after (combined mass moves together at V): (M_A + M_B) × V = (0.8 + 1.6) × V = 2.4 kg × V

Step 4 — apply conservation and solve: 2.4 = 2.4 × V → V = 1.0 m s⁻¹ (in the same direction A was originally moving)

How This Connects to Newton's Third Law

Conservation of momentum isn't a separate rule that appears from nowhere — it's actually a direct consequence of Newton's Third Law. When two trolleys collide, trolley A exerts a force on B, and by the Third Law, B exerts an exactly equal and opposite force back on A (F_B→A = −F_A→B). Because the forces are equal, opposite, and act for the same amount of time (they're in contact simultaneously), the changes in momentum they cause exactly cancel out across the whole system — so total momentum is preserved.

Important subtlety: equal and opposite forces do not mean equal and opposite accelerations. Since a = F/m, if the two colliding objects have different masses, they'll accelerate by different amounts even though the forces on them are identical in size.

Exam Strategy Tip

Momentum questions are often long, wordy word-problems. Don't try to solve them in your head — always sketch a quick "before and after" diagram with each object as a simple circle, labelled with mass and velocity (including sign), before you write any equation. It takes 20 seconds and prevents almost every sign error.

Practice Question

A 1.5 kg ball is thrown at 15 m s⁻¹ toward a stationary 55 kg girl on roller skates. She catches it and they move off together. Find their common velocity after the catch.

What to Memorise

Term / Formula	Meaning
Newton's 1st Law	Object stays at rest or constant velocity unless a resultant force acts on it.
ΣF = ma	Newton's 2nd Law — resultant force = mass × acceleration.
Newton's 3rd Law	Interacting bodies exert equal, opposite, same-type forces on each other (two different objects).
Terminal velocity	Constant maximum speed reached when driving force = opposing (drag) force, so resultant = 0.
W = mg	Weight = mass × gravitational field strength.
g = F/m	Gravitational field strength = force per kg. On Earth, g ≈ 9.81 N kg⁻¹.
Freefall	Falling under gravity alone (drag ignored) — all masses accelerate at the same rate, a = g.
h = ½gt²	SUVAT for electromagnet/trapdoor freefall method — plot h vs t², gradient = ½g.
v² = 2gh	SUVAT for single light-gate method — plot v² vs 2h, gradient = g.
p = mv	Momentum (kg m s⁻¹) = mass × velocity. Vector quantity — can be negative.
Conservation of momentum	Total momentum before = total momentum after, in a closed system with no external forces.

Concepts Checklist

I can state Newton's First Law and identify balanced-force situations.
I can apply ΣF = ma, including converting units (g→kg) correctly.
I can explain why terminal velocity happens using both drag and Newton's laws.
I understand the difference between mass, weight, and gravitational field strength.
I can explain why all objects fall at the same rate in freefall (mass cancels in ma = mg).
I can describe at least two of the Core Practical 1 methods for measuring g, including the SUVAT equation used and what to plot.
I can identify systematic vs random errors in the freefall practicals.
I can state Newton's Third Law and correctly identify genuine Third Law pairs (two objects, same type, equal & opposite).
I can distinguish a Newton's First Law situation from a Newton's Third Law pair on a free-body diagram.
I can calculate momentum (p = mv) and treat direction correctly with positive/negative signs.
I can apply conservation of momentum to solve collision problems, including "sticking together" collisions.
I can explain how conservation of momentum follows from Newton's Third Law.

Exam Tips & Common Mistakes

Trap #1: Confusing First Law and Third Law

The single most common mark-scheme trap. Balanced forces on one object (like a book on a table) = First Law. Equal-and-opposite forces on two different objects (like a foot pushing the ground) = Third Law. Always count the objects involved before answering.

Trap #2: Forgetting Unit Conversions

Mass in grams must become kg (÷1000) before using ΣF = ma or p = mv. Missing this is one of the most frequent lost marks in calculation questions.

Trap #3: Ignoring Direction / Sign in Momentum

Momentum is a vector. If an object reverses direction after a collision, its velocity (and momentum) becomes negative relative to your chosen positive direction — forgetting the sign flip is a very common error in "bounce-back" collision questions.

Trap #4: Assuming Equal Forces Means Equal Accelerations

In a Newton's Third Law pair, the forces are always equal and opposite — but the resulting accelerations are only equal if the masses are equal too (a = F/m). Examiners often test this with unequal-mass collisions.

What Examiners Reward

Clearly labelled diagrams showing chosen positive direction before any momentum calculation.
Explicit statement of "ΣF = 0" or "resultant force = 0" rather than just "forces are balanced" when justifying constant velocity.
In practicals: identifying specific sources of error (e.g. "parallax error reading the ruler") rather than vague statements like "human error."
Showing the rearrangement of a SUVAT equation into y = mx + c form before stating the gradient's physical meaning.

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Also in the full note

1. Force & Acceleration
2. Mass, Weight & Gravitational Field Strength
Exam Tips & Common Mistakes
Method 1: Electromagnet & Trapdoor
Method 2: Card & Single Light Gate
Method 3: Ball Bearing & Two Light Gates
Method 4: Ramp & Trolley (Galileo's method)
Mass, Weight & g

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