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Nudge a supermarket trolley and it rolls; heave on a stiff drawer and it slides open; release a dropped set of keys and they plummet. Behind each of these ordinary moments is a force — a push or a pull — and forces are the thread that runs through the whole of Topic P2. Yet to describe a force honestly you cannot merely state how strong it is; you must also state which way it acts, because a 12 N shove to the left produces an entirely different outcome from a 12 N shove to the right. Quantities that carry a direction as well as a size are called vectors; those that carry only a size are called scalars. This opening lesson of Topic P2 (Forces) of OCR Gateway Combined Science A sorts quantities into these two families, defines force as a vector, separates contact from non-contact forces, teaches you to draw a free-body force diagram, and shows how to find the resultant of several forces.
By the end of this lesson you should be able to define scalar and vector quantities and give examples of each, describe force as a vector measured in newtons, distinguish contact from non-contact forces, draw a free-body force diagram, find the resultant of forces acting in a line, recognise when an object is in equilibrium, and combine two forces at right angles by scale drawing.
This lesson is AO1 for defining scalars, vectors and the two types of force, AO2 for applying those ideas to draw free-body diagrams and combine forces (including a scale drawing of two forces at right angles), and AO3 when you interpret a diagram to decide whether an object is in equilibrium.
A scalar quantity has a size (magnitude) only. To give it in full you need just a number and a unit — no direction is attached. A vector quantity has both a size and a direction; to give it in full you must state the number, the unit and which way it points.
The reason this split matters is that direction can completely alter the effect of a quantity. Two trains each moving at 40 m/s (a scalar speed) might be racing towards each other or running side by side in the same direction — the speed is the same, but the situations are worlds apart, and that difference is carried by velocity, which is a vector.
| Scalar (size only) | Vector (size and direction) |
|---|---|
| distance | displacement |
| speed | velocity |
| mass | weight |
| time | force |
| energy | acceleration |
| temperature | momentum |
Exam Tip: The fastest test is to ask "does a direction matter here?" Mass is simply 50 kg (scalar); weight is 490 N downwards (vector). If you need a direction to describe the quantity fully, it is a vector.
A force is a push or a pull on an object, usually arising from its interaction with another object. Force is measured in newtons (N), named after Isaac Newton, and it is a vector — it has a size and a direction.
Because a force is a vector, we represent it with an arrow. The length of the arrow stands for the size of the force (a longer arrow means a bigger force), and the way the arrow points shows the direction of the force. This simple convention lets us draw every force on an object and read off at a glance how they combine.
A resultant (overall) force can do several things to an object. It can:
Exam Tip: A force is measured in newtons (N) and is always drawn as an arrow whose length shows the size and whose direction shows the direction of the force. Label every arrow with the name of the force and, where you know it, its size in newtons.
Forces divide into two families according to whether the objects have to be touching.
A contact force acts only when two objects are physically touching. Examples include:
A non-contact force acts at a distance, with no need for the objects to touch. There are three you must know:
| Contact forces | Non-contact forces |
|---|---|
| friction | gravitational |
| air resistance / drag | magnetic |
| tension | electrostatic |
| normal contact force | |
| applied push or pull |
Exam Tip: If the two objects must be touching for the force to act, it is a contact force; if it acts across a gap (gravity, magnetism, static electricity), it is a non-contact force. Weight is the everyday name for the gravitational (non-contact) force on an object.
A free-body force diagram shows a single object on its own, with all the forces acting on it drawn as arrows pointing away from it (or from its centre). The object itself is often drawn as a simple box or dot. Each arrow's length represents the size of the force, its direction shows the direction of the force, and it is labelled with the force's name.
The diagram below is a free-body diagram of a lorry driving along a flat road at a steady speed. Four forces act on it: its weight down, the normal contact force from the road up, the driving force from the engine forwards, and drag (air resistance and friction) backwards.
Here the up and down arrows are the same length (weight balances the normal contact force), and the forward and backward arrows are the same length (driving force balances drag), so the lorry travels at a constant speed in a straight line.
Exam Tip: On a free-body diagram, draw only the forces acting on the one object, each as a labelled arrow from the object. Do not include forces the object exerts on other things, and keep the arrow lengths roughly to scale so balanced forces look equal.
When several forces act on an object, their combined effect is the same as that of a single force called the resultant force. The resultant is the single force that would have the same effect as all the original forces acting together.
For forces acting along the same straight line, you find the resultant simply by adding forces that point the same way and subtracting those that point the opposite way. It helps to choose one direction as positive.
A sledge is pulled to the right with a force of 50 N while friction acts to the left with a force of 18 N. Find the resultant force.
Step 1 — choose right as positive: the pull is +50 N and friction is −18 N.
Step 2 — add them: 50+(−18)=50−18=32 N.
Step 3 — state size and direction (force is a vector): the resultant is 32 N to the right.
Answer: the resultant force is 32 N to the right, so the sledge accelerates to the right.
In a tug-of-war one team pulls left with 600 N and the other pulls right with 600 N. Find the resultant force.
Step 1 — take right as positive: the forces are +600 N and −600 N.
Step 2 — add them: 600+(−600)=0 N.
Answer: the resultant force is zero, so the rope does not move — the forces are balanced.
Exam Tip: Always quote a resultant force with both a size and a direction — it is a vector. A frequent slip is to write "32 N" and stop; add "to the right" (or "downwards", and so on) to earn full marks.
When the resultant force on an object is zero, the forces are said to be balanced and the object is in equilibrium. An object in equilibrium does not change its motion: if it was at rest it stays at rest, and if it was moving it carries on at a constant speed in a straight line. (This is Newton's First Law, which you meet in full later in the topic.)
The lorry in the free-body diagram above is in equilibrium — weight balances the normal contact force, and the driving force balances drag — which is exactly why it moves at a steady speed. The tug-of-war with two equal 600 N pulls is also in equilibrium, which is why the rope stays still.
Exam Tip: This is a classic misconception to avoid: equilibrium means zero resultant force, not zero motion. An object in equilibrium can still be moving — it simply moves at a constant velocity (steady speed in a straight line) because nothing is speeding it up, slowing it down or turning it.
Forces along the same line are easy to add or subtract. But two forces acting at an angle to each other (say, one pulling north and one pulling east) cannot be added as plain numbers — they must be combined as vectors. A tidy way to do this without trigonometry is a scale drawing.
To find the resultant of two forces at right angles by scale drawing:
The diagram below combines a 3 N force to the right with a 4 N force upward; drawn tip-to-tail, the resultant is the diagonal, which measures 5 N.
You can check the size with Pythagoras: 32+42=9+16=25=5 N, but at this level a careful scale drawing and measurement is all that is asked for.
Exam Tip: For forces at an angle, use a scale drawing: state your scale, draw the arrows tip-to-tail, and measure the resultant. Always write down the scale you chose, and give the resultant's size and direction.
| Misconception | The correct idea |
|---|---|
| "Speed and velocity are the same thing" | Speed is a scalar (size only); velocity is a vector (size and direction) |
| "A force only needs a size" | Force is a vector — it needs a direction too, which is why it is drawn as an arrow |
| "Gravity is a contact force" | Gravity is a non-contact force; it acts across a gap with no touching |
| "An object in equilibrium must be stationary" | Equilibrium means zero resultant force; the object can move at a constant velocity |
| "You can add forces at an angle like ordinary numbers" | Forces at an angle must be combined as vectors (e.g. by scale drawing), not simply added |
| "A free-body diagram shows all the forces in the situation" | It shows only the forces acting on the one chosen object |
Question (6 marks): A skydiver has just jumped from a plane and is falling, but has not yet reached top speed. Draw and describe the free-body force diagram for the skydiver at this moment, name the two forces, state whether each is contact or non-contact, and explain what the resultant force does to the skydiver's motion.
Mid-band response: "There is weight pulling the skydiver down and air resistance pushing up. The weight is bigger so the skydiver speeds up."
Examiner-style commentary: The two forces and the correct conclusion are there, but the answer does not classify the forces as contact/non-contact, does not name the resultant force, and gives no diagram detail. To climb a band, classify the forces, state the resultant force and its direction, and link it to acceleration.
Stronger response: "On the skydiver, weight acts downwards (a non-contact gravitational force) and air resistance acts upwards (a contact force). On a free-body diagram these are two arrows drawn from the skydiver, the weight arrow longer than the air-resistance arrow. Because the weight is greater than the air resistance, there is a resultant force downwards, so the skydiver accelerates (speeds up) downwards."
Examiner-style commentary: A clear answer that classifies the forces, describes the arrows and identifies the resultant. To reach the top band, state that the resultant is the difference between the two forces, and explain that as the skydiver speeds up the air resistance grows, so the resultant force decreases.
Top-band response: "The free-body diagram shows the skydiver with two force arrows pointing away from them: a weight arrow pointing downwards and a shorter air-resistance (drag) arrow pointing upwards. Weight is a non-contact force (the gravitational pull of the Earth on the skydiver's mass), while air resistance is a contact force (between the moving skydiver and the air). At this moment the weight is greater than the air resistance, so there is a resultant force downwards equal to the difference between them. Because this resultant is not zero, the skydiver is not in equilibrium, so they accelerate downwards (speed up). As their speed rises, the air resistance increases, so the resultant force gradually gets smaller and the acceleration decreases — until eventually the forces balance and terminal velocity is reached."
Examiner-style commentary: Full marks. It describes the labelled arrows, classifies each force correctly, identifies the resultant as the difference, links it to acceleration through the absence of equilibrium, and adds the insight that the resultant shrinks as speed rises — a complete and precise answer.
This content is aligned with OCR Gateway Combined Science A (J250), Topic P2 Forces. Refer to the official OCR specification for exact wording.