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Push a shopping trolley and it rolls forward; pull a door and it swings open; let go of a ball and gravity drags it down. Every one of these everyday events involves a force — a push or a pull — and forces are the single most important idea in this whole topic. But to describe a force properly you cannot just say how big it is; you must also say which way it points, because a 10 N push to the right has a completely different effect from a 10 N push to the left. Quantities that need a direction as well as a size are called vectors, and those that need only a size are called scalars. This lesson opens Topic P2 (Forces) of OCR Gateway Science A by sorting quantities into scalars and vectors, defining force as a vector, distinguishing contact from non-contact forces, drawing free-body force diagrams, and finding the resultant of forces acting on an object.
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 by scale drawing.
A scalar quantity has size (magnitude) only. To state it fully you only need a number and a unit — there is no direction attached. A vector quantity has both a size and a direction; to state it fully you must give the number, the unit and which way it points.
The difference matters because direction can completely change the effect of a quantity. Two cars each travelling at 30 m/s (a scalar speed) might be heading straight towards one another or in the same direction — the speed is identical, but the situations could hardly be more different, and that difference is captured 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 quickest test is to ask "does a direction matter here?" Mass is just 60 kg (scalar); weight is 588 N downwards (vector). If a direction is needed to describe it fully, it is a vector.
A force is a push or a pull acting on an object, usually because of its interaction with another object. Force is measured in newtons (N), named after Isaac Newton, and it is a vector — it has both a size and a direction.
Because force is a vector, we draw it as an arrow. The length of the arrow represents the size of the force (a longer arrow means a bigger force), and the direction the arrow points shows the direction of the force. This simple convention lets us draw all the forces on an object and see at a glance how they combine.
Forces can do several things to an object. A resultant (overall) force 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 known, its size in newtons.
Forces fall into two families depending on whether the objects must 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 to 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 shows the size of the force, its direction shows the direction of the force, and it is labelled with the name of the force.
The diagram below is a free-body diagram of a car driving along a flat road at a steady speed. Four forces act on it: its weight down, the normal contact force (reaction) 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 car 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 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 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 in opposite directions. It helps to pick one direction as positive.
A sledge is pulled to the right with a force of 40 N while friction acts to the left with a force of 15 N. Find the resultant force.
Step 1 — choose right as positive: the pull is +40 N and friction is −15 N.
Step 2 — add them: 40+(−15)=40−15=25 N.
Step 3 — state size and direction (force is a vector): the resultant is 25 N to the right.
Answer: the resultant force is 25 N to the right, so the sledge accelerates to the right.
A tug-of-war has one team pulling left with 500 N and the other pulling right with 500 N. Find the resultant force.
Step 1 — take right as positive: the forces are +500 N and −500 N.
Step 2 — add them: 500+(−500)=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 common slip is to write "25 N" and stop; add "to the right" (or "downwards", etc.) for 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 detail later in the topic.)
The car 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 travels at a steady speed. The tug-of-war with two equal 500 N pulls is also in equilibrium, which is why the rope stays still.
Exam Tip: Equilibrium means zero resultant force, not zero motion. An object in equilibrium can still be moving — it just moves at a constant velocity (steady speed in a straight line) because nothing is speeding it up, slowing it down or turning it.
Forces that act along the same line are easy to add or subtract. But two forces acting at an angle to each other (for example, one pulling north and one pulling east) cannot simply be added as numbers — you must combine them as vectors. A neat 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; 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 in the exam a careful scale drawing and measurement is all that is required at this level.
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 they are 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 present, but the answer does not say which is contact/non-contact, does not mention the resultant force by name, 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 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. This non-zero resultant means the skydiver is not in equilibrium, so they accelerate downwards (speed up). As the speed increases, 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 insightful point that the resultant shrinks as speed rises — an excellent, complete answer.
This content is aligned with OCR Gateway Science A GCSE Physics (J249), Topic P2 Forces (scalar and vector quantities; force as a vector; contact and non-contact forces; free-body diagrams; resultant force; equilibrium; combining forces by scale drawing). Refer to the official OCR specification document for the exact wording.