Revision notes for Edexcel GCSE Physics Forces, vectors and free body diagrams. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Physics (1PH0) specification, so the content matches what's examinable rather than general Physics background.
Forces, vectors and free body diagrams
What you'll learn
- How objects interact by contact and at a distance.
- The difference between scalar and vector quantities.
- How to combine force vectors to find a resultant force.
- How to draw and use free-body diagrams for one object or a system.
Forces start with interactions
A force is never “just there” on its own. It happens because two objects interact. A force can change an object’s speed, change its direction, or change its shape.
Definition
Force
A force is a push or pull caused by an interaction between objects. Its symbol is usually FFF and its unit is the newton, N.
Contact forces
A contact force acts when objects are touching.
Important GCSE examples include:
- Normal contact force: the force from a surface, acting at 90° to the surface. “Normal” means perpendicular.
- Friction: a force that opposes sliding, or the tendency to slide, between surfaces. It acts parallel to the surfaces.
- Tension: a pulling force in a rope, string or cable.
- Air resistance / drag: friction-like forces from moving through air or a fluid.
Non-contact forces and fields
Some forces act at a distance, without objects touching. These are linked to fields.
A field is a region where an object can experience a force without direct contact.
The three field force types you need here are:
- Gravitational field: masses attract other masses. For example, Earth pulls you down; this force is your weight.
- Electrostatic field: charged objects attract or repel other charged objects. For example, a charged balloon can attract small bits of paper.
- Magnetic field: magnets, magnetic materials and electromagnets can attract or repel. For example, a magnet attracts a paperclip.
Key Idea
Forces come from interactions
Every force on an object is caused by another object interacting with it — either by contact or through a field.
Example
Identifying forces on a book on a table
- Choose the object you are interested in: the book.
- Earth pulls the book down through a gravitational field, so the book has a downward weight.
- The table touches the book and pushes it upward, so there is an upward normal contact force.
- If someone tries to slide the book, the table can also exert friction, acting opposite the sliding or attempted sliding.
Force pairs
When two objects interact, each object exerts a force on the other. These are an interaction pair.
For example, if your foot pushes backward on the floor, the floor pushes forward on your foot. The two forces are equal in size and opposite in direction, but they act on different objects.
These forces can be represented as vectors, using arrows. Equal-sized opposite forces are shown with arrows of equal length pointing in opposite directions.
Common Mistake
Equal and opposite does not always mean balanced
Interaction pairs do not cancel each other because they act on different objects. Balanced forces must act on the same object and give zero resultant force.
Scalars and vectors
In physics, quantities are either scalars or vectors.
Definition
Scalar and vector quantities
A scalar has magnitude only, meaning size only. A vector has magnitude and direction.
Examples of scalars:
- mass
- time
- temperature
- distance
- speed
- energy
Examples of vectors:
- force
- weight
- displacement
- velocity
- acceleration
Two common pairs are easy to mix up:
- Distance is how much ground is covered; it is a scalar.
- Displacement is the straight-line change in position from start to finish; it is a vector.
- Speed is how fast something moves; it is a scalar.
- Velocity is speed in a stated direction; it is a vector.
Example
Distance and displacement
A student walks 400 m east, then 300 m west.
- Distance counts the total path travelled, so add the two parts: d=400 m+300 m=700 md=400\ \text{m}+300\ \text{m}=700\ \text{m}d=400 m+300 m=700 m.
- Displacement depends on direction. The 300 m west cancels 300 m of the 400 m east.
- The final displacement is 100 m east, so it must include a direction.
Resultant force
The resultant force is the single overall force that has the same effect as all the forces acting together. It is sometimes called the net force.
If forces act in the same direction, add them. If they act in opposite directions, subtract them and keep the direction of the larger force.
Definition
Equilibrium
An object is in equilibrium when the resultant force on it is zero. Its velocity does not change: it stays at rest or keeps moving at constant velocity.
Balanced forces do not mean “no forces”. They mean the forces on the object cancel to give:
Fresultant=0 NF_{\text{resultant}}=0\ \text{N}Fresultant=0 N
Example
Finding a resultant force in one line
A box has a 60 N pull to the right and a 25 N friction force to the left. Its weight and normal contact force are balanced vertically.
- Choose a positive direction. Let right be positive.
- Subtract the opposing horizontal forces: Fresultant=60 N−25 N=35 NF_{\text{resultant}}=60\ \text{N}-25\ \text{N}=35\ \text{N}Fresultant=60 N−25 N=35 N.
- The larger force is to the right, so the resultant force is 35 N to the right.
- Vertically, the upward and downward forces cancel, so the vertical resultant is zero.
Drawing forces as vectors
A vector diagram uses arrows to show vector quantities. For forces:
- arrow length represents force size
- arrow direction shows force direction
- arrows should be labelled with the force name or value
The Edexcel spec marks detailed vector diagrams, force resolution, free-body diagrams and multi-force resultant examples in this section as Higher Tier content. For this spec, vector diagrams are done using scale drawings only — use a ruler and protractor, not trigonometry.
To combine force vectors:
- Draw the first force arrow to scale.
- Draw the next force from the tip of the previous arrow.
- The resultant goes from the start of the first arrow to the end of the last arrow.
- If the arrows form a closed shape, the resultant is zero and the forces are in equilibrium.
The top diagram shows a resultant force. The bottom diagram shows equilibrium because the vectors close into a triangle.
Example
Finding a resultant using a scale drawing
Two forces act on an object: 30 N east and 40 N north.
- Choose a scale, such as 1 cm on paper represents 10 N.
- Draw a 3 cm arrow to the east for 30 N.
- From the tip of that arrow, draw a 4 cm arrow north for 40 N.
- Draw the resultant from the start of the first arrow to the end of the second arrow.
- Measure the resultant. It should be about 5 cm, so the resultant force is about 50 N, directed north-east.
Resolving a force
Resolution of a force means splitting one force vector into components, usually horizontal and vertical. A component is one part of a vector in a chosen direction.
The components are not extra forces. They are a different way of representing the same force.
Example
Resolving a pull into components
A 20 N pull acts at 30° above the horizontal.
- Use a scale such as 1 cm represents 5 N, so the 20 N force is drawn as a 4 cm arrow.
- Draw the arrow at 30° above the horizontal.
- Complete a right-angled construction by drawing horizontal and vertical component lines from the arrow.
- Measure the component lengths. You might get about 3.5 cm horizontally and 2.0 cm vertically.
- Convert back using the scale: Fhorizontal≈17.5 NF_{\text{horizontal}}\approx17.5\ \text{N}Fhorizontal≈17.5 N and Fvertical≈10 NF_{\text{vertical}}\approx10\ \text{N}Fvertical≈10 N.
Tip
Scale drawing sanity check
A component cannot be bigger than the original angled force. If your horizontal or vertical component is larger than the original force, recheck your scale drawing.
Free-body diagrams
A free-body diagram is a simplified force diagram for one chosen object or system. You remove the surroundings and draw only the forces acting on the chosen object.
Definition
Free-body diagram
A free-body diagram shows all the external forces acting on a single object or chosen system, using labelled force arrows.
Here is a pulled box shown first as a real situation, then as a free-body diagram. Notice that the table and rope disappear from the free-body diagram, but their forces on the box remain.
When drawing one:
- Choose the object or system.
- Draw it as a simple box or dot.
- Add weight downward.
- Add contact forces from surfaces, ropes, engines or fluids.
- Label every force and make arrows point in the correct direction.
Example
Drawing a free-body diagram for a pulled box
A box is pulled right with 30 N. Friction is 18 N left. Its weight is 50 N and the normal contact force is 50 N.
- Choose the object: the box, not the rope or table.
- Draw weight, WWW, downward and normal contact force, RRR, upward. They are equal, so the vertical resultant is zero.
- Draw the pull to the right and friction to the left.
- Find the horizontal resultant: Fresultant=30 N−18 N=12 NF_{\text{resultant}}=30\ \text{N}-18\ \text{N}=12\ \text{N}Fresultant=30 N−18 N=12 N.
- The resultant force is 12 N to the right.
Isolated objects and systems
An isolated object means you focus on one solid object by itself. A system is a group of objects treated as one thing.
This choice matters. Forces between objects inside the system are internal forces, so they are not drawn on the system’s free-body diagram. Forces from outside the system are external forces, and they are drawn.
Example
Choosing one object or a system
Two trolleys are joined by a string and pulled along a bench.
- If you choose just the front trolley, the string force from the back trolley is an external force on that trolley, so you include it.
- If you choose both trolleys together as one system, the string force between them is internal, so you leave it out.
- For the whole system, include only external forces such as the pulling force, total friction, total weight and total normal contact force.
- The resultant force on the system is found from the external forces only.
Exam technique
In the exam
- Choose the object or system first; every arrow must be a force acting on that chosen object or system.
- For vector diagrams, use a clear scale, draw arrows tip-to-tail, and measure the resultant carefully.
- Keep interaction pairs separate from balanced forces: interaction pairs act on different objects, while balanced forces act on the same object.
Self review
Check yourself
- How can a magnet exert a force on a paperclip without touching it?
- What is the difference between speed and velocity?
- In a free-body diagram for a book resting on a table, which forces act on the book?
Recap questions
Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.
Forces and their effects
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