Contact Forces
1. Normal Force
Learning outcomes
- I can define the normal force.
- I can identify normal forces in free-body diagrams.
- I can explain how normal force arises.
- I can calculate normal forces in simple situations.
- I can compare normal force and weight.
Introduction
Whenever you stand on the ground, sit in a chair, or place a book on a table, the surface pushes back on you. This push is called the normal force. Although we cannot see it, the normal force acts whenever two objects are in contact.
The normal force is one of the most common forces encountered in physics. It helps explain why objects do not fall through the floor, how forces balance when an object is at rest, and why the forces acting on an object change when it is placed on an incline. Understanding the normal force is essential before studying friction and more advanced mechanics.
What Is the Normal Force?
The normal force is the support force exerted by a surface on an object in contact with it.
The word normal means perpendicular (at right angles) to a surface.
Definition:
The normal force is the force exerted by a surface on an object, acting perpendicular to the surface.
Key Characteristics
The normal force:
- acts only when two objects are in contact,
- always acts perpendicular to the surface,
- is a contact force,
- prevents objects from passing through surfaces,
- is measured in newtons (N).
How Does the Normal Force Arise?
When an object presses against a surface because of its weight or another applied force, the atoms in the surface are slightly compressed.
These atoms resist being compressed and push back on the object.
This upward (or perpendicular) push is the normal force.
According to Newton's Third Law, the object pushes on the surface, and the surface pushes back on the object with an equal and opposite force.
For example:
- A book pushes down on a table.
- The table pushes up on the book with the normal force.
Direction of the Normal Force
The normal force is always perpendicular to the surface, not necessarily vertical.
Examples:
- On a horizontal floor, the normal force acts upward.
- On a sloping hill, the normal force acts perpendicular to the slope.
- Against a vertical wall, the normal force acts horizontally.
Normal Force on a Horizontal Surface
Consider a book resting on a table.
Two forces act on the book:
- Weight (W) acts downward.
- Normal force (FN) acts upward.
If the book is not accelerating vertically, FN = W
Since W = mg then
where:
- Fₙ = normal force (N)
- m = mass (kg)
- g = gravitational field strength (9.8 m/s² or approximately 10 N/kg)
Worked Example 1
A 5.0 kg book rests on a table.
Calculate the normal force.
Solution
Weight:
Since the book is at rest, FN = 49 N
Answer:
49 N upward
Normal Force with an Additional Downward Force
Sometimes an extra force pushes an object downward.
For example, a person presses down on a box.
In this case, FN = W + Fapplied
The surface must push harder to support the object.
Worked Example 2
A 4.0 kg box rests on the floor.
Someone pushes downward with a force of 20 N.
Calculate the normal force.
Solution
Weight:
Normal force:
Answer:
59.2 N upward
Normal Force When Pulling Upward
If an upward force is applied to an object without lifting it,
the surface supports less of the object's weight.
In this case, FN = W − Fupward
If the upward force becomes equal to the object's weight,
the normal force becomes zero, and the object just begins to lose contact with the surface.
Worked Example 3
A 12 kg suitcase rests on the ground.
Someone pulls upward with a force of 30 N.
Calculate the normal force.
Solution
Weight:
Normal force:
Answer:
87.6 N upward
Normal Force on an Inclined Plane
When an object rests on a slope, its weight still acts vertically downward, but the normal force acts perpendicular to the surface.
Only the component of the weight acting perpendicular to the slope contributes to the normal force.
For an incline with angle θ,
As the slope becomes steeper:
- the normal force decreases,
- the component of weight parallel to the slope increases.
Worked Example 4
A 10 kg box rests on a 30° incline.
Calculate the normal force.
Solution
Weight:
Normal force:
Answer:
Approximately 85 N
Identifying the Normal Force in Free-Body Diagrams
When drawing a free-body diagram (FBD):
- Draw the object as a simple box or dot.
- Draw all external forces.
- Label each force clearly.
- Draw the normal force perpendicular to the surface.
Examples:
Object on a Table
- Weight ↓
- Normal force ↑
Object on a Ramp
- Weight ↓
- Normal force ⟂ to slope
Object Against a Wall
- Applied force →
- Normal force ←
Remember:
The normal force is not always upward—it is always perpendicular to the surface.
Comparing Normal Force and Weight
| Normal Force | Weight |
|---|---|
| Contact force | Non-contact force |
| Exerted by a surface | Exerted by Earth (or another massive body) |
| Perpendicular to the surface | Always acts toward the centre of Earth |
| Depends on contact | Exists even without contact |
| Can change depending on the situation | Depends only on mass and gravitational field strength |
Although they are often equal in magnitude on a flat surface, they are different forces with different causes and directions.
Worked Example 5
A student says:
"The normal force is always equal to the object's weight."
Question
Is this correct?
Solution
No.
The normal force equals the weight only in certain situations, such as when an object rests on a horizontal surface with no other vertical forces.
On an incline or when additional forces act, the normal force is different from the weight.
Common Mistakes
Students often make these errors.
❌ Drawing the normal force vertically upward on every diagram.
✔ The normal force is always perpendicular to the surface.
❌ Thinking the normal force and weight are an action–reaction pair.
✔ They act on the same object. An action–reaction pair acts on different objects.
❌ Assuming the normal force is always equal to the weight.
✔ This is only true in specific situations.
❌ Forgetting that an inclined surface changes the direction of the normal force.
✔ On slopes, the normal force is perpendicular to the slope, not vertical.
Real-World Connection
Normal forces are considered whenever engineers design buildings, bridges, furniture, roads, and vehicles. The strength of a chair must be sufficient to provide the normal force needed to support a person's weight. In motorsport, the normal force between tyres and the road affects grip, while in skiing and snowboarding the normal force changes continuously as athletes move over slopes and jumps.
Did You Know?
Although the floor feels perfectly solid, the normal force actually comes from electromagnetic forces between the atoms in your feet and the atoms in the floor. When you stand on the ground, the atoms are compressed by only an incredibly tiny amount—far too small to notice—but this microscopic compression produces the support force that keeps you standing.
Key Terms
- Normal force (Fₙ) — the support force exerted by a surface, acting perpendicular to that surface.
- Contact force — a force that acts only when two objects touch.
- Weight (W) — the gravitational force acting on an object.
- Free-body diagram (FBD) — a simplified diagram showing all the external forces acting on an object.
- Perpendicular — meeting a surface at an angle of 90°.
- Inclined plane — a flat surface set at an angle to the horizontal.
Key Takeaways
- The normal force is the support force exerted by a surface on an object in contact with it.
- The normal force always acts perpendicular to the surface.
- On a horizontal surface with no additional vertical forces, the normal force equals the object's weight.
- Additional upward or downward forces change the magnitude of the normal force.
- On an inclined plane, the normal force is less than the weight and is given by .
- The normal force and weight are different forces with different causes and directions.
- Correctly identifying the normal force is essential when drawing free-body diagrams and solving force problems.