Introduction

Whenever two surfaces touch and try to move past one another, they resist that motion. This resisting force is called friction.

Friction is everywhere in our daily lives. It allows us to walk without slipping, helps cars stop safely, and enables pencils to write on paper. At the same time, friction can cause machinery to wear out, generate unwanted heat, and reduce efficiency.

Understanding friction helps us explain how objects move and how engineers design safer and more efficient machines.

What is Friction?

Friction is a contact force that opposes the relative motion (or attempted motion) between two surfaces in contact.

Its direction is always:

Opposite to the direction of motion or attempted motion.

For example:

• A box sliding to the right experiences friction acting to the left.
• A bicycle moving forward experiences friction opposing the motion of its tires.
• A book resting on a table experiences no friction unless a force tries to move it.

Friction only acts when two surfaces are in contact.

 

 

 

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What Is Friction?

Friction is a force that opposes the relative motion, or attempted motion, between two surfaces that are in contact.

Whenever one surface moves—or tries to move—across another, friction acts in the direction that opposes that motion.

For example, imagine pushing a box across a floor. You push the box forward, but friction between the box and the floor acts backward.

Push → BOX ← Friction

Friction does not always mean that an object is slowing down. Instead, the key idea is:

Friction opposes relative motion or the tendency for relative motion between surfaces.

This distinction becomes especially important when studying walking, tires, and accelerating vehicles.

What Causes Friction?

Even surfaces that look perfectly smooth are rough when viewed at the microscopic level. They contain tiny bumps and irregularities called asperities.

When two surfaces touch, these irregularities interact. Electromagnetic attractions between atoms and molecules at the points of contact also contribute to friction.

 

 

 

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As one surface tries to move across another, these interactions resist the movement.

The amount of friction therefore depends partly on:

• the materials in contact
• the condition of the surfaces
• how strongly the surfaces are pressed together

Different combinations of materials produce different amounts of friction.

For example, rubber on dry pavement usually produces much greater friction than metal on ice.

Static Friction

Static friction acts between surfaces that are not sliding relative to each other.

Imagine trying to push a heavy cabinet.

You push gently.

The cabinet does not move.

You push harder.

It still does not move.

Why?

Static friction increases to oppose your applied force.

 

 

 

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Suppose you push with 20 N and the cabinet remains stationary.

Applied force = 20 N →

← Static friction = 20 N

The forces are balanced, so:

Resultant force = 0 N

Therefore:

Acceleration = 0 m/s²

An important point is that static friction does not always have one fixed value. It adjusts to match the applied force until it reaches a maximum value.

Maximum Static Friction

Eventually, the applied force may become large enough to overcome static friction.

The maximum possible static friction is:

Fₛ(max) = μₛN

where:

• Fₛ(max) = maximum static friction in newtons (N)
• μₛ = coefficient of static friction
• N = normal force in newtons (N)

The symbol μ is the Greek letter mu.

The coefficient of friction describes how strongly two surfaces resist sliding against each other. It has no units.

Once the applied force exceeds the maximum static friction, the object begins to slide.

Kinetic Friction

Once an object begins sliding, kinetic friction acts between the moving surfaces.

Kinetic friction is sometimes called sliding friction.

 

 

 

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The kinetic friction force can be modeled using:

Fₖ = μₖN

where:

• Fₖ = kinetic friction force (N)
• μₖ = coefficient of kinetic friction
• N = normal force (N)

For most pairs of surfaces:

μₛ > μₖ

This means that it usually takes more force to start an object moving than to keep it moving.

You may have experienced this when pushing heavy furniture. The first movement can be difficult, but once the furniture starts sliding, it becomes somewhat easier to push.

Static vs Kinetic Friction

 

 

 

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A typical friction graph shows static friction increasing as the applied force increases. When the object begins moving, the friction force drops to the lower kinetic-friction value.

The Normal Force

To calculate friction, we often need to know the normal force.

The normal force is the contact force exerted by a surface on an object. It acts perpendicular to the surface.

For an object resting on a horizontal surface with no additional vertical forces:

N = mg

where:

• N = normal force (N)
• m = mass (kg)
• g = gravitational field strength (approximately 9.8 N/kg)

 

 

 

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For a box resting on a horizontal floor:

↑ Normal force

BOX

↓ Weight

If there is no vertical acceleration:

N = mg

However, the normal force is not always equal to weight. If someone pushes downward on the object or pulls upward at an angle, the normal force changes.

Factors Affecting Friction

1. Type of Surface

Different materials have different coefficients of friction.

A rough rubber surface usually produces more friction than smooth ice.

 

 

 

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A larger coefficient of friction means a larger friction force when the normal force is the same.

2. Normal Force

Increasing the normal force generally increases friction.

Consider two identical boxes, but place a heavy object on top of one.

The heavier system pushes harder against the floor.

Therefore:

N increases → friction increases

This follows directly from:

F = μN

3. Surface Conditions

Water, oil, ice, dust, and lubricants can change the amount of friction between surfaces.

Lubricants such as oil create a layer between moving surfaces and can dramatically reduce friction.

This is why lubricants are used inside engines and machinery.

 

 

 

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Friction and Motion

According to Newton's Second Law:

Fnet = ma

Friction contributes to the net force acting on an object.

Suppose a person pushes a box to the right with 50 N while friction acts to the left with 20 N.

Applied force = 50 N →

← Friction = 20 N

The net force is:

Fnet = 50 − 20

Fnet = 30 N to the right

If the box has a mass of 10 kg:

Fnet = ma

30 = 10a

a = 3.0 m/s²

The box therefore accelerates to the right.

Worked Example 1: Calculating Kinetic Friction

A 20 kg box slides across a horizontal floor. The coefficient of kinetic friction is 0.30.

Calculate the friction force.

First calculate the normal force:

N = mg

N = 20 × 9.8

N = 196 N

Now calculate friction:

Fₖ = μₖN

Fₖ = 0.30 × 196

Fₖ = 58.8 N

Therefore, the kinetic friction force is approximately:

59 N

The friction force acts opposite the direction of sliding.

Worked Example 2: Friction and Acceleration

A 10 kg box is pushed across a floor with a force of 50 N. The kinetic friction force is 20 N.

Calculate its acceleration.

First find the net force:

Fnet = Fapplied − Ffriction

Fnet = 50 − 20

Fnet = 30 N

Now use:

Fnet = ma

30 = 10a

a = 30 ÷ 10

a = 3.0 m/s²

Worked Example 3: Will the Object Move?

A box is pushed horizontally with a force of 35 N. The maximum static friction between the box and floor is 42 N.

Will the box move?

Applied force = 35 N

Maximum static friction = 42 N

Because:

35 N < 42 N

the applied force is not large enough to overcome static friction.

Therefore:

The box does not move.

The actual static friction in this situation is 35 N, not 42 N.

That distinction is important.

Friction Can Be Useful

Friction is sometimes described as something that slows objects down, but life would be extremely difficult without it.

Friction allows us to:

• walk without slipping
• grip objects
• write with pencils
• stop vehicles using brakes
• accelerate vehicles using tires
• hold screws and nails in materials
• light a match

 

 

 

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When you walk forward, your foot pushes backward against the ground. Static friction from the ground pushes your foot forward.

This is an important example showing that friction does not simply "act backward." It opposes the relative slipping of the surfaces.

Friction Can Also Be Unwanted

Friction can cause:

• heating
• energy loss
• wear of moving parts
• damage to machinery
• reduced efficiency

For example, friction between moving engine components converts some mechanical energy into thermal energy.

Engineers therefore often try to reduce unwanted friction.

Common methods include:

• lubrication
• ball bearings
• smoother surfaces
• reducing contact forces

 

 

 

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However, engineers sometimes want to increase friction. Tire tread, sports shoes, climbing equipment, and textured handles are designed to provide greater grip.

Friction and Energy

When friction acts on a moving object, mechanical energy can be transformed into thermal energy.

Rub your hands together quickly.

They become warmer because friction converts some of the mechanical energy of the motion into thermal energy.

This is also why:

• car brakes become hot
• drill bits heat up
• machinery requires cooling
• tires become warmer during driving

 

 

 

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Friction does not make energy disappear. Energy is transferred or transformed into other forms, especially thermal energy.

Did You Know?

Formula One racing tires are designed to operate at relatively high temperatures. As the tires warm, their interaction with the track changes, helping them provide the grip required for rapid acceleration, braking, and cornering.

Ice is another interesting example. Its slipperiness is influenced by several processes, including the presence of a very thin mobile layer of water molecules at its surface.

 

 

 

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Key Terms

Friction: A force that opposes relative motion or attempted relative motion between surfaces.

Static friction: Friction acting between surfaces that are not sliding relative to each other.

Kinetic friction: Friction acting between surfaces that are sliding.

Normal force: The contact force exerted perpendicular to a surface.

Coefficient of friction (μ): A dimensionless value describing the frictional interaction between two surfaces.

Net force: The vector sum of all forces acting on an object.

Lubricant: A substance used to reduce friction between surfaces.

Key Equations

Maximum static friction:

Fₛ(max) = μₛN

Kinetic friction:

Fₖ = μₖN

Weight:

Fg = mg

Newton's Second Law:

Fnet = ma

For an object on a horizontal surface with no other vertical forces:

N = mg

Key Takeaways

• Friction opposes relative motion or attempted relative motion between surfaces.
• Friction results from interactions between surfaces at the microscopic level.
• Static friction acts before surfaces begin sliding.
• Kinetic friction acts while surfaces are sliding.
• Maximum static friction is usually greater than kinetic friction.
• Friction depends on the materials involved and the normal force.
• Friction can be calculated using F = μN.
• Friction affects the net force and therefore the acceleration of an object.
• Friction can be useful, such as when walking or braking.
• Friction can also cause unwanted heating, wear, and energy transfer.
• Friction problems often combine F = μN with Fnet = ma.

Now that we understand friction, we can apply our knowledge to kinematic situations:

Moving from one surface to another...

More than one applied force, and forces in vertical direction.