Forces and Newton's Laws
| Site: | Young Education |
| Cursus: | Forces |
| Boek: | Forces and Newton's Laws |
| Afgedrukt door: | Guest user |
| Datum: | vrijdag, 25 september 2026, 03:22 |
1. Newton's Laws of Motion
Learning outcomes
- I can state and explain Newton's three laws of motion.
- I can identify examples of each law in everyday situations.
- I can explain the concept of inertia.
- I can distinguish between balanced and unbalanced forces.
- I can use Newton's laws to predict motion.
Introduction
Every movement you make—from walking across a room to kicking a football or riding a bicycle—is governed by the same set of physical principles. These principles were first described by the English scientist Sir Isaac Newton in the late 1600s. His three Laws of Motion explain how forces affect the motion of objects and form one of the foundations of classical physics.
Newton's laws help us understand why objects start moving, stop moving, speed up, slow down, or change direction. They are used in fields ranging from engineering and sports science to vehicle safety, robotics, and space exploration.
What Is a Force?
A force is a push or pull that can change an object's motion.
A force can:
- Start an object moving.
- Stop an object moving.
- Speed up an object.
- Slow down an object.
- Change the direction of motion.
- Change the shape of an object.
The SI unit of force is the newton (N).
Figure 1. Forces are pushes or pulls that can change an object's motion.
Newton's First Law of Motion
Newton's First Law states:
An object remains at rest or continues moving at constant velocity unless acted upon by a net external force.
This law is sometimes called the Law of Inertia.
It means:
- Objects at rest stay at rest.
- Moving objects continue moving at a constant speed in a straight line.
- Motion changes only when there is an unbalanced force.
Inertia
Inertia is the tendency of an object to resist changes in its motion.
Objects with greater mass have greater inertia.
Examples:
- A heavy truck is harder to start moving than a bicycle.
- A bowling ball is harder to stop than a tennis ball.
- Passengers move forward when a car stops suddenly because their bodies tend to continue moving.
Figure 2. Seatbelts protect passengers because of inertia—the tendency to keep moving when the car stops.
Balanced and Unbalanced Forces
Balanced Forces
Balanced forces are equal in size and opposite in direction.
Result:
- Net force = 0 N.
- No change in motion.
An object may:
- Remain at rest, or
- Continue moving at constant velocity.
Unbalanced Forces
Unbalanced forces produce a non-zero net force.
Result:
- The object's motion changes.
- The object accelerates.
Acceleration may involve:
- Speeding up.
- Slowing down.
- Changing direction.
Newton's Second Law of Motion
Newton's Second Law states:
The acceleration of an object depends on the net force acting on it and its mass.
It is expressed mathematically as:
where:
- F = net force (N)
- m = mass (kg)
- a = acceleration (m/s²)
This law tells us:
- Greater force produces greater acceleration.
- Greater mass produces smaller acceleration for the same force.
Figure 3. Newton's Second Law relates force, mass, and acceleration.
Examples of the Second Law
Shopping Trolley
An empty trolley accelerates more easily than a full trolley because it has less mass.
Football
Kicking the ball harder produces a greater acceleration.
Car
A small car accelerates more than a large truck when the same driving force is applied.
Newton's Third Law of Motion
Newton's Third Law states:
For every action force, there is an equal and opposite reaction force.
Forces always occur in pairs.
The two forces:
- Are equal in magnitude.
- Act in opposite directions.
- Act on different objects.
Examples of the Third Law
Walking
- Your foot pushes backward on the ground.
- The ground pushes forward on your foot.
Swimming
- You push water backward.
- The water pushes you forward.
Rocket Launch
- The rocket pushes exhaust gases downward.
- The exhaust gases push the rocket upward.
Figure 4. Action–reaction force pairs explain movement in many everyday situations.
Comparing Newton's Three Laws
| Law | Main Idea |
|---|---|
| First Law | Objects resist changes in motion unless acted upon by a net force. |
| Second Law | Net force causes acceleration according to . |
| Third Law | Forces always occur in equal and opposite pairs. |
Together, these laws explain nearly all everyday motion.
Predicting Motion
Newton's laws help predict how objects will move.
If:
- Net force = 0 N
Then:
- No acceleration occurs.
If:
- Net force increases
Then:
- Acceleration increases.
If:
- Mass increases
Then:
- Acceleration decreases for the same net force.
These relationships allow scientists and engineers to calculate and predict motion.
Everyday Applications
Newton's laws explain:
- Seatbelt safety.
- Bicycle riding.
- Sports.
- Vehicle design.
- Rocket launches.
- Aircraft flight.
- Machinery.
- Robotics.
Engineers use these laws whenever they design vehicles, buildings, machines, and spacecraft.
Figure 5. Newton's Laws of Motion explain many everyday activities and technologies.
Worked Example
Question
A box is pushed across the floor.
The applied force is 40 N to the right.
Friction acts with 15 N to the left.
Predict the motion.
Solution
Net force:
Because the net force is 25 N to the right, the forces are unbalanced.
According to Newton's Second Law, the box will accelerate to the right.
Real-World Connection
Modern cars are designed using all three of Newton's laws. Seatbelts and airbags reduce injuries caused by inertia (First Law), powerful engines provide the force needed to accelerate the car (Second Law), and tyres push backward against the road while the road pushes the car forward (Third Law). Understanding these laws allows engineers to design vehicles that are both efficient and safe.
Did You Know?
When astronauts float inside the International Space Station, they are not beyond the reach of gravity. Earth's gravity at the station's altitude is still about 90% as strong as it is at Earth's surface. The astronauts appear weightless because both they and the spacecraft are continuously falling around Earth together in orbit, creating the sensation of weightlessness.
Key Terms
Acceleration – The rate at which an object's velocity changes.
Balanced forces – Forces that are equal in magnitude and opposite in direction, producing zero net force.
Force – A push or pull that can change an object's motion.
Inertia – The tendency of an object to resist changes in its state of motion.
Mass – The amount of matter in an object and a measure of its inertia.
Net force – The overall force acting on an object after all forces have been combined.
Newton (N) – The SI unit of force.
Newton's First Law – An object remains at rest or moves with constant velocity unless acted upon by a net external force.
Newton's Second Law – The net force on an object equals its mass multiplied by its acceleration ().
Newton's Third Law – For every action force, there is an equal and opposite reaction force.
Unbalanced forces – Forces that do not cancel, resulting in a non-zero net force and causing acceleration.
Key Takeaways
- Newton's First Law explains that objects resist changes in motion because of inertia.
- Balanced forces produce no change in motion, while unbalanced forces cause acceleration.
- Newton's Second Law relates force, mass, and acceleration through the equation .
- Newton's Third Law states that every force has an equal and opposite force acting on another object.
- Newton's laws can be used to predict how objects will move when forces act on them.
- These laws explain motion in everyday life and are essential in engineering, transportation, sports, and space exploration.
2. Types of Forces
Learning outcomes
- I can distinguish between contact and non-contact forces.
- I can identify common forces acting on objects.
- I can explain force interactions between objects.
- I can represent forces using vectors.
- I can classify forces according to their origin
Introduction
Whenever an object moves, stops, changes direction, or changes shape, one or more forces are acting on it. Forces are responsible for everything from a football flying through the air to planets orbiting the Sun. Some forces require objects to touch, while others act over great distances without any physical contact.
Understanding the different types of forces is one of the most important foundations of mechanics. By identifying the forces acting on an object and representing them correctly, we can explain and predict how objects will behave.
What Is a Force?
A force is a push or pull resulting from an interaction between two objects.
A force can:
- Start motion.
- Stop motion.
- Speed up an object.
- Slow down an object.
- Change direction.
- Change shape.
The SI unit of force is the newton (N).
Forces are always the result of interactions between objects.
Figure 1. Forces are pushes or pulls caused by interactions between objects.
Contact and Non-Contact Forces
Forces are divided into two main categories.
Contact Forces
A contact force acts only when two objects are touching.
Examples include:
- Normal force.
- Friction.
- Tension.
- Air resistance.
- Applied force.
- Spring force.
Without contact, these forces cannot act.
Non-Contact Forces
A non-contact force acts without physical contact.
Examples include:
- Gravitational force.
- Magnetic force.
- Electrostatic force.
These forces can act across empty space.
Figure 2. Contact forces require physical contact, while non-contact forces act at a distance.
Common Contact Forces
Normal Force
The normal force is the support force exerted by a surface.
Examples:
- A table supporting a book.
- The ground supporting a person.
The normal force acts perpendicular (at 90°) to the surface.
Friction
Friction opposes motion between surfaces in contact.
Examples:
- Shoes gripping the ground.
- Bicycle brakes.
- Sliding a box across the floor.
Friction usually acts opposite to the direction of motion or attempted motion.
Tension
Tension is the force transmitted through a stretched rope, string, or cable.
Examples:
- A hanging lamp.
- A tug-of-war rope.
- A suspended bridge.
Tension always pulls along the rope.
Air Resistance (Drag)
Air resistance opposes the motion of objects moving through air.
Examples:
- A falling skydiver.
- A moving cyclist.
- A speeding car.
Air resistance increases as speed increases.
Applied Force
An applied force is a force exerted directly by a person or another object.
Examples:
- Pushing a shopping trolley.
- Pulling a suitcase.
- Kicking a football.
Spring Force
A spring force is exerted when a spring or elastic object is stretched or compressed.
Examples:
- A stretched rubber band.
- A compressed spring.
- A spring balance.
The spring force acts to return the object to its original shape.
Figure 3. Common contact forces include normal force, friction, tension, air resistance, applied force, and spring force.
Common Non-Contact Forces
Gravitational Force
Gravity is the attractive force between objects with mass.
Examples:
- Objects falling to Earth.
- The Moon orbiting Earth.
- Planets orbiting the Sun.
Gravity acts toward the centre of the attracting object.
Magnetic Force
Magnetic forces act between magnets and magnetic materials.
Magnets can:
- Attract.
- Repel.
Magnetic forces are important in motors, generators, and compasses.
Electrostatic Force
Electrostatic forces act between electrically charged objects.
Unlike charges:
- Attract.
Like charges:
- Repel.
Examples:
- A rubbed balloon sticking to a wall.
- Static electricity after walking across carpet.
Figure 4. The three main non-contact forces are gravitational, magnetic, and electrostatic forces.
Force Interactions
Forces always involve two interacting objects.
Examples:
- The Earth pulls on an apple, and the apple pulls on the Earth.
- A person pushes a wall, and the wall pushes back.
- A magnet attracts a paper clip, and the paper clip attracts the magnet.
These interactions follow Newton's Third Law, which states that forces occur in equal and opposite pairs.
Representing Forces Using Vectors
A vector has both:
- Magnitude (size).
- Direction.
Forces are represented by arrows.
The arrow shows:
- The direction of the force.
- The length represents the size of the force.
For example:
- → 5 N (5 newtons to the right)
- ↑ 10 N (10 newtons upward)
Longer arrows represent larger forces.
Figure 5. Forces are vectors, so they are represented by arrows showing both size and direction.
Classifying Forces by Their Origin
| Force | Contact or Non-Contact? | Origin |
|---|---|---|
| Gravity | Non-contact | Masses attracting each other |
| Friction | Contact | Surfaces rubbing together |
| Normal force | Contact | Supporting surface |
| Tension | Contact | Rope, string, or cable |
| Air resistance | Contact | Air particles colliding with an object |
| Spring force | Contact | Elastic deformation |
| Magnetic force | Non-contact | Magnetic fields |
| Electrostatic force. | Non-contact | Electric charges |
| Applied force | Contact | Push or pull from another object |
Classifying forces helps identify which interactions are affecting an object's motion.
Why Understanding Forces Is Important
Understanding forces allows scientists and engineers to:
- Predict motion.
- Design vehicles.
- Build bridges.
- Launch rockets.
- Improve sports performance.
- Develop safer buildings and machines.
Every moving object is influenced by one or more forces.
Worked Example
Question
A book is resting on a table.
Identify the forces acting on the book.
Solution
Two forces act on the book:
- Gravitational force (weight) acting downward.
- Normal force from the table acting upward.
These forces are equal in magnitude and opposite in direction, so they are balanced and the book remains at rest.
Real-World Connection
When a skydiver jumps from an aircraft, several forces act at the same time. Gravity pulls the skydiver downward, while air resistance pushes upward against the motion. As the skydiver speeds up, air resistance increases until it becomes equal to the weight. At this point, the forces are balanced, and the skydiver falls at a constant speed called terminal velocity.
Did You Know?
Although gravity is the weakest of the four fundamental forces of nature, it dominates the motion of planets, stars, and galaxies because it always acts as an attractive force and operates over enormous distances. Even the tiny gravitational attraction between everyday objects exists—it is simply far too small to notice.
Key Terms
Air resistance (drag) – A contact force that opposes the motion of an object through air.
Applied force – A force exerted directly by a person or another object.
Contact force – A force that acts only when two objects are touching.
Electrostatic force – A non-contact force between electrically charged objects.
Force – A push or pull resulting from an interaction between objects.
Friction – A contact force that opposes motion between surfaces in contact.
Gravitational force – The attractive force between objects with mass.
Magnetic force – A non-contact force between magnets or magnetic materials.
Normal force – The support force exerted by a surface, acting perpendicular to it.
Non-contact force – A force that acts without physical contact between objects.
Spring force – A force exerted by a stretched or compressed elastic object.
Tension – The pulling force transmitted through a rope, string, or cable.
Vector – A quantity with both magnitude and direction.
Key Takeaways
- Forces are pushes or pulls that arise from interactions between objects.
- Contact forces require physical contact, while non-contact forces act at a distance.
- Common contact forces include normal force, friction, tension, air resistance, applied force, and spring force.
- The main non-contact forces are gravitational, magnetic, and electrostatic forces.
- Forces are represented by vectors, which show both magnitude and direction.
- Identifying and classifying forces is essential for explaining and predicting the motion of objects.
3. Newton's Second Law
Learning Outcomes
- I can explain the relationship between force, mass, and acceleration.
- I can recall and use Newton's Second Law.
- I can calculate net force, mass, or acceleration.
- I can predict how changing force or mass affects motion.
- I can solve one-dimensional force problems.
Introduction
Imagine pushing an empty shopping trolley and then pushing the same trolley when it is full of groceries. The empty trolley accelerates much more easily because it has less mass. Similarly, kicking a football harder makes it accelerate faster than a gentle tap.
These everyday observations are explained by Newton's Second Law of Motion, which describes the relationship between force, mass, and acceleration. This law is one of the most important principles in physics because it allows us to predict how objects will move when forces act on them.
Newton's Second Law
Newton's Second Law states:
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
In simple terms:
- A larger net force produces a larger acceleration.
- A larger mass produces a smaller acceleration if the net force remains the same.
This relationship can be expressed mathematically.
The Formula
Newton's Second Law is written as:
where:
- Fnet = net force (newtons, N)
- m = mass (kilograms, kg)
- a = acceleration (metres per second squared, m/s²)
The net force is the overall force acting on an object after all forces have been combined.
Understanding the Relationship
The equation shows two important relationships.
Force and Acceleration
If mass stays the same:
- Larger force → Larger acceleration.
- Smaller force → Smaller acceleration.
Example:
A harder kick makes a football accelerate more quickly.
Mass and Acceleration
If force stays the same:
- Larger mass → Smaller acceleration.
- Smaller mass → Larger acceleration.
Example:
An empty shopping trolley accelerates more easily than a full one.
Figure 1. For the same applied force, an object with less mass accelerates more.
The Net Force
The net force is the vector sum of all the forces acting on an object.
If forces act in the same direction:
Add them together.
Example:
30 N right + 20 N right = 50 N right
If forces act in opposite directions:
Subtract the smaller force from the larger.
Example:
40 N right − 15 N left = 25 N right
The direction of the larger force is the direction of the net force.
Rearranging the Formula
The equation can be rearranged to find any of the three quantities.
Finding Force
Finding Mass
Finding Acceleration
Always use SI units:
- Force → newtons (N)
- Mass → kilograms (kg)
- Acceleration → m/s²
Predicting Motion
Newton's Second Law allows us to predict how an object will move.
If:
- Net force increases,
then acceleration increases.
If:
- Mass increases,
then acceleration decreases (for the same net force).
If:
- Net force is zero,
then acceleration is zero and the object either remains at rest or continues moving at constant velocity.
Figure 2. Acceleration increases with force but decreases as mass increases.
Solving One-Dimensional Force Problems
When solving problems:
Step 1
Draw or imagine the forces acting on the object.
Step 2
Calculate the net force.
Step 3
Choose the correct equation.
Step 4
Substitute the known values.
Step 5
Calculate the answer and include units.
Worked Example 1
Question
A 5 kg box is pushed with a net force of 20 N.
Find its acceleration.
Solution
Given:
- Mass = 5 kg
- Net force = 20 N
Use: \( a = \frac{F_{net}}{m} \)
Answer: The box accelerates at 4 m/s².
Worked Example 2
Question
A car accelerates at 3 m/s².
Its mass is 1200 kg.
Find the net force.
Solution
Use:
Answer: The net force is 3600 N.
Worked Example 3
Question
A net force of 50 N produces an acceleration of 10 m/s².
Find the mass.
Solution
Use:
\( m = \frac{F_{net}}{a} \)
Answer: The object's mass is 5 kg.
Everyday Applications
Newton's Second Law explains many everyday situations.
Examples include:
- Pushing a shopping trolley.
- Kicking a football.
- Accelerating a car.
- Launching a rocket.
- Riding a bicycle.
- Pulling a suitcase.
Engineers use this law when designing vehicles, machinery, elevators, roller coasters, and spacecraft.
Figure 3. Newton's Second Law helps explain motion in sports, transportation, and engineering.
Common Mistakes
Students often make these mistakes:
- Using weight instead of mass.
- Forgetting to calculate the net force first.
- Mixing kilograms and grams.
- Omitting units.
- Ignoring the direction of the net force.
Careful use of units and signs helps avoid errors.
Why Newton's Second Law Is Important
Newton's Second Law allows scientists and engineers to:
- Predict motion.
- Design safer vehicles.
- Calculate rocket thrust.
- Develop robots.
- Build efficient machines.
- Understand how forces change motion.
It is one of the most widely used equations in physics.
Figure 4. Engineers apply Newton's Second Law whenever they analyse or design moving systems.
Real-World Connection
Every rocket launch depends on Newton's Second Law. The engines produce an enormous upward thrust (force). As fuel burns, the rocket's mass decreases, so the same engine force produces a greater acceleration. This is one reason rockets accelerate more rapidly as they climb away from Earth.
Did You Know?
Formula One racing cars can accelerate from 0 to 100 km/h in about 2.5 seconds. Their powerful engines provide a very large driving force, while their lightweight construction reduces mass. According to Newton's Second Law, this combination produces extremely high acceleration.
Key Terms
Acceleration – The rate at which an object's velocity changes.
Force – A push or pull that can change an object's motion.
Kilogram (kg) – The SI unit of mass.
Mass – The amount of matter in an object and a measure of its inertia.
Net force – The overall force acting on an object after all forces have been combined.
Newton (N) – The SI unit of force.
Newton's Second Law – The law stating that the net force acting on an object equals its mass multiplied by its acceleration.
Key Takeaways
- Newton's Second Law describes the relationship between net force, mass, and acceleration.
- The law is expressed by the equation .
- Increasing the net force increases acceleration, while increasing the mass decreases acceleration if the force remains constant.
- The net force must be calculated by combining all the forces acting on an object.
- The equation can be rearranged to calculate force, mass, or acceleration.
- Newton's Second Law is widely used to predict motion and solve problems in physics, engineering, transportation, and space exploration.
4. Free-Body Diagrams
Learning outcomes
- I can draw free-body diagrams for simple situations.
- I can identify all forces acting on an object.
- I can distinguish between real and nonexistent forces.
- I can represent forces using correct vector notation.
- I can use free-body diagrams to analyze motion.
Introduction
Before solving any force problem in physics, it is important to identify all the forces acting on an object. A simple and powerful way to do this is by drawing a free-body diagram (FBD).
A free-body diagram isolates a single object and shows every external force acting on it using arrows called vectors. By carefully analysing these diagrams, scientists and engineers can determine whether the forces are balanced or unbalanced and predict how the object will move. Free-body diagrams are one of the most important tools in mechanics and are used extensively in physics, engineering, and robotics.
What Is a Free-Body Diagram?
A free-body diagram (FBD) is a simplified drawing that shows all the external forces acting on one object.
In a free-body diagram:
- The object is represented by a simple shape, usually a box or a dot.
- Every external force is shown as an arrow.
- The arrows show both the magnitude and direction of each force.
- Only forces acting on the chosen object are included.
The purpose of a free-body diagram is to make force analysis easier.
Figure 1. A free-body diagram shows all the external forces acting on a single object.
Why Use Free-Body Diagrams?
Free-body diagrams help us:
- Identify all the forces acting on an object.
- Determine the net force.
- Decide whether forces are balanced or unbalanced.
- Predict motion using Newton's Laws.
- Solve force and acceleration problems.
Almost every mechanics problem begins with a free-body diagram.
Identifying the Object
The first step is to choose one object to analyse.
Examples include:
- A book on a table.
- A car on a road.
- A skydiver.
- A hanging sign.
- A sled being pulled.
Only forces acting on that object are included.
Forces the object exerts on other objects are not shown.
Common Forces in Free-Body Diagrams
Some of the most common forces are:
| Force | Symbol | Direction |
|---|---|---|
| Weight (gravitational force) | Fg or W | Downward |
| Normal force | FN | Perpendicular to the surface |
| Friction | Ff | Opposes motion or attempted motion |
| Tension | FT | Along a rope or cable |
| Applied force | FA | Direction of the push or pull |
| Air resistance (drag) | FD | Opposite the direction of motion |
| Spring force | Fs | Toward the spring's equilibrium position |
Recognising these forces is the key to drawing accurate diagrams.
Figure 2. The most common forces shown in free-body diagrams.
Representing Forces as Vectors
A force is a vector quantity, meaning it has:
- Magnitude.
- Direction.
In a free-body diagram:
- Arrows represent forces.
- Longer arrows represent larger forces.
- The arrow points in the direction of the force.
For example:
- ↑ Normal force
- ↓ Weight
- → Applied force
- ← Friction
The arrows should begin at the object.
Balanced Forces
When the forces are balanced:
- Net force = 0 N.
- No acceleration occurs.
The object:
- Remains at rest, or
- Continues moving with constant velocity.
Example:
A book resting on a table.
The upward normal force equals the downward weight.
Unbalanced Forces
When the forces are unbalanced:
- Net force ≠ 0 N.
- The object accelerates.
Acceleration may involve:
- Speeding up.
- Slowing down.
- Changing direction.
The direction of the acceleration is the same as the direction of the net force.
Figure 3. Balanced forces produce no acceleration, while unbalanced forces cause acceleration.
Real and Nonexistent Forces
A correct free-body diagram includes only real external forces.
Real Forces
Examples:
- Gravity.
- Normal force.
- Friction.
- Tension.
- Air resistance.
- Applied force.
Common Mistakes
Do not include:
- "Force of motion."
- "Force of velocity."
- "Force of acceleration."
- "Force in the direction the object wants to go."
These are not real forces.
Motion itself is not a force.
Only interactions between objects produce forces.
Drawing a Free-Body Diagram
Follow these steps:
Step 1
Choose the object.
Step 2
Draw the object as a box or dot.
Step 3
Identify every external force acting on it.
Step 4
Draw each force as an arrow.
Step 5
Label every force clearly.
Step 6
Compare the sizes and directions of the forces to determine the net force.
Example 1 – Book on a Table
Forces acting:
- Weight downward.
- Normal force upward.
The forces are equal.
Result:
- Balanced forces.
- No acceleration.
Example 2 – Box Being Pushed
Forces acting:
- Applied force to the right.
- Friction to the left.
- Weight downward.
- Normal force upward.
If the applied force is larger than friction:
- Net force acts to the right.
- The box accelerates to the right.
Figure 4. A free-body diagram helps determine the direction of the net force and the resulting motion.
Using Free-Body Diagrams to Analyse Motion
Once the diagram is complete:
- Combine forces in the horizontal direction.
- Combine forces in the vertical direction.
- Calculate the net force.
- Apply Newton's Second Law: Fnet = ma
The free-body diagram provides the information needed to predict the object's motion.
Why Free-Body Diagrams Are Important
Free-body diagrams are used by:
- Physicists.
- Engineers.
- Architects.
- Vehicle designers.
- Aerospace engineers.
- Robotics engineers.
They help analyse everything from bridges and elevators to satellites and spacecraft.
Figure 5. Free-body diagrams are essential tools in science and engineering.
Worked Example
Question
A 10 kg box is pulled across a floor.
The forces acting are:
- Applied force = 50 N to the right.
- Friction = 20 N to the left.
- Weight downward.
- Normal force upward.
Draw the free-body diagram and identify the net force.
Solution
The diagram contains four forces:
- → Applied force (50 N)
- ← Friction (20 N)
- ↑ Normal force
- ↓ Weight
Horizontal net force:
Vertical forces balance.
Therefore:
- Net force = 30 N to the right.
- The box accelerates to the right.
Real-World Connection
Mechanical engineers use free-body diagrams whenever they design vehicles, cranes, bridges, or amusement park rides. Before a bridge is built, engineers draw free-body diagrams of every major component to calculate the forces acting on it. These calculations help ensure that the structure can safely support traffic, wind, and other loads.
Did You Know?
Although free-body diagrams are simple sketches, they are used by engineers working on some of the world's most advanced technologies, including Formula One racing cars, aircraft, rockets, and even Mars rovers. Breaking a complex system into individual objects with carefully drawn force diagrams makes it much easier to understand how each part behaves.
Key Terms
Applied force – A force exerted directly by a person or another object.
Free-body diagram (FBD) – A simplified diagram showing all the external forces acting on a single object.
Friction – A force that opposes motion between surfaces in contact.
Net force – The overall force acting on an object after all forces have been combined.
Normal force – The support force exerted by a surface, acting perpendicular to it.
Tension – The pulling force transmitted through a rope, string, or cable.
Vector – A quantity with both magnitude and direction, represented by an arrow.
Weight – The gravitational force acting on an object.
Key Takeaways
- A free-body diagram shows all the external forces acting on a single object.
- Common forces include weight, normal force, friction, tension, applied force, and air resistance.
- Forces are represented as vectors, with arrows showing both magnitude and direction.
- Only real external forces should appear in a free-body diagram—motion itself is not a force.
- Free-body diagrams help determine the net force and predict an object's motion using Newton's Laws.
- Drawing an accurate free-body diagram is the first step in solving most mechanics problems.
5. Equilibrium and Net Force
Learning outcomes
- I can define equilibrium.
- I can distinguish between static and dynamic equilibrium.
- I can calculate net force.
- I can determine whether an object is in equilibrium.
- I can explain equilibrium using Newton's First Law.
Introduction
Many objects around us appear motionless, such as a book resting on a table or a picture hanging on a wall. Others move steadily, like a car travelling at a constant speed along a straight road. Although these situations seem very different, they have something important in common: the net force acting on the object is zero.
When all the forces acting on an object balance each other, the object is said to be in equilibrium. Understanding equilibrium is essential in physics and engineering because it explains why buildings remain standing, bridges support heavy loads, and vehicles can travel at a constant speed without changing their motion.
What Is Equilibrium?
An object is in equilibrium when the net force acting on it is zero.
In equilibrium:
- All forces are balanced.
- There is no acceleration.
- The object's motion does not change.
An object in equilibrium may:
- Remain at rest, or
- Move with constant velocity in a straight line.
Net Force
The net force is the overall force acting on an object after all the individual forces have been combined.
When forces act:
- In the same direction → Add them.
- In opposite directions → Subtract them.
The direction of the net force is the direction of the larger force.
Calculating Net Force
Forces in the Same Direction
Example:
20 N → + 15 N →
Net force:
Direction:
35 N to the right
Forces in Opposite Directions
Example:
50 N → and 20 N ←
Net force:
Direction:
30 N to the right
If the net force equals 0 N, the object is in equilibrium.
Figure 1. The net force is found by combining all the forces acting on an object.
Static Equilibrium
Static equilibrium occurs when:
- The object is at rest.
- The net force is zero.
Examples include:
- A book resting on a table.
- A parked car.
- A hanging sign.
- A person standing still.
The object remains motionless because the forces balance perfectly.
Dynamic Equilibrium
Dynamic equilibrium occurs when:
- The object is moving at constant velocity.
- The net force is zero.
Examples include:
- A car travelling at a constant speed along a straight road.
- An elevator moving upward at constant speed.
- An aircraft cruising at constant altitude and speed.
Although the object is moving, its velocity does not change because the forces remain balanced.
Figure 2. Objects in static equilibrium are at rest, while objects in dynamic equilibrium move with constant velocity.
Newton's First Law and Equilibrium
Newton's First Law states:
An object remains at rest or continues moving with constant velocity unless acted upon by a net external force.
This law explains equilibrium:
- If the net force is zero, the object's motion does not change.
- If the net force is not zero, the object accelerates.
Equilibrium is therefore a direct consequence of Newton's First Law.
Balanced and Unbalanced Forces
Balanced Forces
Balanced forces:
- Are equal in magnitude.
- Act in opposite directions.
- Produce a net force of 0 N.
Result:
- The object is in equilibrium.
Unbalanced Forces
Unbalanced forces:
- Do not cancel.
- Produce a non-zero net force.
Result:
- The object accelerates.
Figure 3. Balanced forces produce equilibrium, while unbalanced forces cause acceleration.
Determining Whether an Object Is in Equilibrium
To decide whether an object is in equilibrium:
Step 1
Identify all the forces acting on the object.
Step 2
Combine the forces horizontally.
Step 3
Combine the forces vertically.
Step 4
Determine the net force.
- If net force = 0 N, the object is in equilibrium.
- If net force ≠ 0 N, the object is not in equilibrium.
Examples of Equilibrium
Book on a Table
Forces:
- Weight downward.
- Normal force upward.
Net force:
0 N
The book is in static equilibrium.
Car Travelling at Constant Speed
Forces:
- Driving force forward.
- Air resistance and friction backward.
If these forces are equal:
Net force:
0 N
The car is in dynamic equilibrium.
Tug-of-War
If each team pulls with exactly 500 N:
Net force:
0 N
The rope remains stationary because it is in equilibrium.
Figure 4. Many everyday situations involve objects in equilibrium.
Equilibrium and Free-Body Diagrams
A free-body diagram helps determine equilibrium.
In an equilibrium diagram:
- Vertical forces balance.
- Horizontal forces balance.
- Opposite arrows are equal in length.
This indicates:
- Net force = 0 N.
- No acceleration.
Why Equilibrium Is Important
Engineers rely on equilibrium when designing:
- Bridges.
- Buildings.
- Cranes.
- Towers.
- Aircraft.
- Elevators.
If structures are not in equilibrium, they may move, tip, or collapse.
Understanding equilibrium helps ensure safety and stability.
Figure 5. Engineers use equilibrium to design safe and stable structures.
Worked Example
Question
A box is pushed with a force of 40 N to the right.
Friction acts with a force of 40 N to the left.
Determine:
- The net force.
- Whether the box is in equilibrium.
Solution
The forces are equal and opposite.
Net force:
Since the net force is 0 N, the box is in equilibrium.
If it is already moving, it continues moving at a constant velocity.
If it is at rest, it remains at rest.
Real-World Connection
Cruise control in a car is designed to maintain dynamic equilibrium. When driving on a level road at a constant speed, the engine provides a forward driving force that balances air resistance and friction. Because the net force is zero, the car continues moving at the same speed without accelerating.
Did You Know?
One of the world's tallest buildings, the Burj Khalifa, remains standing because engineers carefully designed it so that the forces acting on it are balanced. Even when strong winds push against the building, its structure distributes the forces to maintain equilibrium and keep it stable.
Key Terms
Balanced forces – Forces that are equal in magnitude and opposite in direction, producing zero net force.
Dynamic equilibrium – A state in which an object moves with constant velocity because the net force acting on it is zero.
Equilibrium – A state in which the net force acting on an object is zero.
Net force – The overall force acting on an object after all forces have been combined.
Newton's First Law – The law stating that an object remains at rest or moves with constant velocity unless acted upon by a net external force.
Static equilibrium – A state in which an object remains at rest because the net force acting on it is zero.
Unbalanced forces – Forces that do not cancel, resulting in a non-zero net force and causing acceleration.
Key Takeaways
- An object is in equilibrium when the net force acting on it is zero.
- Static equilibrium describes objects at rest, while dynamic equilibrium describes objects moving with constant velocity.
- The net force is found by combining all the forces acting on an object.
- Balanced forces produce equilibrium, whereas unbalanced forces cause acceleration.
- Newton's First Law explains that objects remain at rest or continue moving at constant velocity when the net force is zero.
- Equilibrium is essential in physics and engineering because it explains the stability and motion of objects in everyday life.