Forces and Newton's Laws
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.