Think about the last time you opened a door. You pushed it. Or pulled it. Either way, you used a force. Now think about a footballer kicking a ball, a mother lifting a child, a magnet attracting a paper clip, a rocket leaving the Earth. Every one of those is a story about force.
Force is one of the most important ideas in all of physics. It explains why things start moving, stop moving, speed up, slow down, or change direction. Without force, the universe would be a still, silent place. Nothing would ever happen. In this chapter, we are going to learn what force is, how to measure it, and how to calculate it. Let us begin.
I remember a student who once asked me, "Sir, if force is everywhere, why can I not see it?" I told him, "You cannot see the wind either, but you can see what it does. Force is like the wind — invisible, but its effects are everywhere." He never forgot that. I hope you will not either.By the end of this chapter, you should be able to:
A force is a push or a pull. That is the simplest definition, and it is a good place to start. But let us go deeper. A force is an interaction between two objects that can change the motion or shape of an object.
Think of a river pushing against a rock. The water pushes, the rock resists. That is a force. Think of two friends arm-wrestling. Each pushes against the other. That is a force. Think of the Earth pulling you down as you jump. That is a force too.
Force is a vector quantity. That means it has both size and direction. Saying "I pushed with 10 N" is not enough. You must also say which way you pushed. A force of 10 N to the right is very different from 10 N to the left.
The SI unit of force is the newton (N). One newton is roughly the force you feel when you hold a small apple in your hand. It is named after Sir Isaac Newton, one of the greatest physicists who ever lived.
Students often ask why we need a special unit for force. Why not just use kilograms? Because kilograms measure mass, not force. A 1 kg mass on Earth has a weight of about 10 N. On the Moon, that same mass would weigh only about 1.6 N. The mass is the same, but the force is different. This is why we need newtons.What can a force do? Let me count the ways:
Notice something: every one of these effects involves a change. Force does not just keep things going — it changes things. This is a deep idea, and we will return to it when we study Newton's laws.
Forces come in many forms. Here are the main ones you will meet:
| Type of Force | Description | Everyday Example |
|---|---|---|
| Gravitational force | Pull between any two masses | An apple falling from a tree |
| Weight | Gravitational force on an object | You standing on the ground |
| Normal force | Push from a surface, perpendicular to it | A book resting on a table |
| Friction | Force that opposes motion between surfaces | Rubbing your hands together |
| Tension | Pull transmitted through a string or rope | A rope in a tug-of-war |
| Spring force | Push or pull from a stretched or compressed spring | A mattress supporting you |
| Magnetic force | Force between magnets or magnetic materials | A magnet picking up a pin |
| Electrostatic force | Force between electric charges | A rubbed balloon attracting hair |
| Applied force | Any push or pull you apply | Pushing a shopping trolley |
| Air resistance | Friction from air | A parachute slowing a skydiver |
| Upthrust | Upward push from a fluid | A boat floating on water |
Forces can be grouped into two big families:
Think of it this way: contact forces are like two friends shaking hands. Non-contact forces are like two people who can affect each other from across the room — like a magnet pulling a paper clip without touching it.
How do we measure force? With a spring balance (also called a newton meter). It works on a simple principle: the more you pull, the more the spring stretches. The stretch is calibrated to show force in newtons.
How to use a spring balance:
Watch how I do this. Suppose I hang a 500 g mass on a spring balance. The reading is 5 N. Why? Because weight = mass × gravity, and 0.5 kg × 10 m/s² = 5 N. The spring balance is really measuring the gravitational pull on the mass.
A spring balance is only as good as its spring. If the spring is overstretched, it may not return to its original length, and the readings will be wrong. Always treat your spring balance gently. Do not exceed its maximum reading.This is one of the most important distinctions in physics. Let me make it clear.
| Mass | Weight |
|---|---|
| Amount of matter in an object | Gravitational force on an object |
| Measured in kilograms (kg) | Measured in newtons (N) |
| Scalar quantity (size only) | Vector quantity (size and direction) |
| Does not change with location | Changes with location |
| Measured with a beam balance | Measured with a spring balance |
Think of an astronaut. On Earth, she has a mass of 60 kg and a weight of about 600 N. On the Moon, her mass is still 60 kg, but her weight is only about 100 N. Why? Because the Moon's gravity is weaker. Her body has not changed — but the pull on her body has.
The formula for weight is:
Weight = Mass × Gravitational Field Strength
W = m × g
W = weight in newtons (N), m = mass in kilograms (kg), g = gravitational field strength in N/kg (about 10 N/kg on Earth, 1.6 N/kg on the Moon)
Here is a deep idea: force changes motion. But how much? That depends on two things — how big the force is, and how heavy the object is.
Think of pushing a shopping trolley. An empty trolley is easy to push. A full trolley is harder. Same push, different result. Why? Because the full trolley has more mass, so it resists the change in motion more.
This relationship is captured by Newton's Second Law, which we will study in detail later. For now, remember: force causes acceleration, and the amount of acceleration depends on mass.
The relationship is:
Force = Mass × Acceleration
F = m × a
F = force in newtons (N), m = mass in kilograms (kg), a = acceleration in metres per second squared (m/s²)
When more than one force acts on an object, the forces can be balanced or unbalanced.
Think of a tug-of-war. If both teams pull equally hard, the rope does not move. Balanced forces. If one team pulls harder, the rope moves toward them. Unbalanced forces.
Here is a beautiful truth: if an object is at rest or moving at constant speed in a straight line, the forces on it are balanced. If it is accelerating, the forces are unbalanced.
This idea is so important that it became Newton's First Law. An object keeps doing what it is doing unless an unbalanced force acts on it. We will study this in detail soon. For now, remember: balanced forces mean no change; unbalanced forces mean change.A free-body diagram is a simple drawing that shows all the forces acting on an object. It is one of the most useful tools in physics.
How to draw one:
Example: a book resting on a table. Forces: weight (downward) and normal force (upward). They are equal and opposite. The book does not move.
Example: a box being pushed to the right with 20 N while friction acts to the left with 15 N. The net force is 5 N to the right. The box accelerates to the right.
Free-body diagrams are like maps. They show you where the forces are and how big they are. Once you can draw one, you can solve almost any force problem. Practice them until they feel natural.Weight: W = m × g
W = weight (N), m = mass (kg), g = gravitational field strength (N/kg)
Force: F = m × a
F = force (N), m = mass (kg), a = acceleration (m/s²)
Net force: F_net = sum of all forces acting on an object
If forces are in opposite directions, subtract. If in the same direction, add.
Common values: g on Earth ≈ 10 N/kg (or 9.8 N/kg for greater precision)
g on the Moon ≈ 1.6 N/kg
Question: A student has a mass of 45 kg. Calculate her weight on Earth, where g = 10 N/kg.
Answer:
Formula: W = m × g
Substitution: W = 45 kg × 10 N/kg
Answer: W = 450 N
Units check: kg × N/kg = N. The answer is in newtons, which is correct for weight. Does 450 N make sense? Yes, a 45 kg student would feel a pull of about 450 N toward the Earth.Question: The same student (mass 45 kg) travels to the Moon, where g = 1.6 N/kg. Calculate her weight on the Moon.
Answer:
Formula: W = m × g
Substitution: W = 45 kg × 1.6 N/kg
Answer: W = 72 N
Units check: the answer is in newtons, correct for weight. Notice how the weight is much smaller on the Moon, but the mass is still 45 kg. Mass does not change; weight does. This is a key idea in physics.Question: A force of 20 N acts on a 4 kg object. Calculate the acceleration.
Answer:
Formula: F = m × a, so a = F / m
Substitution: a = 20 N ÷ 4 kg
Answer: a = 5 m/s²
Units check: N ÷ kg = m/s². The answer is in m/s², which is correct for acceleration. Does 5 m/s² make sense? Yes, the object speeds up by 5 m/s every second.Question: A box is pushed to the right with 30 N. Friction acts to the left with 10 N. Calculate the net force and state its direction.
Answer:
Net force = 30 N − 10 N = 20 N to the right
Units check: the answer is in newtons, correct for force. The direction is important — always state it. A force without a direction is incomplete.Question: A book of weight 8 N rests on a table. What is the normal force from the table? Are the forces balanced?
Answer:
The normal force is 8 N upward. The forces are balanced because the book is at rest and not accelerating.
Units check: the answer is in newtons. Notice that balanced forces do not mean no forces — they mean the forces cancel out. The book still feels both weight and normal force; they just balance.Graphs help us see relationships between force and other quantities.
Suppose you apply different forces to the same object and measure the acceleration each time. If you plot force on the vertical axis and acceleration on the horizontal axis, what do you expect?
A straight line through the origin. Why? Because F = m × a, so force is proportional to acceleration. The gradient of the line is the mass of the object.
What if you plot force on the vertical axis and mass on the horizontal axis, keeping acceleration constant? You would get a straight line through the origin, with gradient equal to acceleration.
Graphs also help us spot anomalous results — points that do not fit the pattern. These may be due to measurement errors and should be investigated.
Think of a graph as a picture of a law of physics. The shape tells you what kind of relationship exists.
Apparatus: A spring balance, several masses (100 g, 200 g, 500 g), a retort stand, a clamp, and a ruler.
Method:
Calculation: For a 500 g mass, W = 0.5 kg × 10 N/kg = 5 N. The spring balance should read about 5 N.
Precautions:
Likely source of error: The spring balance may not be perfectly calibrated. Compare readings with calculated values to check accuracy.
This experiment is a beautiful way to see the difference between mass and weight. The mass is the same everywhere — but the force you feel depends on gravity. Try it with different masses and see the pattern for yourself.Force is a push or pull that can change the motion or shape of an object. It is measured in newtons (N).
Force can start motion, stop motion, change direction, change speed, or change shape. Any three are correct.
Mass is the amount of matter in an object, measured in kg, and does not change with location. Weight is the gravitational force on an object, measured in N, and changes with location.
W = m × g = 60 kg × 10 N/kg = 600 N.
A free-body diagram is a drawing that shows all the forces acting on an object, using arrows to represent size and direction.
Balanced forces are equal in size and opposite in direction. They cancel out, so the object does not accelerate.
Contact: friction, tension, normal force, air resistance. Non-contact: gravitational force, magnetic force, electrostatic force.
A spring balance (newton meter).
(a) Define force and state its SI unit. [2]
(b) A force of 30 N acts on a 6 kg object. Calculate the acceleration. [3]
(c) Explain why a heavy object is harder to push than a light one, using the idea of force and mass. [3]
(a) Force is a push or pull that can change the motion or shape of an object. (1 mark) SI unit: newton (N). (1 mark)
(b) a = F / m = 30 N ÷ 6 kg = 5 m/s². (1 mark for formula, 1 mark for substitution, 1 mark for answer with unit.)
(c) A heavier object has more mass. For the same force, a larger mass produces a smaller acceleration (F = ma). So it is harder to push. (1 mark for mass, 1 mark for F = ma, 1 mark for explanation.)
(a) Distinguish between mass and weight. [4]
(b) A student has a mass of 50 kg. Calculate his weight on Earth (g = 10 N/kg). [2]
(c) What would his weight be on a planet where g = 4 N/kg? [2]
(a) Mass is the amount of matter in an object, measured in kg, and does not change with location. Weight is the gravitational force on an object, measured in N, and changes with location. (2 marks for mass, 2 marks for weight.)
(b) W = m × g = 50 kg × 10 N/kg = 500 N. (1 mark for formula, 1 mark for answer with unit.)
(c) W = 50 kg × 4 N/kg = 200 N. (2 marks.)
(a) Name three types of forces and give an example of each. [3]
(b) A box is pushed to the right with 40 N. Friction acts to the left with 15 N. Calculate the net force and state its direction. [3]
(c) Explain why the box accelerates. [2]
(a) Any three correct, e.g., friction (rubbing hands), tension (tug-of-war), gravitational force (falling apple). (1 mark each.)
(b) Net force = 40 N − 15 N = 25 N to the right. (1 mark for subtraction, 1 mark for answer, 1 mark for direction.)
(c) The forces are unbalanced, so the box accelerates in the direction of the net force. (1 mark for unbalanced, 1 mark for direction.)
An astronaut has a mass of 70 kg. On Earth, her weight is 700 N. On the Moon, her weight is 112 N. Explain why her mass stays the same but her weight changes.
Mass is the amount of matter in her body — it does not depend on where she is. Weight is the gravitational force on her body, which depends on the strength of gravity. The Moon's gravity is weaker than Earth's, so her weight is less. Her mass is still 70 kg because her body has not changed.
Two teams are playing tug-of-war. Team A pulls with 500 N to the left. Team B pulls with 500 N to the right. Describe the motion of the rope and explain your answer using the idea of balanced forces.
The rope does not move because the forces are balanced — equal in size and opposite in direction. Balanced forces cancel out, so there is no net force and no acceleration. The rope stays still.
Why do we say that force is a vector quantity? Give an example where direction matters.
Force is a vector because it has both size and direction. For example, pushing a box with 10 N to the right is different from pushing it with 10 N to the left. The direction determines whether the box moves right or left — or not at all if another force balances it. Without direction, a force is incomplete.
Force is the invisible hand that moves the world — and once you understand it, you see it everywhere.
