Why you lurch forward when a bus brakes and how rockets fly: forces, Newton's three laws, friction and momentum, explained with diagrams and worked examples.
Why does a passenger lurch forward when a bus brakes suddenly? Why is it easy to push an empty shopping trolley but hard to push a full one? Why does a swimmer move forward by pushing water backward? In 1687, in a book called the Principia, Isaac Newton set out three laws of motion that answer questions like these. They are some of the most useful ideas in all of physics: they describe how engineers design cars and bridges, how rockets leave the Earth, and why seat belts save lives. This article explains the laws step by step, with worked examples you can follow and try yourself.
A force is a push or a pull. A force can change an object's speed, change its direction of motion, change its shape, or start or stop its motion. Force is a vector: it has a size and a direction. The SI unit is the newton (N). One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s². A small apple weighs roughly 1 N. Force is measured with a newton meter (a spring balance).
Forces are either contact forces, which need the objects to touch, or non-contact forces, which act across a distance.
| Force | Type | Description |
|---|---|---|
| Weight | Non-contact | Pull of gravity on a mass, downward |
| Normal reaction | Contact | Push of a surface on an object, perpendicular to the surface |
| Friction | Contact | Force opposing sliding between surfaces |
| Tension | Contact | Pull along a rope, string or cable |
| Air resistance (drag) | Contact | Friction with air, opposing motion |
| Upthrust | Contact | Upward push of a fluid on an object in it |
| Magnetic and electric forces | Non-contact | Forces between magnets and between charges |
Mass is the amount of matter in an object. It is measured in kilograms (kg) and does not depend on where the object is. Weight is the force of gravity on the object. It is measured in newtons and does depend on location, because it depends on the strength of gravity there.
W = m × g
g is the gravitational field strength: about 9.8 N/kg on Earth's surface (the standard value is 9.80665 N/kg). It is also the free-fall acceleration in m/s².
| Place | g (N/kg), approximate |
|---|---|
| Earth's surface | 9.8 |
| Moon | 1.6 |
| Mars | 3.7 |
| Jupiter (cloud tops) | 24.8 |
An astronaut has a mass of 60 kg. Find her weight on Earth and on the Moon (gMoon = 1.62 N/kg).
On Earth: W = mg = 60 × 9.8 = 588 N.
On the Moon: W = 60 × 1.62 ≈ 97 N.
Her mass is 60 kg in both places; only her weight changes. She would feel about one-sixth as heavy on the Moon.
An object often has more than one force on it. The single force that has the same effect as all of them together is the resultant force. For forces along one line, add those in one direction and subtract those in the opposite direction.
An object stays at rest, or keeps moving in a straight line at constant speed, unless a resultant force acts on it.
The tendency of an object to resist changes in its motion is called inertia. The larger the mass, the larger the inertia. Before Newton, many people thought a force was needed to keep any object moving; in fact, objects stop on Earth only because friction and air resistance act on them. On an ice rink or in space, where such forces are very small, motion lasts much longer.
The acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass, in the direction of the force.
F = m × a (resultant force in N, mass in kg, acceleration in m/s²)
Double the force on the same mass and the acceleration doubles. Double the mass under the same force and the acceleration halves. This explains why an empty trolley accelerates faster than a full one for the same push.
A car of mass 1200 kg has an engine force of 3000 N forward and resistance forces of 600 N backward. Find its acceleration.
Step 1. Resultant force = 3000 − 600 = 2400 N.
Step 2. a = F ÷ m = 2400 ÷ 1200 = 2.0 m/s².
What resultant force gives a 0.50 kg football an acceleration of 8.0 m/s²?
F = ma = 0.50 × 8.0 = 4.0 N.
The law also explains free fall. The only force on a falling object (no air resistance) is its weight, W = mg. Then a = W ÷ m = mg ÷ m = g. The mass cancels, so all objects fall with the same acceleration, as discussed in the article on motion.
When object A exerts a force on object B, object B exerts a force on object A that is equal in size, opposite in direction, and of the same type.
The two forces of a pair act on different objects, so they never cancel each other out. When you push a wall, the wall pushes back on you with an equal force. When you walk, your foot pushes backward on the ground and the ground pushes forward on you; that forward force is what moves you. A swimmer pushes water backward, and the water pushes the swimmer forward. A gun recoils when it fires a bullet.
Rockets are a clear example. The rocket engine pushes hot gas downward at high speed; the gas pushes the rocket upward with an equal force. A rocket does not need air to "push against", so it works in the vacuum of space.
A book rests on a table. Its weight (pull of Earth on book) and the table's normal reaction (push of table on book) are equal and opposite, but they are not a third-law pair, because they act on the same object and are different types of force. The true pair for the weight is the pull of the book on the Earth. The true pair for the table's push on the book is the book's push on the table.
Friction is the force that opposes the sliding of two surfaces in contact. It arises because even smooth-looking surfaces are rough at microscopic scale. It always acts in the direction opposite to the motion (or intended motion) and depends on the surfaces and on how hard they are pressed together. For many surfaces:
Ffriction = μ × N
N = normal reaction (on a level surface, N = weight), and μ (mu) is the coefficient of friction, which has no units. Static friction (before sliding starts) can be larger than kinetic friction (while sliding).
A 20 kg box on a level floor has μ = 0.40. A student pulls it with a horizontal force of 120 N. Find the friction and the acceleration. (g = 9.8 N/kg)
Step 1. N = weight = 20 × 9.8 = 196 N.
Step 2. Friction = μN = 0.40 × 196 = 78.4 N.
Step 3. Resultant = 120 − 78.4 = 41.6 N.
Step 4. a = F ÷ m = 41.6 ÷ 20 ≈ 2.1 m/s².
Useful friction lets us walk, grip objects, and brake and steer vehicles. Harmful friction wears parts and wastes energy as heat. We reduce it with lubricants (oil, grease), ball bearings, wheels, smooth surfaces, and streamlined shapes that lower air and water resistance. We increase it with rough treads on shoes and tyres, and with sand or grit on icy roads.
Momentum is mass times velocity, and it is a vector. It measures how hard it is to stop a moving object.
p = m × v (unit: kg·m/s)
F = (change in momentum) ÷ time or F × Δt = Δp. This is Newton's second law in its original form; with constant mass it becomes F = ma.
Conservation of momentum: when objects interact and no outside resultant force acts, the total momentum before equals the total momentum after.
A 1000 kg car moving at 10 m/s hits a stationary 1500 kg car, and they lock together. Find their speed just after.
Step 1. Momentum before = 1000 × 10 + 1500 × 0 = 10 000 kg·m/s.
Step 2. Momentum after = (1000 + 1500) × v = 2500v.
Step 3. 2500v = 10 000, so v = 4.0 m/s.
Because F × Δt = Δp, the force in a collision depends on how long the change in momentum takes. Making the time longer makes the force smaller. Seat belts, airbags, crumple zones, cycle helmets and padded playground floors all increase the stopping time.
A passenger of mass 70 kg is moving at 15 m/s and is brought to rest. Compare the average force if this takes 0.10 s (airbag and seat belt) with 0.020 s (hitting a rigid surface).
Change in momentum = 70 × 15 = 1050 kg·m/s.
With 0.10 s: F = 1050 ÷ 0.10 = 10 500 N.
With 0.020 s: F = 1050 ÷ 0.020 = 52 500 N, five times larger.
These are simplified figures, but they show why safety features that lengthen the stopping time reduce injuries. Always wear a seat belt, and use a helmet when cycling.
The same laws explain objects moving in a circle. A mass moving at constant speed on a circular path is constantly changing direction, so it is accelerating and needs a resultant force pointing towards the centre of the circle. This is the centripetal force: it might be tension (a whirled stone), friction (a car on a bend) or gravity (the Moon around the Earth). If the force stops, the object moves off in a straight line, as the first law predicts.
Try each question before opening the answer.
W = mg = 5.0 × 9.8 = 49 N.
300 + 250 − 400 = 150 N in the direction of the push.
a = F ÷ m = 6.0 ÷ 2.0 = 3.0 m/s².
By Newton's first law, the passenger's body tends to continue moving at the original speed until a force (the seat belt) slows it.
p = mv = 0.20 × 5.0 = 1.0 kg·m/s.
Momentum before = 3.0 × 4.0 = 12 kg·m/s. After: (3.0 + 1.0)v = 12, so v = 3.0 m/s.
The ball pushes back on the boot with an equal and opposite force.
It increases the time over which the person's momentum changes, so the average force on the person is smaller.
Easy classroom experiments: pull a trolley with a known force (a hanging mass over a pulley) and use a ticker timer or phone video to find the acceleration; compare how far a trolley travels on carpet, wood and a smooth board; use two spring balances hooked together to show that the readings of an action–reaction pair are equal; use balloon rockets on a string; collide trolleys with Velcro to test conservation of momentum. Keep egg-drop style activities at a low height with padding. Numerical values are rounded; please check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions, constants and historical facts were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: coefficients of friction and crash figures are rounded or illustrative. Please check them against your own syllabus or exam board specification before relying on them.
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