IMAT Physics · Dynamics, Work and Energy

Mass, Weight and Newton's Three Laws

A body keeps its velocity unless a resultant force acts; the resultant force equals mass times acceleration; and forces always come in equal and opposite pairs acting on two different bodies.

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Why this matters

Three past questions test the second law directly: what a constant resultant force does to a train's acceleration and velocity (2018), the starting acceleration of a rocket (2020), and the engine force on a car first at steady speed and then while accelerating (2025).

Concept 1 of 4: Mass and weight are different quantities

Mass is how much matter a body has and how hard it is to speed up; it is the same everywhere. Weight is the pull of gravity on that mass, so it depends on where you are. An astronaut on the Moon keeps her mass but weighs about a sixth as much.

Definition

Mass $m$ : a scalar, in kg, the same everywhere.
Weight $W$ : the gravitational force on a body, a vector pointing down, in newtons.
Gravitational field strength $g$ : the weight per kilogram, in N/kg. On Earth $g \approx 9.8\ \text{N/kg}$ (often rounded to 10); on the Moon about 1.6 N/kg.
The N/kg of field strength is the same unit as the $\text{m/s}^2$ of free-fall acceleration.

Weight

W = mg

$W$ weight, in N
$m$ mass, in kg
$g$ gravitational field strength, in N/kg

Worked example

An astronaut has a mass of 60 kg. What are her mass and her weight on the Moon, where

g = 1.6\ \text{N/kg}

Practice this conceptself-check · 3 quick reps

The kilogram is not a unit of weight

In everyday speech people weigh 60 kg, but in physics weight is a force in newtons. A 60 kg person weighs about 590 N on Earth. An option giving a weight in kg, or a mass in N, is wrong.

Concept 2 of 4: Newton's first law: balanced forces mean constant velocity

A puck on smooth ice slides on and on; it only stops because something pushes on it. A body needs no force to keep moving, only to change how it moves. So when all the forces on a body cancel, it is either at rest or moving in a straight line at a steady speed.

Definition

Newton's first law: a body stays at rest, or keeps moving at constant velocity in a straight line, unless a resultant (net) force acts on it.

Inertia is the tendency to keep the same velocity; mass measures it.
Constant velocity tells you the resultant force is zero: the forces are balanced.
So a car at a steady speed on a level road has an engine force exactly equal to the resistive forces.
A free-body diagram shows one body alone with every force on it as an arrow; only forces ON that body go in it.

Worked example

A lift of total mass 800 kg moves upwards at a steady 2.0 m/s. Taking

g = 10\ \text{N/kg}

, what is the tension in the cable?

Practice this conceptself-check · 3 quick reps

Motion does not need a resultant force

A body moving at constant velocity has zero resultant force. A resultant force is needed to change the velocity, not to keep it. Options claiming that the forward force must exceed the drag for a car to keep moving steadily are wrong.

Concept 3 of 4: Newton's second law: resultant force equals mass times acceleration

Push a trolley harder and it speeds up faster; load it with more mass and the same push speeds it up less. The acceleration follows the RESULTANT force, the sum of all the forces, not any single one. A constant resultant force gives a constant acceleration, so the velocity keeps rising steadily.

Definition

Newton's second law: $F_{\text{net}} = ma$ , and the acceleration is in the direction of the resultant force.

$1\ \text{N}$ is the resultant force that gives 1 kg an acceleration of $1\ \text{m/s}^2$ .
Method: draw the free-body diagram, add the forces along the line of motion with signs, then divide by the mass.
Something pushed up against gravity (a rocket, a lift): $T - mg = ma$ , so $a = T/m - g$ .
A car speeding up against friction: engine force $= f + ma$ .

Newton's second law

F_{\text{net}} = ma

$F_{\text{net}}$ resultant of all forces on the body, in N
$m$ mass, in kg
$a$ acceleration, in m/s²

Worked example

A crane cable lifts a 1200 kg load with a tension of 15 000 N. Taking

g = 10\ \text{N/kg}

, what is the load's acceleration?

Practice this conceptself-check · 3 quick reps

Subtract the weight for anything pushed upwards

A rocket's thrust

T

is not its resultant force: its weight

mg

acts the other way. The starting acceleration is

a = T/m - g

, not

T/m

. Writing

T/m - mg

mixes an acceleration with a force and cannot be right.

At the top of a vertical throw, the weight still acts

The ball is momentarily at rest, but gravity has not switched off. The resultant force is the weight, and the acceleration is

g

downwards, the same as at every other point of the flight.

Concept 4 of 4: Newton's third law: action and reaction pairs

You cannot push on something without it pushing back on you: lean on a wall and the wall holds you up. Every force is one half of an interaction between two bodies. The two halves are equal in size, opposite in direction, and act on different bodies, which is why they never cancel each other.

Definition

Newton's third law: if body A exerts a force on body B, then B exerts a force on A that is equal in size, opposite in direction and of the same type.

The two forces of a pair act on different bodies, so they never appear in the same free-body diagram and never cancel.
A book's weight and the table's push on the book are equal (when nothing accelerates) but are not a third-law pair: both act on the book, and they are different types of force.

Force	Its third-law partner	Type
Earth pulls a book down (its weight)	The book pulls the Earth up	gravitational
Table pushes up on the book	Book pushes down on the table	contact (normal)
Your foot pushes the ground backwards	The ground pushes your foot forwards	friction
A rocket pushes exhaust gas backwards	The gas pushes the rocket forwards	contact
A swimmer pushes water backwards	The water pushes the swimmer forwards	contact

Practice this conceptself-check · 3 quick reps

Weight and the normal force are not a third-law pair

Both act on the same body, and they are different kinds of force. They are equal only when the body is not accelerating vertically. The real partner of a body's weight is its gravitational pull on the Earth.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Mass and weight are different quantities
Weight
$W = mg$
Newton's second law: resultant force equals mass times acceleration
Newton's second law
$F_{\text{net}} = ma$

Reference tables (1)

Newton's third law: action and reaction pairs5 rows

Force	Its third-law partner	Type
Earth pulls a book down (its weight)	The book pulls the Earth up	gravitational
Table pushes up on the book	Book pushes down on the table	contact (normal)
Your foot pushes the ground backwards	The ground pushes your foot forwards	friction
A rocket pushes exhaust gas backwards	The gas pushes the rocket forwards	contact
A swimmer pushes water backwards	The water pushes the swimmer forwards	contact

Watch out for (5)

The kilogram is not a unit of weight
→ Mass and weight are different quantities
Motion does not need a resultant force
→ Newton's first law: balanced forces mean constant velocity
Subtract the weight for anything pushed upwards
→ Newton's second law: resultant force equals mass times acceleration
At the top of a vertical throw, the weight still acts
→ Newton's second law: resultant force equals mass times acceleration
Weight and the normal force are not a third-law pair
→ Newton's third law: action and reaction pairs

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