Force and Laws of Motion • Topic 1 of 3

Balanced & Unbalanced Forces; Inertia

What is a force? A force is a push or a pull that one object exerts on another. We cannot see a force itself, only its effects. A force can (i) make a stationary object move, (ii) stop or slow down a moving object, (iii) change the speed of an object, (iv) change the direction of motion, and (v) change the shape or size of an object. Force is a vector quantity, so it has both magnitude and direction; its SI unit is the newton ($\text{N}$).

Balanced forces. When two or more forces act on an object and their net (resultant) force is zero, the forces are said to be balanced. Balanced forces do not change the state of motion of an object. A book lying on a table stays at rest because its weight (acting down) is exactly balanced by the normal reaction of the table (acting up). In a tug of war, when both teams pull equally hard the rope does not move.

Unbalanced forces. When the net force on an object is not zero, the forces are unbalanced. An unbalanced force changes the state of motion: it can set a body moving, speed it up, slow it down, or change its direction. To accelerate a body you always need an unbalanced force.

Newton's First Law (Law of Inertia). An object remains in its state of rest or of uniform motion in a straight line unless acted upon by an unbalanced (external) force. This means a body cannot change its velocity by itself.

Inertia. The natural tendency of an object to resist any change in its state of rest or of uniform motion is called inertia. There are three kinds:

Inertia of rest — a body at rest tends to stay at rest (dust falls off a carpet when beaten).
Inertia of motion — a moving body tends to keep moving (a passenger lurches forward when a bus brakes suddenly).
Inertia of direction — a body resists a change in its direction of motion (mud flies off tangentially from a spinning wheel).

Mass is a measure of inertia. The greater the mass of a body, the greater its inertia and the harder it is to change its motion. A loaded truck is much harder to start or stop than an empty bicycle. Thus mass is the quantitative measure of inertia.

Solved Examples

Worked Example

Two teams pull a rope in a tug of war. Team A pulls with $400\ \text{N}$ to the left and Team B pulls with $400\ \text{N}$ to the right. State whether the forces are balanced and what happens to the rope.

Solution

Forces act in opposite directions with equal magnitudes: $400\ \text{N}$ left and $400\ \text{N}$ right.
Net force $= 400 - 400 = 0\ \text{N}$.
A zero net force means the forces are balanced, so the state of motion does not change.

Answer: The forces are balanced (net force $0\ \text{N}$); the rope stays at rest.

Worked Example

A box is pushed to the right with $60\ \text{N}$ while friction opposes it with $25\ \text{N}$. Find the net force and state its effect.

Solution

Applied force (right) $= 60\ \text{N}$; friction (left) $= 25\ \text{N}$.
Net force $= 60 - 25 = 35\ \text{N}$ to the right.
Since the net force is not zero, the forces are unbalanced.

Answer: Net force $= 35\ \text{N}$ to the right; the box accelerates to the right.

Worked Example

Explain why a passenger standing in a moving bus falls forward when the driver suddenly applies the brakes. Name the type of inertia involved.

Solution

While the bus moves, the passenger's whole body shares the forward motion of the bus.
When the brakes are applied, the lower body (in contact with the bus floor) stops with the bus.
The upper body tends to continue in its forward motion due to its tendency to keep moving.

Answer: The upper body continues forward because of inertia of motion, so the passenger falls forward.

Worked Example

A coin is placed on a stiff card resting on the mouth of a glass. The card is flicked away sharply. Predict what happens to the coin and explain.

Solution

The coin is at rest and tends to remain at rest (inertia of rest).
The flick acts only on the card for a very short time, so the coin barely experiences any sideways force.
With the card gone, gravity pulls the coin straight down.

Answer: The card flies off but the coin, by inertia of rest, drops straight into the glass.

Worked Example

Which is harder to set in motion from rest: a loaded truck of mass $8000\ \text{kg}$ or an empty cart of mass $50\ \text{kg}$? Justify using the idea of inertia.

Solution

Inertia is the resistance of a body to a change in its state of motion.
Mass is the measure of inertia: greater mass means greater inertia.
The truck ($8000\ \text{kg}$) has far more mass than the cart ($50\ \text{kg}$).

Answer: The loaded truck is harder to set in motion because its larger mass gives it greater inertia.

Worked Example

A book of weight $12\ \text{N}$ rests on a horizontal table. Identify the forces acting on it and state whether they are balanced.

Solution

The weight of the book acts vertically downward $= 12\ \text{N}$.
The table pushes up on the book with a normal reaction force.
The book is at rest, so by Newton's First Law the net force must be zero; hence the normal reaction $= 12\ \text{N}$ upward.

Answer: Weight ($12\ \text{N}$ down) and normal reaction ($12\ \text{N}$ up) are equal and opposite; the forces are balanced.

Key Points

A force is a push or pull; it can change an object's speed, direction or shape. SI unit: newton ($\text{N}$).
Balanced forces give zero net force and do not change the state of motion; unbalanced forces give a non-zero net force and produce acceleration.
Newton's First Law: a body stays at rest or in uniform straight-line motion unless an unbalanced force acts on it.
Inertia is the tendency to resist change in motion; its three types are inertia of rest, of motion and of direction.
Mass is the measure of inertia: more mass means more inertia.

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Which of the following is the SI unit of force?

Explanation: Force is measured in newtons ($\text{N}$).

Q2.When the net force on a body is zero, the forces are said to be:

Explanation: Zero net force means the forces balance each other.

Q3.The tendency of a body to resist a change in its state of motion is called:

Explanation: This property is inertia; it is measured by mass.

Q4.A passenger jerks backward when a bus starts suddenly. This is due to:

Explanation: The body at rest tends to stay at rest while the bus moves forward.

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