Chapter 6: How Forces Affect Motion

In the previous chapter, we studied motion using terms like position, velocity and acceleration. In this chapter, we learn what causes changes in motion.

The chapter explains:

• What force is
• Balanced and unbalanced forces
• Friction
• Newton’s three laws of motion
• Forces acting on a system of objects

Force is the main cause that can change the state of rest or motion of an object.

A force is a push or pull acting on an object.

A force can:

• Move an object at rest
• Stop a moving object
• Change the speed of an object
• Change the direction of motion
• Change the shape of an object

Examples

• A football starts moving when it is kicked.
• A cricket bat changes the direction of a moving ball.
• A lemon changes shape when it is squeezed.

Important Points

• Force has both magnitude and direction.
• The magnitude of force tells us how strong the force is.
• The SI unit of force is newton.
• Symbol of newton is N.

Example:

A force of 10 N towards the right means the force has:

• Magnitude = 10 N
• Direction = towards the right

Note

If either the magnitude or the direction of a force changes, the effect of the force also changes.

The magnitude of force can be measured using a spring balance.

A spring balance can measure:

• Weight of an object
• Magnitude of applied force

Weight as a Force

The weight of an object is the gravitational force with which the Earth pulls the object.

So,

Weight = Force due to gravity

A spring balance measures this force.

In real life, usually more than one force acts on an object.

For example:

• When a box is pushed, the applied force acts forward and friction acts backward.
• A floating ball has gravitational force downward and buoyant force upward.

Balanced Forces

When two or more forces acting on an object are equal in magnitude but opposite in direction, they are called balanced forces.

Effect of Balanced Forces

Balanced forces:

• Do not change the state of rest or motion of an object.
• Produce zero net force.
• Do not produce acceleration.

Example

In a tug of war, if both teams pull with equal force in opposite directions, the rope does not move.

Unbalanced Forces

When forces acting on an object are not equal, they are called unbalanced forces.

Effect of Unbalanced Forces

Unbalanced forces:

• Produce a non-zero net force
• Can change the speed of an object
• Can change the direction of motion
• Can produce acceleration

Net Force

The net force is the overall force acting on an object.

Case 1: Forces in the Same Direction

If two forces act in the same direction, they are added.

Example:

Force 1 = 10 N

Force 2 = 6 N

Net force = 10 N + 6 N = 16 N

Case 2: Forces in Opposite Directions

If two forces act in opposite directions, the smaller force is subtracted from the larger force.

Example:

Force 1 = 10 N towards right

Force 2 = 6 N towards left

Net force = 10 N − 6 N = 4 N towards right

Important Note

Multiple forces may act on an object, but its motion depends only on the net force.

Friction is a force that opposes the motion of an object.

It acts between two surfaces in contact.

Direction of Friction

The force of friction acts in a direction opposite to the direction of motion.

Example

When we push a box on the floor:

• Applied force acts forward.
• Friction acts backward.

The box starts moving only when the applied force is greater than friction.

Forces Acting on a Box Kept on a Surface

When a box is pushed on a surface, the following forces may act on it:

• Applied force — force applied by hand
• Frictional force — acts opposite to motion
• Gravitational force / weight — acts downward
• Normal force — force exerted by the surface upward

The weight and normal force are usually balanced.

Why Does a Moving Object Stop?

A moving object stops because of friction.

Examples

• A bicycle slows down when we stop pedalling.
• A rolling ball stops after some distance.
• A sliding box eventually comes to rest.

This happens because friction acts opposite to motion and reduces the velocity.

Friction Depends on the Nature of Surfaces

Friction is different for different surfaces.

• Rough surfaces produce more friction.
• Smooth surfaces produce less friction.

Examples

• A coin stack travels less distance on a rough wooden surface.
• It travels more distance on a smooth tiled or marble surface.

Conclusion

When friction is smaller:

• Velocity decreases more slowly.
• Object travels a larger distance before stopping.

When friction is larger:

• Velocity decreases quickly.
• Object stops after a shorter distance.

Galileo Galilei was one of the first scientists to question the old idea that force is always required to keep an object moving.

He argued through thought experiments that:

If all obstacles and friction are removed, an object moving on a horizontal surface will continue to move forever with constant velocity.

This idea helped in the development of Newton’s first law of motion.

Isaac Newton used the idea of inertia to explain motion.

Inertia

Inertia is the tendency of an object to resist any change in its state of rest or uniform motion.

Newton gave the three laws of motion in 1687.

The SI unit of force, newton, is named after Isaac Newton.

Important Point

• Full form of unit: newton
• Symbol: N

Newton’s first law of motion states:

An object at rest remains at rest and an object in motion continues to move with a constant velocity, unless a net force acts upon the object.

Meaning of Newton’s First Law

If the net force on an object is zero:

• An object at rest will remain at rest.
• A moving object will keep moving with constant velocity.
• The object will not accelerate.

Acceleration is zero when net force is zero.

Newton’s First Law and Inertia

Newton’s first law is also called the law of inertia.

This is because it explains that objects resist changes in their motion.

Examples of Newton’s First Law

Example 1: Object at Rest

A book lying on a table remains at rest unless a force is applied to move it.

Example 2: Object in Motion

If friction is absent, a moving ball will continue moving with constant velocity.

Example 3: Box Moving with Balanced Forces

If a person pushes a box forward with a force equal to friction acting backward, the net force is zero. The box will continue moving with constant velocity.

Graphical Representation

Object at Rest

• Position-time graph: horizontal straight line
• Velocity-time graph: line at zero velocity

Object Moving with Constant Velocity

• Position-time graph: straight inclined line
• Velocity-time graph: horizontal straight line above zero

Newton’s second law explains what happens when a net force acts on an object.

It states:

When a net force acts on an object, the object accelerates in the direction of the net force. The magnitude of acceleration is directly proportional to the net force and inversely proportional to the mass of the object.

Important Relations

Acceleration and Force

For the same object:

• Greater force produces greater acceleration.
• Smaller force produces smaller acceleration.

So,

Acceleration ∝ Force

Acceleration and Mass

For the same force:

• A lighter object gets more acceleration.
• A heavier object gets less acceleration.

So,

Acceleration ∝ 1 / Mass

Mathematical Form of Newton’s Second Law

a = (F)/(m)

or

F = ma

Where:

• F = force
• m = mass
• a = acceleration

Definition of One Newton

One newton is the force that produces an acceleration of 1 m s⁻² in an object of mass 1 kg.

1 N = 1 kg m s⁻²

Force Due to Gravity

The gravitational force acting on an object is:

F = mg

Where:

• m = mass of object
• g = acceleration due to gravity

Near the surface of Earth:

g = 9.8 m s⁻²

For quick calculations:

g \approx 10 m s⁻²

Applications of Newton’s Second Law

1. Catching a Cricket Ball

A fielder pulls their hands backward while catching a fast-moving ball.

This increases the time taken to stop the ball.

As a result:

• Acceleration decreases.
• Force on hands decreases.
• Chances of injury reduce.

2. Airbags in Vehicles

During an accident, airbags increase the time of impact.

This reduces:

• Acceleration
• Force on the body
• Risk of serious injury

3. Cracking a Coconut

When a coconut hits the ground at high speed, it stops in a very short time.

This produces a very large force, which breaks the shell.

Newton’s third law states:

Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal and opposite force on the first object.

Important Points

• Forces always occur in pairs.
• The two forces are equal in magnitude.
• The two forces are opposite in direction.
• These forces act on two different objects.
• Therefore, they do not cancel each other.

Examples of Newton’s Third Law

1. Kicking a Ball

When the foot applies force on the ball, the ball applies an equal and opposite force on the foot.

2. Walking

While walking:

• The foot pushes the ground backward.
• The ground pushes the foot forward.

This forward force helps us move.

Here, friction helps in walking.

3. Cycling Without Pedalling

A cyclist can push the ground backward with the feet. The ground pushes the cyclist forward.

4. Rowing a Canoe

The canoeist pushes water backward with the paddle.

Water pushes the paddle and canoe forward.

If the canoeist pushes harder, the forward force becomes larger and the canoe moves faster.

5. Rocket Launch

A rocket engine pushes gases downward.

The gases push the rocket upward with an equal and opposite force.

If this upward force is greater than the weight of the rocket, the rocket lifts off.

6. Balloon Activity

When air rushes out of a balloon backward, the balloon moves forward.

This is also due to Newton’s third law.

Newton’s Third Law and Non-contact Forces

Newton’s third law applies to both:

• Contact forces
• Non-contact forces

Examples of Non-contact Forces

• Magnetic force between two magnets
• Electrostatic force between charged objects
• Gravitational force between Earth and a fruit

Why Does the Earth Not Move Towards a Falling Fruit Noticeably?

The Earth and the fruit exert equal and opposite gravitational forces on each other.

But the Earth has a very large mass.

Using:

a = (F)/(m)

Since Earth’s mass is huge, its acceleration is extremely small and cannot be noticed.

Newton’s laws can be applied not only to a single object but also to a system of objects.

A system means two or more objects considered together.

Example: Two Boxes Connected by a String

Suppose two boxes of masses m₁ and m₂ are connected by a string and pulled by force F on a frictionless surface.

The two boxes can be treated as one system.

Total mass of system

m₁ + m₂

Acceleration of system

a = (F)/(m₁ + m₂)

Internal and External Forces

Internal Forces

Forces acting between objects inside the system are called internal forces.

Example:

• Tension in the string between two boxes

Internal forces are not considered when studying the motion of the whole system.

External Forces

Forces acting from outside the system are called external forces.

Example:

• Pulling force applied from outside

Only external forces affect the motion of the system.

Important Point

Treating connected objects as one system often makes the study of motion simpler.

• Force is a push or pull that can change the state of rest, motion, direction, speed or shape of an object.
• Force has both magnitude and direction.
• The SI unit of force is newton (N).
• A spring balance is used to measure force.
• Balanced forces are equal and opposite forces acting on an object.
• Balanced forces produce zero net force.
• Unbalanced forces produce a non-zero net force and can cause acceleration.
• Friction is a force that opposes motion.
• Friction acts opposite to the direction of motion.
• Rough surfaces produce more friction than smooth surfaces.
• Newton’s first law states that an object remains at rest or in uniform motion unless acted upon by a net force.
• Newton’s first law is also called the law of inertia.
• Newton’s second law states that acceleration is directly proportional to net force and inversely proportional to mass.
• Formula:

F = ma

• One newton is the force required to produce an acceleration of 1 m s⁻² in a mass of 1 kg.
• Force due to gravity is:

F = mg

• Newton’s third law states that every action has an equal and opposite reaction.
• Action and reaction forces act on different objects, so they do not cancel each other.
• Newton’s laws apply to both single objects and systems of objects.
• For a system of two connected objects:

a = (F)/(m₁ + m₂)

This chapter explains how forces affect motion. A force can change the speed, direction or shape of an object. When forces are balanced, the net force is zero and there is no change in motion. When forces are unbalanced, they cause acceleration. Friction is an important force that opposes motion. Newton’s first law explains inertia, Newton’s second law gives the relation F = ma, and Newton’s third law explains action-reaction force pairs. The chapter also shows how Newton’s laws can be applied to a system of objects.