1. Learn
  2. Quick Notes
  3. List
  4. Solve problems involving F= ma
Back

Effect of a Force

2.6 Force - Pandai Quick Note
PHYSICS • Form 4 • Chapter 2: Force and Motion I

2.6 Force

Forces are involved in most of our daily activities and can change the state of motion of an object. When a force acts on an object along a straight line, it changes the object's velocity, causing acceleration and altering its momentum over time.

Learning Objectives

  • State the relationship between acceleration and force when mass is kept constant.
  • State the relationship between acceleration and mass when force is kept constant.
  • State Newton's Second Law of Motion and express it in mathematical form (\(F \propto ma\) and \(F = ma\)).
  • Define the S.I. unit of force, the newton (N).
  • Solve numerical problems involving the formula \(F = ma\) and linear motion equations.

Relationships Between Force, Mass, and Acceleration (\(F = ma\))

Compare the two direct proportionality graphs and see how they combine to formulate Newton's Second Law.

Graph 1: \(a\) against \(F\)

When mass is constant, acceleration is directly proportional to force. The graph is a straight line passing through the origin.

a F a ∝ F (m constant)

Graph 2: \(a\) against \(\frac{1}{m}\)

When force is constant, acceleration is inversely proportional to mass. The graph is a straight line passing through the origin.

a 1/m a ∝ 1/m (F constant)

Combining the two relationships

\(F = ma\)

Newton's Second Law of Motion: the rate of change of momentum is directly proportional to the force and acts in the direction of the applied force.

Short Explanation

Force and Acceleration

When an unbalanced force acts on an object, the object accelerates in the direction of the force. If the mass is kept constant, applying a larger force produces a proportionally larger acceleration (\(a \propto F\)).

Mass and Acceleration

If the applied force is kept constant, an object with a larger mass will experience a smaller acceleration. Acceleration is inversely proportional to mass (\(a \propto \frac{1}{m}\)).

Newton's Second Law of Motion

The rate of change of momentum is directly proportional to the force and acts in the direction of the applied force. Mathematically, \(F \propto ma\) and \(F = ma\).

Definition of 1 Newton

In S.I. units, 1 N is the force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) when applied on a mass of \(1\ \mathrm{kg}\).

Derivation of Newton's Second Law

\(F \propto \dfrac{mv - mu}{t}\)

Since \(a = \dfrac{v - u}{t}\), the rate of change of momentum is \(\dfrac{mv - mu}{t}\).

Quantity Symbol SI Unit
Force \(F\) newton (N)
Mass \(m\) kilogram (kg)
Acceleration \(a\) metre per second squared (m s⁻²)
Change of momentum \(mv - mu\) kg m s⁻¹
Rate of change of momentum \(\dfrac{mv - mu}{t}\) kg m s⁻² or N

Try to Answer First

Answer in your mind, then press "Check Answer".

1

State Newton's Second Law of Motion.

Check Answer
Answer: Newton's Second Law of Motion states that the rate of change of momentum is directly proportional to the force and acts in the direction of the applied force.
2

Define the unit of force, 1 newton (1 N).

Check Answer
Answer: 1 newton is the force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) when applied on a mass of \(1\ \mathrm{kg}\).
3

A force of 80 N acts on a stationary object for 7 s and causes it to reach a velocity of 35 m s⁻¹. Calculate the mass of the object.

Check Answer
Answer: Acceleration, \(a = \dfrac{v - u}{t} = \dfrac{35 - 0}{7} = 5\ \mathrm{m\,s^{-2}}\). Mass, \(m = \dfrac{F}{a} = \dfrac{80\ \mathrm{N}}{5\ \mathrm{m\,s^{-2}}} = 16\ \mathrm{kg}\).

Common Mistakes

  • !Forgetting that acceleration must be along the same direction as the net applied force.
  • !Omitting the negative sign or failing to explain its physical meaning when dealing with deceleration and braking forces. A negative force indicates it opposes the direction of motion.
  • !Plotting \(a\) directly against mass \(m\) expecting a straight line, instead of plotting \(a\) against the reciprocal of mass (\(\frac{1}{m}\)).
  • !Confusing change of momentum (\(mv - mu\)) with rate of change of momentum (\(\frac{mv - mu}{t}\)).

Concept Misunderstandings

Misunderstanding

A constant force is needed to keep an object moving at a constant velocity.

Correct Concept

According to \(F = ma\), if velocity is constant, acceleration \(a = 0\), so the net force \(F = 0\). A net force causes an object to change velocity (accelerate), not simply maintain it.

Misunderstanding

Doubling the mass of an object will double its acceleration under the same force.

Correct Concept

Acceleration is inversely proportional to mass (\(a \propto \frac{1}{m}\)). Doubling the mass halves the acceleration when the force is constant.

Summary

  • When mass \(m\) is constant, acceleration is directly proportional to force: \(a \propto F\).
  • When force \(F\) is constant, acceleration is inversely proportional to mass: \(a \propto \frac{1}{m}\).
  • Newton's Second Law of Motion: The rate of change of momentum is directly proportional to the applied force and acts in the direction of the force (\(\text{Force} \propto \frac{mv - mu}{t}\)).
  • Formula: \(F = ma\), where \(F\) is in newtons (N), \(m\) in kilograms (kg), and \(a\) in metres per second squared (m s⁻²).
  • Definition of 1 N: The force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) on a mass of \(1\ \mathrm{kg}\).

Short Activity

Objective: Test your understanding of force, mass, acceleration and Newton's Second Law.

A. Objective Quiz

1 What happens to the acceleration of a trolley if the pulling force applied on it is doubled while its mass is kept constant?

2 According to Newton's Second Law of Motion, the applied force acting on an object is directly proportional to the:

B. Fill in the Blanks

3 In S.I. units, 1 N is the force that produces an acceleration of 1 m s⁻² when applied on a mass of kg.

4 When a constant force acts on an object, its acceleration is inversely proportional to its .

C. Matching / Drag and Drop

Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.

Choices
Change of momentum
Rate of change of momentum
Newton's Second Law Formula
Graph of a against 1/m
Meanings
The difference between final momentum and initial momentum, mv – mu.Correct ✓Try againEmpty
The change of momentum divided by time, (mv – mu) / t.Correct ✓Try againEmpty
The equation relating force, mass, and acceleration, F = ma.Correct ✓Try againEmpty
A straight line passing through the origin showing acceleration is inversely proportional to mass.Correct ✓Try againEmpty
 

Keywords

Force (\(F\)) Acceleration (\(a\)) Mass (\(m\)) Momentum (\(p\)) Rate of change of momentum Newton's Second Law of Motion Newton (N) Friction-compensated runway
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

Effect of a Force

2.6 Force - Pandai Quick Note
PHYSICS • Form 4 • Chapter 2: Force and Motion I

2.6 Force

Forces are involved in most of our daily activities and can change the state of motion of an object. When a force acts on an object along a straight line, it changes the object's velocity, causing acceleration and altering its momentum over time.

Learning Objectives

  • State the relationship between acceleration and force when mass is kept constant.
  • State the relationship between acceleration and mass when force is kept constant.
  • State Newton's Second Law of Motion and express it in mathematical form (\(F \propto ma\) and \(F = ma\)).
  • Define the S.I. unit of force, the newton (N).
  • Solve numerical problems involving the formula \(F = ma\) and linear motion equations.

Relationships Between Force, Mass, and Acceleration (\(F = ma\))

Compare the two direct proportionality graphs and see how they combine to formulate Newton's Second Law.

Graph 1: \(a\) against \(F\)

When mass is constant, acceleration is directly proportional to force. The graph is a straight line passing through the origin.

a F a ∝ F (m constant)

Graph 2: \(a\) against \(\frac{1}{m}\)

When force is constant, acceleration is inversely proportional to mass. The graph is a straight line passing through the origin.

a 1/m a ∝ 1/m (F constant)

Combining the two relationships

\(F = ma\)

Newton's Second Law of Motion: the rate of change of momentum is directly proportional to the force and acts in the direction of the applied force.

Short Explanation

Force and Acceleration

When an unbalanced force acts on an object, the object accelerates in the direction of the force. If the mass is kept constant, applying a larger force produces a proportionally larger acceleration (\(a \propto F\)).

Mass and Acceleration

If the applied force is kept constant, an object with a larger mass will experience a smaller acceleration. Acceleration is inversely proportional to mass (\(a \propto \frac{1}{m}\)).

Newton's Second Law of Motion

The rate of change of momentum is directly proportional to the force and acts in the direction of the applied force. Mathematically, \(F \propto ma\) and \(F = ma\).

Definition of 1 Newton

In S.I. units, 1 N is the force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) when applied on a mass of \(1\ \mathrm{kg}\).

Derivation of Newton's Second Law

\(F \propto \dfrac{mv - mu}{t}\)

Since \(a = \dfrac{v - u}{t}\), the rate of change of momentum is \(\dfrac{mv - mu}{t}\).

Quantity Symbol SI Unit
Force \(F\) newton (N)
Mass \(m\) kilogram (kg)
Acceleration \(a\) metre per second squared (m s⁻²)
Change of momentum \(mv - mu\) kg m s⁻¹
Rate of change of momentum \(\dfrac{mv - mu}{t}\) kg m s⁻² or N

Try to Answer First

Answer in your mind, then press "Check Answer".

1

State Newton's Second Law of Motion.

Check Answer
Answer: Newton's Second Law of Motion states that the rate of change of momentum is directly proportional to the force and acts in the direction of the applied force.
2

Define the unit of force, 1 newton (1 N).

Check Answer
Answer: 1 newton is the force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) when applied on a mass of \(1\ \mathrm{kg}\).
3

A force of 80 N acts on a stationary object for 7 s and causes it to reach a velocity of 35 m s⁻¹. Calculate the mass of the object.

Check Answer
Answer: Acceleration, \(a = \dfrac{v - u}{t} = \dfrac{35 - 0}{7} = 5\ \mathrm{m\,s^{-2}}\). Mass, \(m = \dfrac{F}{a} = \dfrac{80\ \mathrm{N}}{5\ \mathrm{m\,s^{-2}}} = 16\ \mathrm{kg}\).

Common Mistakes

  • !Forgetting that acceleration must be along the same direction as the net applied force.
  • !Omitting the negative sign or failing to explain its physical meaning when dealing with deceleration and braking forces. A negative force indicates it opposes the direction of motion.
  • !Plotting \(a\) directly against mass \(m\) expecting a straight line, instead of plotting \(a\) against the reciprocal of mass (\(\frac{1}{m}\)).
  • !Confusing change of momentum (\(mv - mu\)) with rate of change of momentum (\(\frac{mv - mu}{t}\)).

Concept Misunderstandings

Misunderstanding

A constant force is needed to keep an object moving at a constant velocity.

Correct Concept

According to \(F = ma\), if velocity is constant, acceleration \(a = 0\), so the net force \(F = 0\). A net force causes an object to change velocity (accelerate), not simply maintain it.

Misunderstanding

Doubling the mass of an object will double its acceleration under the same force.

Correct Concept

Acceleration is inversely proportional to mass (\(a \propto \frac{1}{m}\)). Doubling the mass halves the acceleration when the force is constant.

Summary

  • When mass \(m\) is constant, acceleration is directly proportional to force: \(a \propto F\).
  • When force \(F\) is constant, acceleration is inversely proportional to mass: \(a \propto \frac{1}{m}\).
  • Newton's Second Law of Motion: The rate of change of momentum is directly proportional to the applied force and acts in the direction of the force (\(\text{Force} \propto \frac{mv - mu}{t}\)).
  • Formula: \(F = ma\), where \(F\) is in newtons (N), \(m\) in kilograms (kg), and \(a\) in metres per second squared (m s⁻²).
  • Definition of 1 N: The force that produces an acceleration of \(1\ \mathrm{m\,s^{-2}}\) on a mass of \(1\ \mathrm{kg}\).

Short Activity

Objective: Test your understanding of force, mass, acceleration and Newton's Second Law.

A. Objective Quiz

1 What happens to the acceleration of a trolley if the pulling force applied on it is doubled while its mass is kept constant?

2 According to Newton's Second Law of Motion, the applied force acting on an object is directly proportional to the:

B. Fill in the Blanks

3 In S.I. units, 1 N is the force that produces an acceleration of 1 m s⁻² when applied on a mass of kg.

4 When a constant force acts on an object, its acceleration is inversely proportional to its .

C. Matching / Drag and Drop

Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.

Choices
Change of momentum
Rate of change of momentum
Newton's Second Law Formula
Graph of a against 1/m
Meanings
The difference between final momentum and initial momentum, mv – mu.Correct ✓Try againEmpty
The change of momentum divided by time, (mv – mu) / t.Correct ✓Try againEmpty
The equation relating force, mass, and acceleration, F = ma.Correct ✓Try againEmpty
A straight line passing through the origin showing acceleration is inversely proportional to mass.Correct ✓Try againEmpty
 

Keywords

Force (\(F\)) Acceleration (\(a\)) Mass (\(m\)) Momentum (\(p\)) Rate of change of momentum Newton's Second Law of Motion Newton (N) Friction-compensated runway
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Force and Motion I
Topic : Solve problems involving F= ma
Form 4 Physics
Related notes

Report this note
© 2026 Pandai.org All Rights Reserved

Quiz
View video m
Notes
Account