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C3.3 · State and apply Newton’s laws qualitatively

Learn to state and apply newton’s laws qualitatively through clear examples and targeted practice.

Ontario Grade 11 Physics

Forces

Ontario Grade 11 Physics — C3.3

A book rests on a table. A bicycle speeds up as its rider pedals. A swimmer pushes water backward and moves forward. Newton’s laws help explain each situation. A force is a push or pull. Motion means a change in position over time. Before using the laws, we need to identify what object we are studying and how we describe its motion.

What you will learn

  • State Newton’s three laws of motion in clear language.
  • Use the laws to explain how forces affect an object’s motion.
  • Identify when forces are balanced and when they are unbalanced.
  • Explain why an action–reaction pair acts on two different objects.

1. Start with the object and its motion

In physics, the system is the object or group of objects we choose to study. For example, if we study a rolling ball, the ball is the system. Other objects, such as the floor, can exert forces on it.
A reference frame is the viewpoint used to describe position and motion. In this lesson, use the floor as the reference frame unless a question says otherwise. A person standing beside a moving bicycle and a person riding on it may describe the motion differently because they use different reference frames.
A scalar has size only. Time and mass are scalars. A vector has both size and direction. Force, velocity, and acceleration are vectors. Acceleration describes a change in velocity. An object can accelerate by speeding up, slowing down, or changing direction.
To track direction, choose a positive direction. For a ball moving along a straight floor, we might call right positive and left negative. This choice is a sign convention. It helps organize descriptions, but it does not change the physical motion.
  • Name the system before explaining its motion.
  • State the reference frame and positive direction when direction matters.
  • Forces and acceleration have directions; mass and time do not.

2. Newton’s first law: motion does not change without a net force

Newton’s first law is also called the law of inertia. Inertia is an object’s tendency to resist a change in its motion. An object at rest remains at rest, and an object moving at constant velocity continues with that velocity, unless a net force acts on it.
Constant velocity means that both speed and direction stay the same. The net force is the combined effect of all the forces on the system. If forces balance, the net force is zero. Balanced forces do not change the object’s velocity. They do not necessarily mean that no forces act.
For example, a book resting on a table has gravity pulling down and a support force from the table pushing up. If those forces balance, the book stays at rest. In a different situation, a moving object can continue at constant velocity when the forces on it balance.
Mass is a measure of how much inertia an object has. For the same change in motion, an object with greater mass is harder to change. This is why a full shopping cart is harder to start moving or stop than an empty one.
\vec{F}_{net\text{net}}=0\ \Rightarrow\ constant velocity
  • Balanced forces mean no change in velocity, not necessarily no motion.
  • A change in velocity requires an unbalanced force.
  • Greater mass means greater resistance to a change in motion.

3. Newton’s second law: net force changes motion

Newton’s second law describes how an unbalanced, or net, force changes an object’s motion. The acceleration points in the same direction as the net force. A stronger net force produces greater acceleration for the same mass. A greater mass produces less acceleration for the same net force.
The familiar relationship uses force in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). It summarizes how force, mass, and acceleration are connected. In this lesson, use it to reason about direction and relative changes, not to carry out numerical calculations.
A free-body diagram is a simple drawing that shows the forces acting on one chosen system. Each arrow represents a force. The arrow points in the force’s direction. For example, if a box is pushed right across a floor, the push arrow points right, friction points left, gravity points down, and the floor’s support force points up. The horizontal net force depends on the push and friction together.
If the rightward net force is not zero, the box accelerates right. If the forces balance, its velocity does not change. It may remain at rest or keep moving at constant velocity.
F⃗net=ma⃗\vec{F}_{\text{net}}=m\vec{a}
  • Acceleration points in the direction of the net force.
  • Compare objects fairly: keep mass the same when comparing force, or force the same when comparing mass.
  • A free-body diagram shows forces on one system, not the motion itself.

4. Newton’s third law: forces come in pairs

Newton’s third law says that when one object exerts a force on a second object, the second object exerts a force back on the first. These forces are equal in strength and opposite in direction. They act on different objects, so they do not cancel each other on one object’s free-body diagram.
For example, when a hand pushes on a wall, the hand pushes the wall. The wall pushes back on the hand. The two forces have opposite directions, but one acts on the wall and the other acts on the hand.
The third law does not mean that two objects must move in the same way. Each object’s motion depends on the forces acting on that object and its mass. A large wall may show very little motion when pushed, while the person’s hand may feel a clear push back.
F⃗A on B=−F⃗B on A\vec{F}_{A\text{ on }B}=-\vec{F}_{B\text{ on }A}
  • Third-law forces are equal and opposite.
  • The paired forces act on two different objects.
  • Do not place both members of a third-law pair on one object’s free-body diagram.

Worked example

A book resting on a desk

Use Newton’s laws to explain why a book resting on a level desk remains at rest. Take the book as the system and up as positive.
  1. Choose the system
    The system is the book. Earth pulls the book downward through gravity, and the desk pushes it upward with a support force.
  2. Compare the forces
    The book remains at rest, so its velocity is not changing. The upward and downward forces balance. The net force on the book is zero.
    F⃗net=0\vec{F}_{\text{net}}=0
  3. Apply the first law
    Newton’s first law says that an object’s velocity does not change when the net force is zero. The book therefore stays at rest.
Answer: The book stays at rest because the forces on it balance.
Check: The conclusion fits the observation: a book at rest does not begin moving when the net force on it is zero.

Worked example

Pushing two carts

Two carts are pushed with the same net force in the same direction. Cart A has less mass than cart B. Compare their accelerations using Newton’s second law.
  1. Set the direction
    Treat each cart as its own system. Choose the push direction as positive. The net force on each cart points in that positive direction.
  2. Compare mass and force
    The net force is the same for both carts, but cart A has less mass. Newton’s second law predicts a greater acceleration when the same net force acts on less mass.
    F⃗net=ma⃗\vec{F}_{\text{net}}=m\vec{a}
  3. State the motion
    Both carts accelerate in the direction of the net force. Cart A has the greater acceleration, so its velocity changes more quickly.
Answer: Both carts accelerate in the push direction, and cart A accelerates more.
Check: The result has the correct direction: acceleration follows the net force. It is also reasonable that the less massive cart changes its motion more under the same net force.

Worked example

A swimmer pushes water

A swimmer pushes water backward. Use Newton’s third law to explain the force on the swimmer and the swimmer’s motion.
  1. Identify the interacting objects
    The swimmer and the water are the two interacting objects. Consider the force the swimmer exerts on the water and the force the water exerts on the swimmer.
  2. Match the force pair
    The swimmer exerts a backward force on the water. The water exerts an equal-strength force forward on the swimmer. These forces act on different objects.
    F⃗swimmer on water=−F⃗water on swimmer\vec{F}_{\text{swimmer on water}}=-\vec{F}_{\text{water on swimmer}}
  3. Connect force to motion
    The forward force from the water can contribute to a forward net force on the swimmer. If the swimmer’s net force is forward, the swimmer accelerates forward.
Answer: The water pushes the swimmer forward with a force equal in strength and opposite in direction to the swimmer’s backward force on the water.
Check: The force directions are opposite, and the forces act on different objects. The swimmer’s forward acceleration depends on the net force on the swimmer.

Common mistakes and how to avoid them

Thinking that a moving object must have a net force in its direction of motion.
Correction: A moving object can have constant velocity when its net force is zero. A net force is needed to change velocity.
Assuming balanced forces mean that an object must be at rest.
Correction: Balanced forces mean the velocity does not change. The object may be at rest or moving at constant velocity.
Saying that a third-law force pair cancels on one object.
Correction: The paired forces act on different objects. Draw a separate free-body diagram for each object.
Assuming that a larger force always gives a larger acceleration, without considering mass.
Correction: Compare both net force and mass. For the same mass, a larger net force gives greater acceleration. For the same net force, greater mass gives less acceleration.

Lesson summary

  • Newton’s first law connects zero net force with constant velocity.
  • Newton’s second law connects net force, mass, and acceleration. Acceleration points in the direction of the net force.
  • Newton’s third law describes equal and opposite forces between two objects.
  • Use a clearly identified system and force directions to decide which law explains a situation.

Check your understanding

Question 1

A puck moves in a straight line at constant velocity. What can you conclude about the net force on it?
  1. It points in the direction of motion.
  2. It points opposite the direction of motion.
  3. It is zero.
  4. It must be getting larger.
Show answer and explanation
It is zero.
Constant velocity means the velocity is not changing. By Newton’s first law, the net force is zero.

Question 2

The same net force acts on two objects. One has greater mass. Which has the greater acceleration?
  1. The object with greater mass.
  2. The object with less mass.
  3. Both always have the same acceleration.
  4. Neither accelerates.
Show answer and explanation
The object with less mass.
For the same net force, the less massive object has the greater acceleration.

Question 3

A person presses a hand against a wall. Which statement describes the third-law pair?
  1. The hand pushes the wall, and the wall pushes the hand in the opposite direction.
  2. The hand pushes the wall, and the wall pushes the floor in the same direction.
  3. The wall’s force exists only if the wall moves.
  4. Both forces act on the hand.
Show answer and explanation
The hand pushes the wall, and the wall pushes the hand in the opposite direction.
The hand’s force on the wall and the wall’s force on the hand are equal and opposite, and act on different objects.

Key terms

Acceleration
A change in velocity, including a change in speed or direction.
Balanced forces
Forces whose combined effect, or net force, is zero.
Free-body diagram
A drawing that shows the forces acting on one chosen system.
Inertia
An object’s tendency to resist a change in its motion.
Net force
The combined effect of all forces acting on a system.
Reference frame
The viewpoint used to describe an object’s position and motion.
System
The object or group of objects chosen for study.
Vector
A quantity with both size and direction.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Physics (SPH3U), expectation C3.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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