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C3.1 · Distinguish forces and describe how they change velocity

Learn to distinguish forces and describe how they change velocity through clear examples and targeted practice.

Ontario Grade 11 Physics

Forces

SPH3U study topic C3.1: distinguish forces and describe how they change velocity

A force is a push or a pull. Forces can change an object's velocity. Velocity tells both how fast an object moves and its direction. An object can therefore change velocity by speeding up, slowing down, changing direction, or changing both speed and direction. Begin by choosing the object to study and the viewpoint used to describe its motion. Then identify the forces acting on that object and consider their combined effect. This lesson uses diagrams and everyday situations to explain those changes.

What you will learn

Distinguish contact forces from non-contact forces.
Identify forces acting on a chosen object and describe their directions.
Describe the combined effect of forces acting on an object.
Explain how force direction relates to changes in velocity.

1. Motion, vectors, and a clear point of view

A scalar has size, or magnitude, only. Time and mass are examples. A vector has both magnitude and direction. Force and velocity are vectors. For example, eastward velocity and westward velocity are different, even if their speeds are equal.

Speed tells how fast an object moves. Velocity includes speed and direction. A change in velocity can be a change in speed, a change in direction, or both. A cyclist moving around a bend at steady speed changes velocity because the direction changes.

A system is the object or group of objects chosen for study. A reference frame is the viewpoint used to describe motion. In this lesson, use the ground as the reference frame. Choose a positive direction before using signs. For example, if east is positive, west is the opposite direction. The choice helps describe directions; it does not change the motion.

A force diagram helps keep the system clear. Draw the chosen object as a dot or box. Draw and label arrows for forces acting on it. Each arrow points in the force's direction. Do not include forces that the object exerts on something else in this diagram.

Velocity and force are vectors: each has a direction as well as a size.
Name the system and reference frame before describing its motion.
A change in velocity can involve speed, direction, or both.

2. Recognizing forces and finding their combined effect

Forces are measured in newtons, with the symbol N. A contact force acts when objects touch. An applied force is a push or pull from a person or another object. Friction acts between touching surfaces and usually opposes sliding or attempted sliding. Tension is a pull carried by a taut rope or string. A support force is a push from a surface on an object touching it.

A non-contact force acts without the objects touching. Gravity is a non-contact force. Near Earth, gravity pulls objects toward Earth. Magnetic and electric forces are also non-contact forces. These examples show the difference: contact forces require touching, while non-contact forces do not.

A free-body diagram is a simple drawing of the forces acting on one selected system. Consider a book resting on a table. The system is the book. Earth pulls down on it through gravity. The table pushes up on it through a support force. The book also pushes on the table, but that force acts on the table, not on the book. It does not belong on the book's free-body diagram.

The net force, written as

\vec F_{\text{net}}

, is the combined effect of all forces acting on a system. The arrow above

F

shows that force is a vector. To find the net force, combine the force vectors, taking their directions into account. In one dimension, if two opposing forces act, compare their magnitudes: equal forces balance, and the net force is zero; otherwise, the net force points in the direction of the larger force. For forces in different directions, combine the vectors rather than choosing one force as the overall direction.

For a book resting on a table, the upward support force and downward gravitational force balance. The net force is zero. In a diagram, these two arrows point in opposite directions. This example distinguishes individual forces from their combined effect.

\vec F_{\text{net}}=\sum \vec F

Contact forces involve touching; non-contact forces do not.
A free-body diagram shows forces acting on the chosen system only.
The net force is the vector sum of all forces acting on the system.
For opposing forces along one line, compare their magnitudes to determine whether they balance and, if not, which way the net force points.

3. Describing how forces change velocity

The net force describes the direction of a change in velocity. If the net force is zero, velocity does not change. An object at rest stays at rest, and an object already moving continues with constant velocity. Constant velocity means the same speed in the same direction. Balanced forces do not necessarily mean that an object is stopped.

If the net force is not zero, velocity changes in the net-force direction. A net force in the direction of an object's motion makes it speed up. A net force opposite its motion makes it slow down. A net force in another direction changes its direction of travel. These descriptions concern the net force, not just one force selected from the diagram.

Do not assume that a force always points in the direction an object moves. An object can move one way while its velocity changes another way. For example, a cart moving east with a net force west changes velocity westward. While it continues moving east, it slows down.

A useful explanation has three parts: name the system, describe the forces and their directions, then state what happens to velocity. If the situation does not tell you whether forces balance, do not assume that they do. If the object's current motion is not stated, you can describe the direction of its velocity change, but you may not be able to say whether it speeds up or slows down.

Zero net force means no change in velocity, not necessarily no motion.
A nonzero net force changes velocity in the net-force direction.
Compare the net-force direction with the motion direction to describe speeding up, slowing down, or turning.

4. A consistent way to explain a force situation

First name the system and reference frame. State a positive direction if you will use signs. Next, list only the forces acting on the system. Classify each as contact or non-contact, and draw or imagine a labelled arrow for each one.

Then consider all force directions together to describe the net force. Do not predict a velocity change from one force if other forces also act. Finally, compare the net-force direction with the object's current velocity. Matching directions mean that the object speeds up. Opposite directions mean that it slows down. A net force in another direction changes its direction of travel.

Keep your explanation tied to the information given. If the current motion is not stated, do not claim that the object speeds up or slows down. If forces point in different directions, describe their combined effect as a vector result; do not use a one-dimensional comparison unless the forces act along the same line.

Name the system and viewpoint first.
Use all forces acting on the system to describe the net force.
State what changes about velocity and connect it to the force directions.

Net force and velocity change

Situation	Net-force direction	Velocity description
Object moving in the net-force direction	Same direction as motion	Speeds up
Object moving opposite the net force	Opposite direction to motion	Slows down
Object moving in another direction	Different direction from motion	Changes direction
Balanced forces	No net force	Velocity stays constant

Worked example

1. A cart pulled against friction

A cart rolls east across a floor. A person pulls it east, while friction from the floor acts west. The eastward pull is stronger than the opposing friction. Describe the force types and the cart's velocity change.

Choose the system
The system is the cart, and the reference frame is the ground. Take east as positive. The person's pull is an applied contact force. Friction is also a contact force because it acts between touching surfaces.
Combine the forces
The forces act along the same line in opposite directions. The pull is stated to be stronger, so the net force points east.
Describe the motion change
The cart is already moving east, and the net force also points east. Its velocity changes eastward, so it speeds up in its current direction.

Answer: The cart's net force points east, and it speeds up while moving east.

Check: The net-force direction matches the cart's direction of motion, so speeding up is reasonable. No force magnitudes or measurements were supplied or needed.

Worked example

2. A ball thrown upward

A ball has just left a person's hand and is moving upward. Ignore air resistance. Describe the force acting on the ball and its velocity change.

Choose the system and direction
The system is the ball, viewed from the ground. Take upward as positive. The hand is no longer touching the ball, so it does not exert a continuing contact force on it.
Identify the force
Earth's gravitational force acts downward without contact. With air resistance ignored, gravity is the only force in this situation, so the net force is downward.
Relate force to velocity
The ball moves upward while its velocity changes downward. The directions are opposite, so the ball slows as it rises. Gravity points downward even though the ball is moving upward.

Answer: Gravity acts downward, so the ball's velocity changes downward and it slows while rising.

Check: The force and velocity-change directions agree. Since the ball's motion is upward, a downward velocity change means it slows as it rises.

Worked example

3. A puck turning on a smooth surface

A puck moves north across a smooth horizontal surface. A player briefly pushes it east. Describe how the push affects its velocity while the push acts.

Name the system and directions
The system is the puck, and the reference frame is the ground. The puck's motion is north. The player's push is east and is a contact force because the player touches the puck.
Describe the force effect
The eastward push changes the puck's velocity toward the east while the push acts. The puck's northward motion does not make the eastward force point north.
Describe the resulting motion
The puck has northward motion while its velocity changes eastward. Its direction of travel therefore turns toward the east. This is a change in velocity even though the puck's speed is not specified.

Answer: The eastward push changes the puck's velocity eastward and turns its motion toward the east.

Check: The conclusion follows from the stated directions. It does not claim a particular speed or amount of turning.

Common mistakes and how to avoid them

Thinking that zero net force means an object must be stopped.

Correction: Zero net force means velocity is not changing. The object may be at rest or moving at constant velocity.

Using one force to predict motion while ignoring other forces.

Correction: Consider all forces acting on the system. Their vector sum determines the net force and the direction of the velocity change.

Treating velocity as another word for speed.

Correction: Velocity includes direction. An object can change velocity by turning even if its speed stays the same.

Putting a force exerted by the system onto its own free-body diagram.

Correction: A free-body diagram shows forces acting on the chosen system. A force the system exerts acts on a different object.

Assuming a force always points along an object's motion.

Correction: Force direction and motion direction can differ. Compare the net-force direction with the current velocity to describe the change.

Lesson summary

A force is a push or pull and is measured in newtons.
Contact forces require touching; non-contact forces do not.
The net force is the vector sum of forces acting on one chosen system.
Zero net force means velocity stays constant. A nonzero net force changes velocity in its direction.
Compare net-force direction with motion direction to explain whether an object speeds up, slows down, or turns.

Check your understanding

Question 1

A box slides north while balanced forces act on it. What happens to its velocity?

It stops at once.
It stays constant.
It changes southward.
It must turn east.

Show answer and explanation

It stays constant.

Balanced forces mean there is no net force, so velocity does not change. The box can keep moving north at constant velocity.

Question 2

A ball moves east while its net force points west. What happens to its velocity?

Its velocity changes westward, so it slows while moving east.
Its velocity changes eastward, so it speeds up.
Its velocity does not change.
It immediately moves west at the same speed.

Show answer and explanation

Its velocity changes westward, so it slows while moving east.

A nonzero net force changes velocity in its direction. The ball moves east while its velocity changes westward, so it slows while moving east.

Question 3

A puck moves north and receives a brief push east. Which statement best describes the effect of the push?

The puck's velocity changes eastward, turning its motion toward the east.
The puck's velocity cannot change because it was already moving north.
The push is a non-contact force.
The puck must stop before its direction can change.

Show answer and explanation

The puck's velocity changes eastward, turning its motion toward the east.

The player's push is a contact force. Its eastward direction changes the puck's velocity eastward, so the puck's direction of travel turns toward the east.

Key terms

Contact force: A force that acts when objects touch.
Free-body diagram: A drawing that shows forces acting on one selected system.
Net force: The vector sum, or combined effect, of all forces acting on a system.
Non-contact force: A force that acts without the objects touching.
Reference frame: The viewpoint used to describe an object's motion.
Scalar: A quantity with magnitude only.
System: The object or group of objects chosen for study.
Vector: A quantity with magnitude and direction.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation C3.1. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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