English:Forces and Newton’s Laws
Forces and Newton’s Laws
Introduction
A push on a door, a bicycle slowing down, a ball changing direction, and a rocket lifting from the ground all involve forces. A force is an interaction that can change an object's motion. Forces have both size and direction, so two forces can strengthen each other, oppose each other, or balance.
In this aiMOOC, you will use forces, motion, mass, acceleration, and free-body diagrams to understand Newton's three laws of motion. The course is designed for Grades 7–8 and focuses on explaining everyday events, drawing force diagrams, making simple calculations, and testing ideas safely.
The diagram above gives everyday examples of all three laws. As you work through the course, return to it and explain each example using the language of force, mass, acceleration, inertia, and interaction.
Learning Goals
By the end of the course, you should be able to explain what a force is, distinguish balanced from unbalanced forces, calculate simple net forces, describe inertia, use the relationship between net force, mass, and acceleration, identify action–reaction pairs, and draw basic free-body diagrams. You should also be able to apply Newton's laws to sports, transport, spaceflight, and everyday safety.
Who Was Isaac Newton?
Isaac Newton was an English mathematician and physicist who lived from 1642 to 1727. In 1687, his book Philosophiæ Naturalis Principia Mathematica, usually called the Principia, presented laws of motion that became foundations of classical mechanics.
Newton did not invent every idea about motion from nothing. His work built on earlier investigations by scientists such as Galileo Galilei. Science develops when people test, improve, and connect ideas over time.
Forces and Motion
What Is a Force?
A force is a push or pull caused by an interaction between objects. In physics, force is measured in newtons, with the symbol N. One newton is the force needed to accelerate a mass of one kilogram by one metre per second squared.
Because a force has direction as well as size, force is a vector quantity. A 5 N force to the right and a 5 N force to the left do not produce 10 N to the right. Instead, they cancel and give a net force of zero.
Common forces include gravity, friction, the normal force from a surface, tension in a rope or cable, air resistance, spring force, and applied pushes or pulls.
| Force | What causes it? | Typical direction |
|---|---|---|
| Gravity | Attraction between masses; near Earth it pulls objects downward. | Toward Earth's centre |
| Friction | Contact between surfaces that resists relative sliding. | Opposite the sliding or attempted sliding |
| Normal force | A surface pushes on an object touching it. | Perpendicular to the surface |
| Tension | A stretched rope, string, or cable pulls on an object. | Along the rope or cable |
| Drag | Air or another fluid resists motion through it. | Opposite motion relative to the fluid |
Mass and Weight Are Different
Mass tells you how much inertia an object has and is measured in kilograms. Weight is the gravitational force acting on that mass and is measured in newtons. Near Earth's surface, weight can be estimated with weight = mass × gravitational field strength. For school calculations, gravitational field strength is often rounded to about 10 N/kg; a more precise value near Earth's surface is about 9.8 N/kg.
If a book rests on a horizontal table, gravity pulls the book downward while the table provides an upward normal force. When these two forces are equal in size and opposite in direction, the vertical net force is zero.
Net Force: Add Forces with Direction
The net force is the overall force after all external forces on one object are combined. Forces in the same direction add. Forces in opposite directions subtract.
Suppose two students push a cart. One pushes 30 N to the right and the other pushes 20 N to the left. The net force is 10 N to the right. Because the net force is not zero, the cart accelerates to the right.
If the forces are balanced, the net force is zero. That does not mean the object must be stopped. It may be at rest, or it may move at constant velocity in a straight line.
Free-Body Diagrams
A free-body diagram is a simplified drawing that shows the external forces acting on one chosen object. Draw the object as a simple box or dot, then draw and label an arrow for each external force. The arrow points in the force direction, and its length can show relative size.
A useful checking question is: Which object is this force acting on? Only forces acting on the chosen object belong on its free-body diagram. Forces that the chosen object exerts on something else do not belong there.
Newton's First Law: Inertia
Newton's first law says that an object remains at rest, or continues moving with constant velocity in a straight line, unless a nonzero net external force acts on it. The law is often called the law of inertia.
Inertia is the tendency of an object to resist a change in its velocity. More mass means more inertia. A loaded shopping cart is harder to start, stop, or turn than an empty cart because the loaded cart has greater mass.
Seat belts are a practical example. If a moving car stops suddenly, your body tends to continue moving forward. The seat belt provides the force that changes your motion with the car.
Balanced Forces and Constant Velocity
Imagine a puck sliding on a nearly frictionless surface. If the net force on the puck is zero, its velocity does not change. In everyday life, friction often hides this idea because moving objects slow down when friction or drag provides an unbalanced force.
This is why the statement "a force is needed to keep something moving" is misleading. A net force is needed to change velocity, which means changing speed, direction, or both.
Newton's Second Law: Force, Mass, and Acceleration
Newton's second law connects net force, mass, and acceleration. For an object whose mass is constant:
net force = mass × acceleration
This relationship is often written as Fnet = m × a. Acceleration points in the same direction as the net force.
If the same mass experiences a larger net force, it has a larger acceleration. If the same net force acts on a larger mass, the acceleration is smaller.
Worked Examples
Example 1: Finding acceleration. A 4 kg cart experiences a net force of 12 N to the right. Its acceleration is 12 divided by 4, so the acceleration is 3 m/s² to the right.
Example 2: Finding net force. A 6 kg object accelerates at 2 m/s². The net force is 6 multiplied by 2, so the net force is 12 N in the direction of the acceleration.
Example 3: Comparing masses. The same 20 N net force acts on a 2 kg cart and a 5 kg cart. The 2 kg cart accelerates at 10 m/s², while the 5 kg cart accelerates at 4 m/s². The smaller mass changes its velocity faster.
Friction and the Second Law
Friction often reduces the net force available to accelerate an object. If you push a box with 50 N to the right while friction acts with 20 N to the left, the horizontal net force is 30 N to the right.
Do not automatically set friction equal to the applied force. Compare all forces acting on the object. Friction can balance an applied force in some situations, but it can also be smaller, giving a nonzero net force.
Newton's Third Law: Interaction Pairs
Newton's third law says that when object A exerts a force on object B, object B simultaneously exerts an equal-magnitude force in the opposite direction on object A. These two forces are often called an action–reaction pair.
The two forces do not cancel each other because they act on different objects. If you push a wall, the wall pushes you back. If a swimmer pushes water backward, the water pushes the swimmer forward.
The skaters push on each other with equal-magnitude, opposite-direction forces. Their accelerations can still be different because acceleration also depends on each skater's mass.
Rockets and Collisions
A rocket engine pushes exhaust gases backward, and the gases push the rocket forward. This is a third-law interaction. The rocket does not need to push against air, which is why rockets can accelerate in space.
In a collision, each object exerts a force on the other. The forces are equal in magnitude and opposite in direction, even if the objects have very different masses. Their accelerations may differ because of Newton's second law.
A Newton's cradle is especially useful for thinking about collisions. Its motion also involves conservation of momentum and energy, topics that go beyond the three laws themselves. During each contact, however, the colliding balls exert third-law force pairs on one another.
Connecting the Three Laws
Newton's laws work together rather than as three unrelated facts. First identify the object you are studying and the external forces acting on it. Then find the net force. If the net force is zero, Newton's first law describes the motion. If the net force is not zero, Newton's second law connects that force to acceleration. Newton's third law helps you identify the partner force that acts on the other interacting object.
A reliable problem-solving sequence is to choose one object, draw its free-body diagram, combine the forces with direction, decide whether the net force is zero, and then use the appropriate law.
Common Misconceptions
Misconception: An object moving forward must have a forward net force. Not always. An object can move forward at constant velocity while the net force is zero.
Misconception: Heavier objects always fall faster. In ideal free fall without air resistance, objects near Earth have the same gravitational acceleration regardless of mass.
Misconception: Third-law forces cancel. They do not cancel on one free-body diagram because the pair acts on two different objects.
Misconception: Mass and weight mean the same thing. Mass is measured in kilograms; weight is a force measured in newtons.
Misconception: A larger force always means a larger acceleration. Acceleration depends on both net force and mass.
Interactive Tasks
Quiz: Test Your Knowledge
What quantity tells you the overall effect of all external forces on one object? (Net force) (!Mass) (!Speed) (!Distance)
What happens to an object moving at constant velocity when the net force is zero? (It keeps the same velocity) (!It must speed up) (!It must stop) (!It must turn)
Which word describes resistance to a change in motion? (Inertia) (!Friction) (!Velocity) (!Tension)
Which unit is used for force? (Newton) (!Kilogram) (!Metre) (!Second)
For the same mass, what happens when net force increases? (Acceleration increases) (!Acceleration decreases) (!Mass increases) (!Inertia disappears)
For the same net force, which object has the smaller acceleration? (The object with greater mass) (!The object with smaller mass) (!The object with greater speed) (!The object with smaller speed)
Which force usually acts opposite sliding motion between surfaces? (Friction) (!Tension) (!Gravity) (!Normal force)
Where do the two forces in a third law pair act? (On two different objects) (!On one object only) (!At different times) (!Only on moving objects)
Which statement about a book resting on a table is correct? (Its vertical forces can be balanced) (!It has no gravity) (!It has no forces) (!Its mass becomes zero)
What should a free body diagram show? (External forces on one chosen object) (!Every object in the room) (!Only the direction of motion) (!Only forces the object creates)
Memory Game
| Inertia | Resistance to a change in velocity |
| Net force | Vector sum of external forces on an object |
| Friction | Contact force that resists relative sliding |
| Tension | Pull transmitted by a stretched rope or cable |
| Weight | Gravitational force acting on a mass |
| Acceleration | Rate at which velocity changes |
| Normal force | Support force perpendicular to a surface |
| Interaction pair | Equal-magnitude opposite-direction forces on two objects |
Drag and Drop
| Match the correct terms. | Topic |
|---|---|
| Newton's first law | Constant velocity continues when net force is zero |
| Newton's second law | Net force and mass determine acceleration |
| Newton's third law | Interacting objects exert equal and opposite forces |
| Free-body diagram | External forces on one chosen object are represented by arrows |
| Balanced forces | Combined external force is zero |
Crossword Puzzle
| Inertia | What is the tendency to resist a change in velocity? |
| Newton | What is the SI unit of force? |
| Friction | What force resists sliding between surfaces? |
| Tension | What force is transmitted through a stretched rope? |
| Gravity | What force gives an object weight near Earth? |
| Acceleration | What quantity describes a change in velocity over time? |
LearningApps
Cloze Text
Open-Ended Tasks
Easy
- Force Hunt: Find five examples of pushes or pulls at home or school, photograph or sketch them, and label the objects that interact.
- Balanced Force Sketch: Draw an object at rest and add force arrows that show how its forces can balance.
- Inertia Storyboard: Create a four-panel storyboard showing what happens to a passenger when a bus starts or stops suddenly.
- Friction Test: Slide the same small object across two safe surfaces and write a short comparison of how friction changes its motion.
Standard
- Cart Investigation: Use a toy cart or another safe rolling object to test how changing the applied push changes its acceleration, and record your observations.
- Mass and Acceleration Investigation: Keep the push as similar as possible while changing the cart's mass, then explain the pattern using Newton's second law.
- Free-Body Diagram Gallery: Create three free-body diagrams for everyday situations such as a hanging object, a book on a table, and a person pushing a box.
- Third Law Interview: Interview a classmate, coach, or teacher about an activity involving pushing, jumping, swimming, or skating, then identify an action–reaction pair from the activity.
Advanced
- Sports Physics Video: Produce a short video that analyzes one sports movement using all three of Newton's laws and at least one free-body diagram.
- Seat Belt Engineering: Research how seat belts or head restraints reduce injury risk, then create an evidence-based poster linking the design to inertia and force.
- Rocket Model Analysis: Build or observe a safe balloon-rocket setup, collect measurements such as travel distance or time, and explain the motion using Newton's second and third laws.
- Force Model Challenge: Design a small experiment in which two explanations make different predictions, gather data, and argue which explanation is better supported by the evidence.
Learning Assessment
- Force Diagram Reasoning: Draw and explain a free-body diagram for a cyclist moving at constant speed on level ground, including why a zero net force does not mean zero forces.
- Second Law Transfer: Compare two carts with different masses pushed by the same net force and predict which accelerates more, then justify your answer using Newton's second law.
- Interaction Pair Analysis: For a person jumping from the ground, identify the third-law force pair and explain why those forces do not cancel on the person's free-body diagram.
- Motion Evidence: Given a description of an object's velocity changing over time, infer the direction of its net force and explain your reasoning.
- Safety Application: Explain how inertia and force help account for the purpose of a seat belt during sudden braking, using cause-and-effect reasoning.
- Experimental Evaluation: Review a simple force-and-motion experiment, identify one source of measurement error or uncontrolled variation, and propose a practical improvement.
Evidence of Learning
Important evidence of learning includes accurate use of the terms force, net force, mass, weight, inertia, velocity, and acceleration; correct identification of balanced and unbalanced forces; clear free-body diagrams with forces attached to the correct object; correct use of Newton's first, second, and third laws; simple calculations with force, mass, and acceleration; explanations that distinguish third-law pairs from balanced forces; safe investigations with recorded observations or data; and products such as diagrams, posters, reports, experiments, or videos that transfer the laws to unfamiliar situations.
OERs on the Topic
You can extend your learning with NASA's Newton's Laws of Motion and the OpenStax Physics: Force.
Linked Learning Areas