Forces and Free-Body Diagrams

Welcome, students 👋 In this lesson, you will learn how to identify forces and represent them with free-body diagrams, a skill that is essential in AP Physics 1. Forces explain why objects speed up, slow down, turn, or stay still. Free-body diagrams help you organize those forces so you can use physics ideas clearly and correctly. By the end of this lesson, you should be able to describe common forces, draw accurate diagrams, and connect those diagrams to motion using Newton’s laws.

Lesson objectives:

Explain the main ideas and vocabulary behind forces and free-body diagrams.
Draw and interpret free-body diagrams for objects in common situations.
Use force diagrams to reason about motion in one dimension.
Connect free-body diagrams to the larger topic of force and translational dynamics.
Support your reasoning with real-world examples and evidence.

What Is a Force?

A force is a push or pull that can change an object’s motion. In AP Physics 1, forces are measured in newtons, written as $\text{N}$. A force can make an object start moving, stop moving, speed up, slow down, or change direction. For example, when you push a shopping cart, your hand applies a force that can increase the cart’s speed. When a book rests on a table, the table applies an upward force that supports the book.

Forces are vector quantities, which means they have both size and direction. This matters a lot because two forces of the same size but opposite directions can cancel each other. For example, if you pull a rope to the right with $50\,\text{N}$ and someone else pulls to the left with $50\,\text{N}$, the net force is $0\,\text{N}$, so the rope does not accelerate.

In AP Physics 1, the most important idea is the net force, written as $\sum \vec{F}$. This means the total of all forces acting on an object after directions are considered. Newton’s second law links net force to acceleration:

$$\sum \vec{F} = m\vec{a}$$

This equation shows that if the net force is not zero, the object accelerates. If the net force is zero, the object’s acceleration is zero.

Common Forces You Must Know

To draw a free-body diagram correctly, students, you need to recognize the common forces that appear in many situations. The most important ones are listed below.

Weight or gravitational force

The weight of an object is the force of gravity acting on it. Near Earth’s surface, the weight is

$$F_g = mg$$

where $m$ is mass and $g$ is the acceleration due to gravity, about $9.8\,\text{m/s}^2$ near Earth.

A 2 kg textbook has a weight of

$$F_g = (2)(9.8) = 19.6\,\text{N}$$

downward. Gravity always points toward the center of the Earth, so in most classroom problems it points downward.

Normal force

The normal force is the support force from a surface. It acts perpendicular to the surface. If a book rests on a table, the table pushes upward on the book with a normal force. The normal force is not always equal to weight; it depends on the situation. If an elevator accelerates upward, the normal force can be greater than weight. If an object is on a ramp, the normal force points perpendicular to the ramp, not straight up.

Tension

Tension is a pulling force transmitted through a rope, string, cable, or chain. If a mass hangs from a rope, the rope pulls upward on the mass with tension. In ideal AP Physics 1 problems, a rope is often assumed to be light and inextensible, which means its mass is negligible and its length does not change.

Friction

Friction is a force that opposes relative motion or attempted motion between surfaces. It acts parallel to the surface. If you push a heavy box across the floor, friction may act opposite the direction of motion. There are two main types:

Static friction, which prevents motion from starting.
Kinetic friction, which acts when surfaces are sliding.

Static friction can adjust its size up to a maximum value. Kinetic friction is often modeled as

$$f_k = \mu_k N$$

where $\mu_k$ is the coefficient of kinetic friction and $N$ is the normal force.

Applied force

An applied force is a push or pull from a person or another object. It might be your hand pushing a cart, a bat hitting a ball, or a motor pulling a sled. Applied forces are often the starting point in a problem, but they are only one part of the full force picture.

What Is a Free-Body Diagram?

A free-body diagram is a simple drawing of a single object with all forces acting on it shown as arrows. The object is treated as if it were isolated, which helps you focus on the forces that matter. The diagram does not show the surroundings in detail; it only shows the object and the forces on it.

Here is the basic process:

Choose the object of interest.
Draw the object as a dot or simple box.
Identify every external force acting on it.
Draw an arrow for each force, pointing in the correct direction.
Label each force clearly.

A good free-body diagram is not about artistic detail. It is about physical accuracy. Each arrow should represent one force only. Do not include motion arrows unless your teacher specifically asks for them, because a free-body diagram is about forces, not velocity.

Example: Book on a table

Imagine a book resting on a table. The forces on the book are:

Weight $F_g$ downward
Normal force $N$ upward

If the book is at rest, then the net force is zero:

$$\sum F_y = N - F_g = 0$$

So,

$$N = F_g$$

This is a common situation where the book is not moving, but forces are still acting on it.

Example: Box being pulled across a floor

Suppose a box is pulled to the right by an applied force $F_{\text{app}}$. Friction acts to the left, gravity acts downward, and the normal force acts upward. If the box accelerates to the right, then the horizontal forces are not balanced:

$$\sum F_x = F_{\text{app}} - f_k = ma$$

If $F_{\text{app}} > f_k$, the box speeds up to the right. If the forces are equal, the box moves at constant velocity or stays at rest, depending on the starting condition.

How to Use Free-Body Diagrams in Problem Solving

Free-body diagrams help you turn a story problem into physics equations. This is one of the most useful habits in AP Physics 1. students, the key is to think one direction at a time.

Step 1: Pick axes

Usually, you choose $x$ and $y$ directions. For flat surfaces, $x$ is horizontal and $y$ is vertical. For ramps, it is often helpful to choose axes parallel and perpendicular to the ramp. This makes the equations easier.

Step 2: Separate forces by direction

For each axis, add up only the forces in that direction. If you choose upward as positive, then upward forces are positive and downward forces are negative.

Step 3: Apply Newton’s second law

Use

$$\sum F_x = ma_x$$

and

$$\sum F_y = ma_y$$

A huge AP Physics 1 idea is that acceleration in one direction depends on the net force in that same direction. If vertical acceleration is zero, then the vertical forces balance. If horizontal acceleration is not zero, then the horizontal forces do not balance.

Example: Elevator problem

A student stands in an elevator. The student’s weight is downward and the floor’s normal force is upward. If the elevator accelerates upward, then

$$N - mg = ma$$

Since $a > 0$, the normal force must be larger than weight. This explains why you feel heavier when an elevator starts moving upward.

Connecting Free-Body Diagrams to Translational Dynamics

Translational dynamics is the study of how forces affect straight-line motion. Free-body diagrams are the bridge between the physical situation and the math used to predict motion. They help explain why an object accelerates the way it does.

If the net force is zero,

$$\sum \vec{F} = 0$$

then the object is in equilibrium. It may be at rest, or it may move with constant velocity. If the net force is not zero, then the object accelerates in the direction of the net force.

This is why free-body diagrams are so important in AP Physics 1. They let you see whether forces are balanced and whether motion will change. In real life, this idea helps explain many situations:

A bicycle speeds up when the forward friction force from the road is greater than air resistance.
A parachute slows a skydiver because air resistance becomes very large.
A parked car stays still because the forces on it are balanced.

Common Mistakes to Avoid

Students often make a few predictable errors when drawing free-body diagrams. Watch out for these, students:

Drawing force arrows for motion instead of actual forces.
Including extra forces that do not exist.
Forgetting that weight is always downward near Earth.
Drawing the normal force straight up on a ramp instead of perpendicular to the surface.
Mixing up action-reaction pairs with forces on the same object.

Remember: action-reaction forces act on two different objects. If Earth pulls down on a book, the book pulls up on Earth. Those two forces are equal and opposite, but they do not cancel on the same object because they act on different objects.

Conclusion

Forces and free-body diagrams are essential tools in AP Physics 1 because they connect everyday situations to Newton’s laws. A force is a push or pull that can change motion, and a free-body diagram is a focused way to show all the forces on one object. When you can identify weight, normal force, tension, friction, and applied force, you can use $\sum \vec{F} = m\vec{a}$ to predict acceleration and understand motion. This topic is a major part of force and translational dynamics, so building strong diagram skills now will help you in many later physics problems 🚀

Study Notes

A force is a push or pull measured in newtons, $\text{N}$.
Forces are vectors, so direction matters.
The net force is written as $\sum \vec{F}$.
Newton’s second law is $\sum \vec{F} = m\vec{a}$.
Weight is the gravitational force: $F_g = mg$.
The normal force is a surface’s support force and is perpendicular to the surface.
Tension acts through ropes, strings, cables, and chains.
Friction opposes relative motion or attempted motion.
Static friction prevents slipping; kinetic friction acts during sliding.
A free-body diagram shows one object and all external forces on it.
Each force on a free-body diagram should be drawn as a labeled arrow.
If $\sum \vec{F} = 0$, the object is in equilibrium and has no acceleration.
If $\sum \vec{F} \neq 0$, the object accelerates in the direction of the net force.
Free-body diagrams are the starting point for solving many translational dynamics problems.