2.2 Forces and Free-Body Diagrams

A force is a push or pull that comes from one object interacting with another, and it is a vector, so it has both size and direction. A free-body diagram shows every external force acting on one chosen object as arrows starting from a single dot, which helps you connect the physical situation to Newton's laws.

Almost every force, energy, and momentum problem starts with choosing an object, drawing its forces, and finding the net force, and a wrong diagram makes all the math after it wrong too. The Qualitative/Quantitative Translation question in the free-response section asks you to make a claim with reasoning, derive equations, and connect the two, which is the same switch between description, diagram, and algebra.

External Forces on One Object Set the Net Force

• A force is always an interaction between two objects, and no object can exert a net force on itself.
• Contact forces (like normal force and friction) come from objects touching, and are large-scale effects of interatomic electric forces.
• A free-body diagram shows only the external forces acting on one chosen object, drawn as straight arrows from a center-of-mass dot.
• Each force gets its own arrow; forces pointing the same way are drawn side by side, not stacked or overlapping.
• The net force is the vector sum of all forces on the object, and it controls how the object accelerates.
• Picking a coordinate axis along the direction of acceleration (for example, parallel to an incline) makes the algebra much cleaner.

Forces as Interactions

A force is just a push or a pull, but the key idea is that it always involves two objects. A force exerted on an object is always due to its interaction with another object or system. Because of this, an object cannot exert a net force on itself.

Forces are vector quantities, so each one has both magnitude (how strong) and direction (which way). You can represent a force with an arrow, where a longer arrow means a larger magnitude.

Contact Forces

Contact forces happen when one object physically touches another. On a large scale they look like simple pushes and rubs, but they actually come from interatomic electric forces between the surfaces. Common contact forces you will see on diagrams include:

• Normal force (N): exerted by a surface on an object, always perpendicular to the surface and pointing away from it.
• Friction (f): acts parallel to the surface and opposes relative motion or the tendency to move.
• Tension (T): the pull transmitted through a rope, string, or cable.
• Applied force (F_app): a direct push or pull from a person or another object.

Gravity is different because it acts at a distance rather than through contact. In AP Physics 1, the only at-a-distance force you will diagram is the gravitational force (weight), which points downward toward Earth.

Free-Body Diagrams

A free-body diagram is a tool for visualizing every force acting on one single object or system. It strips away everything else so you can see the forces clearly and write the equations that match the situation.

What Goes on the Diagram

• Pick one object or system to analyze. This choice is what defines which forces count.
• Show only the forces exerted on that object by the environment. Forces the object exerts on other things do not belong on its diagram.
• Represent the object as a dot at its center of mass. The system is treated as though all its mass sits at that point.
• Draw each force as a straight arrow that starts on the dot and points in the direction of the force.

Typical forces from the environment include the gravitational force (weight) pointing down, the normal force perpendicular to a surface, tension along a rope, applied pushes or pulls, and friction parallel to a surface.

Drawing Rules That Match the Exam

On AP Physics exams, free-body diagrams follow specific rules:

• Draw individual forces as individual straight arrows originating on the dot.
• Forces in the same direction must be drawn side by side, not overlapping.
• Do not draw force components on the diagram itself. You are expected to show the actual forces, not their x and y pieces.

Breaking a force into components is an algebra step you do after the diagram, not something you put on the picture.

Choosing a Coordinate System

A smart coordinate choice makes the math easier. Set one axis parallel to the direction of the object's acceleration. For an object on a ramp, that means tilting your axes so one axis runs parallel to the surface of the incline and the other runs perpendicular to it. This way the acceleration lies along a single axis instead of being split across both.

Finding the Net Force

Once your diagram is complete, the net force is the vector sum of all the forces on the object. Forces that point the same way add; forces that point opposite ways subtract. Then you can connect the net force to motion using Newton's second law, $\vec{F}_{net} = m\vec{a}$ (covered fully in Topic 2.5).

Drawing Force Diagrams and Writing Net Force Equations

Free Response: When a question hands you a scenario, your first move is almost always to draw a clean free-body diagram for the object named in the prompt. Use the exam drawing rules: arrows from a dot, one arrow per force, same-direction forces side by side. Then translate the diagram into a net force equation along the axis of acceleration.

Problem Solving:

1. Choose your object and draw the dot.
2. Add only the external forces acting on that object.
3. Pick axes, ideally with one axis along the acceleration.
4. Write the net force in each direction by adding the vectors.
5. Connect net force to acceleration when the problem asks for motion.

Common Trap: Reading a force "from the wrong side." If the question asks about the box, draw forces on the box. Do not include the force the box exerts on the floor or on a hand, since those act on other objects.

Worked Example

A 10 kg box is pushed across a floor. A person applies 50 N to the right, and the floor exerts 30 N of friction to the left.

1. Draw a free-body diagram showing every force on the box.
2. Find the net force.
3. Use Newton's second law to find the acceleration.

Solution

1. Four forces act on the box: a 50 N applied force to the right, a 30 N friction force to the left, the gravitational force (weight) downward, and the normal force upward. Each is a straight arrow from the dot.
2. Horizontally, $F_{net,x} = 50\,\text{N} - 30\,\text{N} = 20\,\text{N}$ to the right. Vertically the weight and normal force balance, so $F_{net,y} = 0$.
3. Using $F_{net,x} = ma$: $20\,\text{N} = (10\,\text{kg})(a)$, so $a = 2\ \text{m/s}^2$ to the right.

Notice how the vertical forces canceling tells you the motion is purely horizontal, which is why choosing horizontal and vertical axes worked cleanly here.

Common Misconceptions

• Misconception: An object can push itself forward.
  Actually: No object can exert a net force on itself. Every force on your diagram comes from another object.
• Misconception: Put both action and reaction forces on one diagram.
  Actually: A free-body diagram shows forces on one object only. Paired interaction forces act on two different objects, so they never appear together on the same diagram.
• Misconception: Normal force always equals weight.
  Actually: Normal force is whatever the surface pushes back with, perpendicular to that surface. On an incline or when something is accelerating vertically, it does not equal $mg$.
• Misconception: Draw the x and y components on the diagram.
  Actually: Components are an algebra step. The diagram itself should show the real forces as straight arrows, not their split-up pieces.
• Misconception: Friction always points backward along motion.
  Actually: Friction opposes relative motion or the tendency to move, so its direction depends on the situation, not on a fixed rule.
• Misconception: A bigger object always has a bigger normal force arrow.
  Actually: Arrow length should match force magnitude, and normal force depends on the full force balance perpendicular to the surface, not just on size.

Related AP Physics 1 Guides

• 2.1 Systems and Center of Mass
• 2.3 Newton's Third Law
• 2.4 Newton's First Law
• 2.5 Newton's Second Law
• 2.6 Gravitational Force
• 2.7 Kinetic and Static Friction