Free body diagrams show all external forces acting on one chosen object. Students need this reference because clear force diagrams are the first step in solving most Newton's laws problems. A good diagram helps separate real forces from motion, velocity, or acceleration, which are not forces.
This cheat sheet summarizes the forces, labels, and setup steps used in grades 9-12 physics.
Key Facts
- A free body diagram shows only the external forces acting on one object, with each force drawn as an arrow starting at the object.
- Weight is the gravitational force on an object and is calculated by , where near Earth's surface.
- Newton's second law connects the net force to acceleration using in one dimension or as a vector equation.
- On a horizontal surface with no vertical acceleration, the normal force often equals weight, so .
- Static friction can adjust up to a maximum value given by .
- Kinetic friction has magnitude and acts opposite the direction of sliding motion.
- For an object on an incline, the weight components are down the slope and into the surface.
- If the acceleration is zero, the net force is zero, so and .
Vocabulary
- Free Body Diagram
- A drawing that represents one object as a point or simple shape and shows all external forces acting on it.
- Net Force
- The vector sum of all forces on an object, written as .
- Weight
- The gravitational force on an object, calculated by .
- Normal Force
- A contact force exerted by a surface perpendicular to that surface.
- Friction
- A contact force that opposes sliding or the tendency to slide between two surfaces.
- Tension
- A pulling force transmitted through a string, rope, cable, or chain.
Common Mistakes to Avoid
- Drawing velocity or acceleration as forces is wrong because a free body diagram includes forces only. Show acceleration separately if needed, but do not label it as .
- Including forces the object exerts on other objects is wrong because the diagram should show only forces acting on the chosen object. Action-reaction pairs act on different objects.
- Assuming in every problem is wrong because the normal force changes on inclines, in elevators, and when other vertical forces act. Always use to check.
- Pointing friction in the same direction as motion is often wrong because friction opposes relative sliding or the tendency to slide. Decide the likely slipping direction before drawing or .
- Forgetting to split angled forces into components makes Newton's second law harder to apply. Use and when the angle is measured from the horizontal.
Practice Questions
- 1 A box rests on a level floor. Find its weight using and state the normal force if there is no vertical acceleration.
- 2 A block is pulled to the right by while kinetic friction is to the left. Find the net force and acceleration.
- 3 A cart is on a frictionless incline. Find the component of gravity parallel to the slope using .
- 4 A book sits at rest on a table. Explain why the normal force and weight are equal in magnitude but are not a Newton's third law action-reaction pair.
Understanding Free Body Diagrams Reference
A force diagram is really an inventory of interactions. Each arrow must have a physical source. Earth pulls an object downward.
A table pushes upward on an object touching it. A rope pulls along its length. A wall can push sideways.
This source check prevents invented arrows. For example, a box moving to the right does not receive a rightward force just because it moves right. If nobody pushes or pulls it horizontally and friction is absent, it can keep moving right at constant speed.
Motion describes what the object does. Forces explain changes in motion.
Start by choosing the object with care. In a problem about two blocks tied by a string, draw one diagram for each block if you need to find the tension or contact force. The force that one block exerts on the other belongs on the receiving block's diagram.
Newton's third law pairs act on different objects, so they never cancel within a single diagram. A book pushes down on a table, while the table pushes up on the book.
Those forces are equal in size when appropriate, but only the upward force belongs on a diagram of the book. This distinction is one of the most useful habits in mechanics.
Choose coordinate directions that make the calculation simpler. On level ground, horizontal and vertical axes usually work well. On a ramp, use one axis parallel to the surface and one perpendicular to it.
Then resolve weight into two parts before writing the force equations. The part down the ramp tends to produce sliding. The part into the ramp affects the normal force.
A normal force is not always equal to weight. It changes when an object is on a slope, when someone pushes down on it, or when an elevator accelerates. The word normal means perpendicular to a surface, not ordinary or constant.
Friction requires especially careful thinking. Static friction appears when surfaces do not slide relative to each other. It takes only the amount needed to prevent slipping, up to its maximum possible value.
Therefore, do not automatically use the maximum static friction in every problem. A parked car on a gentle hill may need a small friction force. Kinetic friction applies after sliding begins and is often treated as constant in school problems.
Its direction opposes the relative sliding tendency between surfaces. This is why friction can point up a ramp even when an object is not yet moving.
After drawing the forces, add them separately along each chosen axis. The net force in an axis gives mass times acceleration in that axis. A zero net force means zero acceleration, not necessarily zero speed.
This explains steady driving, skydiving at terminal speed, and a laptop resting on a desk. Check units in newtons, check arrow directions, and keep unknown forces as symbols until the equations are set up. A clean diagram often reveals whether an answer makes physical sense before any arithmetic is done.