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Free Body Diagrams Reference cheat sheet - grade 9-12

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Physics Grade 9-12

Free Body Diagrams Reference Cheat Sheet

A printable reference covering free body diagrams, weight, normal force, friction, tension, drag, and Newton's second law for grades 9-12.

TopicsForcesNewton's LawsFrictionDragGravityVectorsPhysicsLabeled Diagram
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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 Fg=mgF_g = mg, where g≈9.8 m/s2g \approx 9.8\,\text{m/s}^2 near Earth's surface.
  • Newton's second law connects the net force to acceleration using ∑F=ma\sum F = ma in one dimension or ∑F⃗=ma⃗\sum \vec{F} = m\vec{a} as a vector equation.
  • On a horizontal surface with no vertical acceleration, the normal force often equals weight, so FN=Fg=mgF_N = F_g = mg.
  • Static friction can adjust up to a maximum value given by fs≤μsFNf_s \leq \mu_s F_N.
  • Kinetic friction has magnitude fk=μkFNf_k = \mu_k F_N and acts opposite the direction of sliding motion.
  • For an object on an incline, the weight components are Fg,∥=mgsin⁡θF_{g,\parallel} = mg\sin\theta down the slope and Fg,⊥=mgcos⁡θF_{g,\perp} = mg\cos\theta into the surface.
  • If the acceleration is zero, the net force is zero, so ∑Fx=0\sum F_x = 0 and ∑Fy=0\sum F_y = 0.

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 ∑F⃗\sum \vec{F}.
Weight
The gravitational force on an object, calculated by Fg=mgF_g = mg.
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 FF.
  • 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 FN=mgF_N = mg in every problem is wrong because the normal force changes on inclines, in elevators, and when other vertical forces act. Always use ∑Fy=may\sum F_y = ma_y 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 fsf_s or fkf_k.
  • Forgetting to split angled forces into components makes Newton's second law harder to apply. Use Fx=Fcos⁡θF_x = F\cos\theta and Fy=Fsin⁡θF_y = F\sin\theta when the angle is measured from the horizontal.

Practice Questions

  1. 1 A 12 kg12\,\text{kg} box rests on a level floor. Find its weight using g=9.8 m/s2g = 9.8\,\text{m/s}^2 and state the normal force if there is no vertical acceleration.
  2. 2 A 5.0 kg5.0\,\text{kg} block is pulled to the right by 30 N30\,\text{N} while kinetic friction is 8 N8\,\text{N} to the left. Find the net force and acceleration.
  3. 3 A 20 kg20\,\text{kg} cart is on a frictionless 25∘25^\circ incline. Find the component of gravity parallel to the slope using Fg,∥=mgsin⁡θF_{g,\parallel} = mg\sin\theta.
  4. 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.