AP Physics – Free-Body Diagrams and Net Force

AP Physics – Free?Body Diagrams and Net Force

AP Physics: Free-Body Diagrams and Net Force – Exam-Ready Study Guide

What This Is

A free-body diagram (FBD) is a simple sketch that shows all the forces acting on a single object. The net force is the vector sum of those forces, and it determines the object’s acceleration (via Newton’s Second Law, F = ma). This topic is essential on the AP exam—you’ll see it in multiple-choice questions, FRQs, and even lab-based problems. Real-world example: When you push a stalled car, the forces acting on it (your push, friction, gravity, and the normal force from the road) combine to determine whether it moves. If the net force is zero, the car stays stuck; if not, it accelerates.

Key Terms & Concepts

• Force (F): A push or pull on an object, measured in newtons (N). Forces are vectors (have magnitude and direction).
• Free-Body Diagram (FBD): A diagram isolating one object and showing all forces acting on it as arrows (vectors) pointing in their direction.
• Net Force (F_net): The vector sum of all forces acting on an object. If F_net = 0, the object is in equilibrium (no acceleration).
• Newton’s First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion at constant velocity unless acted on by a net force.
• Newton’s Second Law: F_net = m·a (Net force = mass × acceleration). Key: Acceleration is in the same direction as F_net.
• Newton’s Third Law: For every action force, there’s an equal and opposite reaction force. Important: These forces act on different objects (e.g., you push the wall, the wall pushes you).
• Weight (F_g): The force of gravity on an object. F_g = m·g (where g = 9.8 m/s² on Earth).
• Normal Force (F_N): The perpendicular force a surface exerts to support an object. Not always equal to weight! (e.g., on an incline or in an elevator).
• Friction (F_f): A force opposing motion. F_f = ?·F_N (where ? = coefficient of friction).
• Tension (F_T): The pulling force exerted by a rope, string, or cable. Assumed massless unless stated otherwise.
• Equilibrium: When F_net = 0 (object is at rest or moving at constant velocity).
• Inclined Plane: A ramp where forces are resolved into components parallel (F_? = m·g·sin?) and perpendicular (F_? = m·g·cos?) to the surface.

Step-by-Step: Solving Net Force Problems

1. Identify the object of interest and draw a free-body diagram (FBD).
2. Isolate the object and sketch all forces acting on it (e.g., gravity, normal force, friction, tension, applied forces).

3. Label each force with its type (e.g., F_g, F_N, F_f) and direction.

4. Choose a coordinate system.

5. For flat surfaces: Use x (horizontal) and y (vertical).

6. For inclines: Align x parallel to the ramp and y perpendicular to it.

7. Resolve forces into components (if needed).

8. Break angled forces (e.g., tension at an angle) into x and y components using trigonometry (F_x = F·cos?, F_y = F·sin?).

9. Write equations for net force.

10. Sum forces in x and y directions separately:
    • ?F_x = m·a_x
    • ?F_y = m·a_y

11. If the object is in equilibrium (a = 0), set ?F = 0 in both directions.

12. Solve for the unknown.

13. Use algebra to find the missing force, acceleration, or mass.

14. Check units: Forces in N, mass in kg, acceleration in m/s².

15. Interpret the result.

16. Does the answer make sense? (e.g., friction can’t exceed ?·F_N, tension can’t be negative).

Common Mistakes

• Mistake: Forgetting to include all forces in the FBD (e.g., omitting normal force or friction). Correction: Always ask: What is touching the object? (surfaces, ropes) and What forces act at a distance? (gravity, magnetism).

• Mistake: Assuming F_N = F_g in all cases (e.g., on an incline or in an accelerating elevator). Correction: F_N only equals F_g on a flat, non-accelerating surface. On an incline, F_N = m·g·cos?.

• Mistake: Mixing up action-reaction pairs (Newton’s Third Law) with net force. Correction: Action-reaction pairs act on different objects (e.g., Earth pulls you down, you pull Earth up). Net force is the sum of forces on one object.

• Mistake: Ignoring direction when adding forces (e.g., treating leftward and rightward forces as positive). Correction: Assign a sign convention (e.g., right/up = positive, left/down = negative) and stick to it.

• Mistake: Using F = ma when F_net = 0 (equilibrium). Correction: If F_net = 0, a = 0 (object is at rest or moving at constant velocity).

AP Exam Insights

• FRQs often test FBDs + net force in multi-part questions (e.g., a block on an incline with friction, or a system of masses connected by strings).
• Tricky distinction: F_net vs. individual forces. The AP exam loves asking, “What is the net force?”—not just “What forces act on the object?”
• Inclined planes are a favorite. Remember: F_? = m·g·sin? (parallel to ramp) and F_? = m·g·cos? (perpendicular to ramp).
• Multiple-choice traps:
• Forces that don’t belong in the FBD (e.g., the force the object exerts on another object).
• Forgetting to resolve forces into components (e.g., tension at an angle).
• Misapplying F = ma when a = 0 (equilibrium).

Quick Check Questions

1. Multiple Choice: A 5 kg block is at rest on a horizontal surface. What is the normal force acting on the block? A) 0 N B) 5 N C) 49 N D) 98 N Answer: C) 49 N. The normal force balances the weight (F_g = m·g = 5 kg × 9.8 m/s² = 49 N).

2. Short FRQ: A 10 kg box is pulled to the right with a force of 50 N, while a 20 N frictional force acts to the left. Draw a free-body diagram and calculate the acceleration of the box. Answer: F_net = 50 N – 20 N = 30 N (right). a = F_net/m = 30 N / 10 kg = 3 m/s² (right).

3. Multiple Choice: A 2 kg object is in free fall near Earth’s surface. What is the net force acting on it? A) 0 N B) 2 N C) 19.6 N D) 9.8 N Answer: C) 19.6 N. Only gravity acts (F_g = m·g = 2 kg × 9.8 m/s² = 19.6 N), so F_net = F_g.

Last-Minute Cram Sheet

1. FBD = isolate object + all forces as arrows (label types: F_g, F_N, F_f, F_T, etc.).
2. F_net = ?F (vector sum; direction matters!).
3. F_net = m·a (Newton’s Second Law; a is in the direction of F_net).
4. Equilibrium = F_net = 0 (object at rest or constant velocity).
5. F_g = m·g (weight; g = 9.8 m/s² on Earth).
6. F_N = m·g·cos? on an incline (not always equal to F_g!).
7. F_f = ?·F_N (friction; ? = coefficient of friction).
8. Action-reaction pairs act on different objects (Newton’s Third Law).
9. On inclines: F_? = m·g·sin? (parallel), F_? = m·g·cos? (perpendicular).
10. Tension is the same throughout a massless rope (even over pulleys!).