🧠 Force vs Displacement: Understanding the Relationship in Physics

MCAT Physics
Written By Heath Rutledge-Jukes

A force vs displacement graph illustrates how force changes as an object moves. It helps in understanding work done, energy transfer, and system behavior.

🧠 Force vs Displacement: Understanding the Relationship in Physics

⚙️ Key Features of the Graph

1. Constant Force Region (0–20 m)

  • Force remains constant at 100 N

  • Indicates uniform force application

  • Work increases linearly

2. Critical Displacement (20 m)

  • Turning point in the system

  • Marks change in force behavior

3. Decreasing Force Region (20–30 m)

  • Force decreases from 100 N to 0 N

  • Indicates resistance or release of force

📋 Summary Table

Region Displacement Range Force Behavior Work Contribution Interpretation
Constant Region 0 – 20 m Constant (100 N) High (2000 J) Steady applied force
Critical Point 20 m Transition — Change in system behavior
Decreasing Region 20 – 30 m Linearly decreasing Moderate (500 J) Resistance or relaxation
Final Point 30 m Zero force — No further work

📐 Work Done Calculation

Work Done Table
Section Shape Formula Work Done
0–20 m Rectangle F × d 100 × 20 = 2000 J
20–30 m Triangle ½ × base × height ½ × 10 × 100 = 500 J
Total — — 2500 J

🧠 Physical Interpretation

This graph can represent:

  • Stretching a spring

  • Mechanical systems reaching limits

  • Gradual loss of applied force

📉 Why It Matters

Understanding this graph helps in:

  • Calculating work and energy

  • Designing engineering systems

  • Studying material response

📌 Key Takeaways

  • Force is constant up to 20 m

  • After that, it decreases linearly

  • Total work done = 2500 J

  • Area under graph = energy transferred

 

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Heath Rutledge-Jukes