18. Free Body Diagrams & Resultant Forces

1. What is a Free Body Diagram?

• Definition: A simple diagram used to show all the forces acting on a single, isolated object.

• Force Arrows: Each force is represented by an arrow.

  • Direction: The way the arrow points shows the direction of the force.

  • Magnitude: The length of the arrow (and its label in Newtons) represents the size of the force.

• Example (Plane): A plane in flight would have arrows for Thrust (forwards), Drag/Air Resistance (backwards), Lift (upwards), and Weight (downwards).

2. Calculating Resultant Force

• Definition: The Resultant Force is the single, overall force that remains after all forces acting on an object have been added together or canceled out.

• Method: Analyze horizontal and vertical forces separately.

Step-by-Step Calculation (Using a Plane Example):

1. Vertical Component: If the Lift is 80,000 N up and the Weight is 80,000 N down, they cancel each other out ($80,000 - 80,000 = 0$ N).

2. Horizontal Component: If the Thrust is 120,000 N right and Drag is 90,000 N left, you subtract the smaller force from the larger ($120,000 - 90,000 = 30,000$ N).

3. Result: The overall resultant force is 30,000 N to the right.

3. Equilibrium

• Definition: An object is in equilibrium when the resultant force acting on it is zero.

• Condition: This happens when all horizontal forces are balanced and all vertical forces are balanced.

• Physical State: An object in equilibrium is either stationary or moving at a constant velocity (it is not accelerating).

4. Summary Table