1.4 Fluids and Free-Body Diagrams

1.4 Fluids and Free-Body Diagrams

Fluids and Free-Body Diagrams (FBDs)

Free-Body Diagrams (FBDs) are an essential tool in physics, offering a visual way to analyze forces acting on an object. In AP Physics 2, FBDs are just as vital as in Physics 1, but here they are often used to solve complex problems or explain scenarios in more depth. Let’s explore how FBDs apply to fluid mechanics.

Key Forces in Fluid FBDs

1. Gravitational Force (Weight):

   • Acts downward due to gravity.

   • Denoted as or .

2. Buoyant Force:

   • Acts upward, opposing gravity.

   • Present when an object is submerged in or floating on a fluid.

3. Normal Force:

   • Acts upward but only when the object is in contact with a solid surface (e.g., the bottom of the fluid container).

4. Resistive Force (Drag):

   • Acts opposite to the direction of motion.

   • Depends on the object’s velocity in the fluid. If the object is stationary, this force is zero.

FBD Scenarios in Fluids

1. Floating Object (🟦 Blue):

• Forces:

  • Gravitational Force (Weight)

  • Buoyant Force

• The object’s weight is balanced by the buoyant force, resulting in equilibrium.

2. Sinking Object (🟨 Yellow):

• Forces:

  • Gravitational Force (Weight)

  • Buoyant Force

  • Resistive Force (Drag)

• The object accelerates downward but is slowed by the resistive force.

3. Object at the Bottom (🟪 Pink):

• Forces:

  • Gravitational Force (Weight)

  • Buoyant Force

  • Normal Force

• The normal force balances the net downward force, keeping the object stationary.

Steps to Draw an FBD for Fluid Problems

1. Identify the Object:

   • Determine the object for which the FBD is being created.

2. Identify the Forces:

   • Consider all relevant forces, such as weight, buoyant force, drag, or normal force.

3. Draw the Object:

   • Represent the object with a reference point or line.

4. Add Force Vectors:

   • Draw arrows representing each force. Ensure the length of the arrows corresponds to the magnitude of the forces.

5. Label the Forces:

   • Use symbols (e.g., , ) and, if possible, include magnitudes.

6. Include Annotations:

   • Add details such as fluid density or object volume, if necessary.

7. Verify the FBD:

   • Ensure all forces are accounted for and check if forces are balanced for equilibrium scenarios.

Tips for Success

• Buoyant Force: Always acts upward and is proportional to the displaced fluid’s weight.

• Normal Force: Only appears when contact with a surface exists.

• Resistive Force: Increases with velocity and is negligible for stationary objects.

• Balance Forces: For equilibrium, the sum of forces must be zero.