Fluids and Free-Body Diagrams

Free-body diagrams (FBDs) are essential tools for solving physics problems, especially in fluid mechanics. Let's break down how to use them effectively for AP Physics 2!

Key Forces in Fluid FBDs

In AP Physics 2, you'll encounter these forces frequently when dealing with fluids:

• Weight (W or Fg): The force of gravity acting on an object. Always points downwards.
• Buoyant Force (Fb): The upward force exerted by a fluid on an object. Crucial for understanding floating and sinking. See more in Buoyancy.
• Normal Force (N): A contact force exerted by a surface on an object. Only present when an object is resting on a surface, like the bottom of a container.
• Resistive Force (Fr): A force that opposes motion through a fluid. Increases with the object's velocity. Often called drag force.

Here’s a step-by-step guide to drawing FBDs for fluid problems:

1. Identify the Object: Determine the object you are analyzing.
2. List the Forces: Identify all forces acting on the object (weight, buoyant, normal, resistive).
3. Draw the Object: Represent the object with a simple shape (often a dot or a horizontal line).
4. Draw Force Vectors: Draw arrows representing each force, pointing in the correct direction. The length of the arrow should be proportional to the force's magnitude.
5. Label Vectors: Label each force vector with its symbol (e.g., W, Fb, N, Fr).
6. Add Annotations: Include any relevant information, such as fluid density or object volume.
7. Check for Accuracy: Ensure all forces are included and that the diagram reflects the scenario.

FBD Examples

Let’s look at some common scenarios:

🟦Object Floating in Water

• Forces: Weight (W) downwards, Buoyant Force (Fb) upwards.
• Net Force: Zero (object is in equilibrium).

🟨Object Sinking in Water

• Forces: Weight (W) downwards, Buoyant Force (Fb) upwards, Resistive Force (Fr) upwards.
• Net Force: Non-zero (object is accelerating downwards until terminal velocity).

🟪Object Sunk to the Bottom

• Forces: Weight (W) downwards, Buoyant Force (Fb) upwards, Normal Force (N) upwards.
• Net Force: Zero (object is in equilibrium).

• Always start with an FBD: It helps visualize the forces and set up equations.
• Relate FBDs to Newton's Laws: Use ΣF = ma to analyze forces and motion.
• Be consistent with directions: Choose a positive direction and stick with it.

• Forgetting forces: Always account for all relevant forces, including buoyant and resistive forces.
• Incorrect directions: Make sure force vectors point in the correct direction.
• Confusing normal and buoyant forces: Normal force is a contact force; buoyant force is due to fluid displacement.
• Assuming zero resistive force: Resistive force is often significant in fluids; don’t ignore it.

We Believe Nice Rabbits! (Helps remember the forces: Weight, Buoyant, Normal, Resistive)

Practice Question

Practice Questions

Multiple Choice Questions

1. A block is submerged in water and is sinking at a constant velocity. Which of the following is true about the forces acting on the block? (A) The buoyant force is equal to the weight of the block. (B) The buoyant force is greater than the weight of the block. (C) The buoyant force is less than the weight of the block, and the resistive force is equal to the difference between the weight and buoyant force. (D) The buoyant force is less than the weight of the block, and the resistive force is zero.

2. A ball is floating at the surface of a liquid. Which forces are acting on the ball? (A) Only the weight of the ball. (B) Only the buoyant force. (C) The weight of the ball and the buoyant force. (D) The weight of the ball, the buoyant force, and the normal force.

Free Response Question

A small, solid metal sphere of mass m and radius r is released from rest at the surface of a large container of viscous fluid with density ρf. The sphere experiences a buoyant force Fb and a resistive force Fr given by Fr = bv, where v is the velocity of the sphere and b is a constant. Assume the sphere is dense enough to sink.

(a) Draw a free-body diagram of the sphere as it sinks through the fluid. Label all forces.

(b) Derive an expression for the terminal velocity vt of the sphere in terms of m, g, ρf, r, and b.

(c) If the sphere were replaced with a larger sphere of the same material, how would the terminal velocity change? Explain your reasoning.

Answer Key

Multiple Choice

1. (C) The buoyant force is less than the weight of the block, and the resistive force is equal to the difference between the weight and buoyant force.
2. (C) The weight of the ball and the buoyant force.

Free Response Question

(a) Free-body diagram should include:

• Weight (W = mg) acting downwards [1 point]
• Buoyant force (Fb) acting upwards [1 point]
• Resistive force (Fr) acting upwards [1 point]

(b) Derivation of terminal velocity:

• At terminal velocity, the net force is zero: ΣF = 0 [1 point]
• mg - Fb - bv = 0 [1 point]
• Fb = ρfVg = ρf(4/3πr³)g [1 point]
• mg - ρf(4/3πr³)g - bvt = 0 [1 point]
• vt = (mg - ρf(4/3πr³)g) / b [2 points]

(c) Effect of larger sphere:

• A larger sphere will have a greater mass and volume. [1 point]
• Since the buoyant force increases with volume and the weight increases with mass, the difference between the weight and buoyant force will increase.
• As a result, the terminal velocity will increase. [2 points]

Final Exam Focus

• Master FBDs: They are the foundation for solving fluid problems. Always start with a clear and accurate FBD.
• Understand Buoyancy: Know how to calculate buoyant force and relate it to density and volume. Buoyancy
• Apply Newton's Laws: Use ΣF = ma to analyze forces and motion in fluid scenarios.
• Practice, Practice, Practice: Solve a variety of problems involving different fluid scenarios to build confidence.

With a clear understanding of these concepts and practice, you'll be well-prepared for the AP Physics 2 exam! You've got this! 💪