#Buoyancy and Apparent Weight: Your Ultimate AP Physics 2 Guide 🚀

Hey there, future physicist! Let's dive into buoyancy and apparent weight – key topics for your AP Physics 2 exam. Think of this as your personal cheat sheet, designed to make everything click. Let's get started!

#Buoyancy: The Upward Push

Buoyancy is all about that upward force a fluid exerts on an object. It's like the fluid is trying to push the object back up! This force happens because pressure increases with depth, creating a net upward push.

• What causes it? Pressure difference! Higher pressure at the bottom of an object pushes it up. ⬆️

• Buoyant Force (Fb): This upward force is equal to the weight of the fluid displaced by the object. That's Archimedes' Principle in action! 💡

  

  Caption: An object submerged in water experiences an upward buoyant force equal to the weight of the water it displaces. 🌊

#Archimedes' Principle

Imagine you drop a baseball into a bucket of water. Some water spills out, right? The weight of that spilled water is exactly the buoyant force acting on the baseball. 🚣🏼‍♀️

Formula:

$$F_b = V_{object} \cdot \rho_{fluid} \cdot g$$

Where:

• $F_b$ = Buoyant Force
• $V_{object}$ = Volume of the object (or the volume of fluid displaced)
• $\rho_{fluid}$ = Density of the fluid
• $g$ = Acceleration due to gravity (approx. 9.8 m/s² or 10 m/s²)

#Example Problem

Let's calculate the net force on a box with a mass of 15 kg and a volume of 0.2 m³ when fully submerged in water:

1. Buoyant Force (Fb): $$F_b = (0.2 \text{ m}^3) \cdot (1000 \text{ kg/m}^3) \cdot (10 \text{ m/s}^2) = 2000 \text{ N}$$
2. Force of Gravity (Fg): $$F_g = (15 \text{ kg}) \cdot (10 \text{ m/s}^2) = 150 \text{ N}$$
3. Net Force (Fnet): $$F_{net} = F_b - F_g = 2000 \text{ N} - 150 \text{ N} = 1850 \text{ N}$$

So, the net upward force is 1850 N. The box will accelerate upwards!

Fun Fact: Archimedes used buoyancy to expose a fraud! He figured out that a king's crown wasn't pure gold by measuring its buoyant force. 👑

#Apparent Weight: How Heavy Feels

Apparent weight is how heavy an object feels when submerged in a fluid. It's not the object's actual weight, but the net force you experience when trying to lift it. Think about lifting someone in a pool – it feels lighter, right? That's because the buoyant force helps you out! 😝

• What is it? The force an object exerts on a scale or measuring device while in a fluid.

• Why does it change? The buoyant force counteracts gravity, making the object feel lighter.

  

  Caption: The apparent weight of an object in a fluid is less than its actual weight due to the upward buoyant force. 🏋️

#Calculating Apparent Weight

The apparent weight ($W_a$) is the difference between the object's true weight ($F_g$) and the buoyant force ($F_b$):

$$W_a = F_g - F_b$$

Where:

• $W_a$ = Apparent Weight
• $F_g$ = True Weight (mass × gravity)
• $F_b$ = Buoyant Force

Key Points About Apparent Weight:

• If $F_b > F_g$, the object floats and has an apparent weight of zero (or is pushed upwards).
• If $F_b < F_g$, the object sinks, and its apparent weight is less than its true weight.
• If $F_b = F_g$, the object is neutrally buoyant, and its apparent weight is zero.

#Connections Between Buoyancy and Other Units

• Fluids: Buoyancy is a direct application of fluid mechanics. Understanding pressure and density is crucial.
• Forces: Buoyant force is a force, so remember Newton's laws. Net force determines acceleration. 💡
• Density: Density plays a key role in both buoyant force and whether an object floats or sinks. Remember that density is mass per unit volume ($\rho = \frac{m}{V}$).

#Final Exam Focus

• High-Priority Topics:
  • Archimedes' Principle and its applications.
  • Calculating buoyant force using density, volume, and gravity.
  • Distinguishing between true weight and apparent weight.
  • Understanding the conditions for floating, sinking, and neutral buoyancy.
• Common Question Types:
  • Multiple-choice questions testing your understanding of the concepts.
  • Free-response questions involving calculations of buoyant force and apparent weight. Often combine buoyancy with other topics like forces and fluids.
  • Conceptual questions asking you to explain why objects float or sink.
• Last-Minute Tips:
  • Time Management: Quickly identify the core concepts in each question. Don't get bogged down in complex calculations if you can get the answer conceptually.
  • Common Pitfalls: Be careful with units! Make sure everything is in SI units (kg, m, s). Don't forget to consider the direction of the forces.
  • Strategies: Draw free-body diagrams to visualize the forces acting on an object. This helps in solving complex problems. 📝

Practice Question

#Practice Questions

#Multiple Choice Questions

1. A block of wood with a volume of 0.1 m³ and a density of 700 kg/m³ is placed in water (density 1000 kg/m³). What is the buoyant force on the block? (A) 100 N (B) 700 N (C) 980 N (D) 1000 N

2. A 2 kg object is submerged in a fluid. If the buoyant force on the object is 15 N, what is the apparent weight of the object? (A) 5 N (B) 15 N (C) 20 N (D) 35 N

3. A boat floats in water. Which of the following statements is true? (A) The weight of the boat is greater than the buoyant force. (B) The weight of the boat is less than the buoyant force. (C) The weight of the boat is equal to the buoyant force. (D) The buoyant force is zero.

#Free Response Question

A solid metal sphere of mass 5 kg and volume 0.002 m³ is suspended from a string and then completely submerged in a liquid of unknown density. The tension in the string is measured to be 30 N.

(a) Calculate the weight of the sphere in air. (b) Calculate the buoyant force on the sphere when it is submerged in the liquid. (c) Calculate the density of the liquid. (d) If the sphere is released from the string, will it sink or float? Explain your answer.

Scoring Rubric:

(a) (2 points) * 1 point for correct formula ($F_g = mg$) * 1 point for correct answer: $F_g = (5 \text{ kg})(10 \text{ m/s}^2) = 50 \text{ N}$

(b) (2 points) * 1 point for correct concept (Tension + Buoyant Force = Weight) * 1 point for correct answer: $F_b = 50 \text{ N} - 30 \text{ N} = 20 \text{ N}$

(c) (3 points) * 1 point for using the correct formula $F_b = V \rho g$ * 1 point for correct substitution: $20 \text{ N} = (0.002 \text{ m}^3) \cdot \rho \cdot (10 \text{ m/s}^2)$ * 1 point for correct answer: $\rho = 1000 \text{ kg/m}^3$

(d) (2 points) * 1 point for stating it will sink * 1 point for correct explanation: The buoyant force (20 N) is less than the weight (50 N), so it will sink.