AP Physics B - 2013 #1 (Fluids - Bouyancy)
TLDRThis script from a 2013 AP Physics B exam video discusses a fluid physics problem involving a sailboat and an anchor. It emphasizes the importance of accurate free body diagrams for calculating forces acting on the anchor submerged in water. The video guides through calculating buoyant force using Archimedes' principle and determining the tension in the rope using Newton's Second Law. It concludes with the effect on the boat's depth when the anchor is brought on board, illustrating changes in buoyant force and equilibrium.
Takeaways
- 📝 The problem involves a sailboat with an anchor suspended 4 meters below water, focusing on fluid physics.
- ⚖️ The mass of the anchor is 50 kg, and its volume and the density of water are provided.
- 🖍️ A free body diagram for the anchor includes buoyant force (upward), weight (downward), and tension (upward).
- 📐 Correctly drawing the free body diagram earns three out of ten points.
- 💡 Buoyant force (B) is calculated using the formula B = ρVg.
- 🌊 The density of water is 1000 kg/m³, the volume of the anchor is 6.25 x 10^-3 m³, and g (gravity) is taken as 10 m/s².
- 🔢 The buoyant force acting on the anchor is calculated to be 62.5 Newtons.
- 🪢 The tension in the rope is found by applying Newton's Second Law and considering the anchor's equilibrium.
- ⚖️ The net force on the anchor is zero, resulting in a calculated tension of 437.5 Newtons.
- ⛵ Lifting the anchor back into the boat increases the boat's weight, causing it to sink deeper to maintain equilibrium.
Q & A
What is the context of the problem discussed in the transcript?
-The problem is from the 2013 AP Physics B exam and involves a fluid physics scenario with a sailboat, an anchor, and the forces acting on the anchor underwater.
What forces act on the anchor when it is submerged underwater?
-The forces acting on the submerged anchor are the buoyant force (upward), the gravitational force or weight (downward), and the tension from the rope (upward).
How do you calculate the buoyant force acting on the anchor?
-The buoyant force is calculated using the equation F_b = ρVg, where ρ is the density of the fluid (water), V is the volume of the displaced fluid (volume of the anchor), and g is the acceleration due to gravity.
What values are used in the calculation of the buoyant force in the transcript?
-The density of water is 1000 kg/m^3, the volume of the anchor is 6.25 x 10^-3 m^3, and the acceleration due to gravity is taken as 10 m/s^2.
What is the calculated buoyant force on the anchor using the given values?
-The calculated buoyant force is 62.5 Newtons.
How is the tension in the rope supporting the anchor determined?
-The tension in the rope is determined by applying Newton's Second Law and considering that the net force on the anchor is zero since it is not accelerating. The tension is calculated as T = mg - F_b, where mg is the weight of the anchor and F_b is the buoyant force.
What is the calculated tension in the rope?
-The calculated tension in the rope is 437.5 Newtons.
What happens to the boat’s depth in the water when the anchor is lifted back into the boat?
-When the anchor is lifted back into the boat, the boat's depth in the water increases because the boat's weight increases, requiring more buoyant force to stay in equilibrium. This means the boat displaces more water and sinks deeper.
How many points are allocated to each part of the problem in the AP Physics B exam?
-The free body diagram (part A) is worth 3 points, the calculation of the buoyant force (part B) is worth 2 points, the calculation of the tension (part C) is worth 3 points, and the explanation of the boat’s depth change (part D) is worth 2 points.
What is the significance of drawing the free body diagram accurately in part A?
-Drawing the free body diagram accurately is important because it is worth 3 points, and any extra or incorrect forces included in the diagram can result in losing points. It helps in visualizing and correctly identifying the forces acting on the anchor.
Outlines
⚓️ Fluid Physics Problem from 2013 AP Physics B Exam
This paragraph introduces a fluid physics problem from the 2013 AP Physics B exam, worth 10 points. It involves a sailboat with an anchor submerged in water. The problem requires drawing a free body diagram of the forces acting on the anchor, including the buoyant force, weight due to gravity, and tension from the supporting rope. Emphasis is placed on accurately representing the forces to earn points, with penalties for inaccuracies.
📐 Calculating the Buoyant Force
In this section, the magnitude of the buoyant force acting on the submerged anchor is calculated using the equation ρVg, where ρ is the density of water, V is the volume of the anchor, and g is the acceleration due to gravity. The calculation is detailed, and the importance of using correct units and constants, such as the density of water (1000 kg/m³) and g (10 m/s²), is highlighted. The final buoyant force is calculated to be 62.5 Newtons.
🪢 Determining the Tension in the Rope
This paragraph explains how to determine the tension in the rope holding the submerged anchor by applying Newton's Second Law. The anchor is in equilibrium, so the net force is zero. The forces considered are the buoyant force, tension, and weight of the anchor. By isolating and solving for tension, the final value is found to be 437.5 Newtons. The paragraph also mentions the point value for this part of the problem.
🚤 Effect of Anchor on Boat Depth
In the final part, the scenario changes to lifting the anchor back into the boat. The paragraph explores how this affects the boat's depth in the water. With the anchor in the boat, the boat's weight increases, requiring a greater buoyant force to maintain equilibrium. Consequently, the boat displaces more water and sinks deeper. This change in depth is explained conceptually, emphasizing the principle of buoyancy and equilibrium. This part is worth the remaining points in the problem.
Mindmap
Keywords
💡free body diagram
💡buoyant force
💡tension
💡Newton's Second Law
💡density
💡volume
💡acceleration due to gravity
💡equilibrium
💡displacement
💡force due to gravity
Highlights
Introduction to a fluid physics problem from the 2013 AP Physics B exam.
The problem involves a sailboat with an anchor in the water, illustrating key principles in fluid mechanics.
The anchor has a mass of 50 kg and is suspended 4 meters below the surface by a rope with negligible mass and volume.
Explanation of the forces acting on the anchor, including buoyant force, gravitational force, and tension.
Free body diagram requirements and tips for accurately depicting the forces.
Importance of not adding incorrect forces to the free body diagram, which can reduce points.
Calculation of the buoyant force using the equation ρVG.
Substituting values: density of water (1000 kg/m³), volume of anchor (6.25 x 10^-3 m³), and gravitational acceleration (10 m/s²).
Resulting buoyant force calculated as 62.5 N (Newton).
Discussion on using 10 m/s² for gravity in AP exams versus 9.81 m/s² for more precision.
Calculation of tension in the rope by applying Newton's Second Law and recognizing the anchor is in equilibrium.
Formulating the equation for net force as zero, combining buoyant force, tension, and gravitational force.
Isolating tension and solving, resulting in a tension of 437.5 N.
Final scenario: lifting the anchor back into the boat and analyzing the impact on the boat's depth.
Explanation that the boat will sink deeper to displace more water and balance the increased weight.
Transcripts
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