AP Free Response Question
2013 B1
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A sailboat at rest on a calm lake has its anchor dropped a distance of 4.0 m below the surface of the water. The anchor is suspended by a rope of negligible mass and volume. The mass of the anchor is 50 kg, and its volume is 6.25 x 10
^{-3}
m
^{3}
. The density of water is 1000 kg/m
^{3}
.
(a) On the dot below that represents the anchor, draw and label the forces (not components) that act on the anchor.
(b) Calculate the magnitude of the buoyant force acting on the anchor. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. DO NOT add anything to the figure in part (a).
(c) Calculate the tension in the rope. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. DO NOT add anything to the figure in part (a).
(d) The bottom of the boat is at a depth d below the surface of the water. Suppose the anchor is lifted back into the boat so that the bottom of the boat is at a new depth d' below the surface of the water. How does d' compare to d? Justify your answer.
Topic Formulas
Description
Published Formula
actual pressure in a fluid
Bernoulli's Equation
buoyancy
Continuity Equation
friction
gravitational potential energy
Hooke's Law
mass density
Newton's 2nd Law
Newton's Law of Universal Gravitation
pressure
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Fluids At Rest
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Fluids In Motion
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Action-Reaction #2
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Archimedes Principle #1
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Archimedes Principle #2
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Equilibrium on an Inclined Plane
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Falling and Air Resistance
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Force and Acceleration
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Force and Weight
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Force Vectors and the Parallelogram Rule
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Gases
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Gravitational Interactions
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Inertia
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Newton's Law of Motion: Friction
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Static Equilibrium
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Syringes and Vacuum Pumps
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Tensions and Equilibrium
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Air Resistance #1
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Boat
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Buoyant Forces
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Falling Rock
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Falling Spheres
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Floating Ice Cube
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Floating Wood
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Freely-Falling Elevator
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Friction
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Rotating Disk
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Sailboats #2
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Scale Reading
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Terminal Velocity
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Tug of War #1
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Tug of War #2
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Two-block Systems
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Verge of Sinking
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Water Level
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Advanced Properties of Freely Falling Bodies #1
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Advanced Properties of Freely Falling Bodies #2
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Calculating Force Components
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Charged Projectiles in Uniform Electric Fields
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Combining Kinematics and Dynamics
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Distinguishing 2nd and 3rd Law Forces
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Force vs Displacement Graphs
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Freebody Diagrams #1
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Freebody Diagrams #2
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Freebody Diagrams #3
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Freebody Diagrams #4
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Introduction to Springs
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Lab Discussion: Inertial and Gravitational Mass
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Fluids At Rest
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Systems of Bodies (including pulleys)
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