AP Free Response Question
2005 C2
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A student is given the set of orbital data for some of the moons of Saturn shown below and is asked to use the data to determine the mass M
_{S}
of Saturn. Assume the orbits of these moons are circular.
(a) Write an algebraic expression for the gravitational force between Saturn and one of its moons.
Use your expression from part (a) and assumption of circular orbits to derive an equation for the orbital period
T
of a moon as a function of its orbital radius
R
.
Which quantities should be graphed to yield a straight line whose slope could be used to determine Saturn's mass?
(d) Complete the data table by calculating the two quantities that you decided should be graphed. Label the top of each column, including units.
(e) Plot the graph on the axes below. Label the axes with the variables and appropriate numbers to indicate the scale.
Using the graph, calculate a value for the mass of Saturn.
Topic Formulas
Description
Published Formula
centripetal acceleration
Hooke's Law
period of a simple pendulum
period of a spring
potential elastic energy
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A Derivation of the Formulas for Centripetal Acceleration
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Advanced Gravitational Forces
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Advanced Satellites
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Centripetal Acceleration and Angular Motion
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Conservation of Energy and Springs
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Gravitational Potential Energy
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Kepler's Laws
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LC Circuit
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Magnetic Forces on Particles (Part II)
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Period of a Pendulum
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The Law of Universal Gravitation
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Thin Rods: Moment of Inertia
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Uniform Circular Motion: Centripetal Forces
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Universal Gravitation and Satellites
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Universal Gravitation and Weight
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Vertical Circles and Non-Uniform Circular Motion
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Review: Circular Motion and Universal Gravitation
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Big Al
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Ring Around the Collar
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The Satellite
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The Spring Phling
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Timex
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Centripetal Acceleration
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Centripetal Force
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Gravitational Interactions
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Satellites: Circular and Elliptical
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Circular Orbits
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Pendulum
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Rotating Disk
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Spiral Tube
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Advanced Properties of Freely Falling Bodies #3
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Basic Practice with Springs
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Inertial Mass Lab Review Questions
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Introduction to Springs
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Kepler's Laws: Worksheet #1
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Kepler's Laws: Worksheet #2
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Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
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More Practice with SHM Equations
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Parallel Reading - The Atom
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Pendulum Lab Review
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Pendulum Lab Review
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Practice: SHM Equations
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Practice: Uniform Circular Motion
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Practice: Vertical Circular Motion
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SHM Properties
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Standard Model: Particles and Forces
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Static Springs: The Basics
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Universal Gravitation and Satellites
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Vertical Circular Motion #1
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Centripetal Acceleration
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Centripetal Force
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