AP Free Response Question
2000 C1
Printer Friendly Version
You are conducting an experiment to measure the acceleration due to gravity,
g
_{u}
, at an unknown location. In the measurement apparatus, a simple pendulum swings past a photogate located at the pendulum's lowest point, which records the time t
_{10}
for the pendulum to undergo 10 full oscillations. The pendulum consists of a sphere of mass
m
at the end of a string and has a length
. There are four versions of this apparatus, each with a different length. All four are at the same unknown location and the data shown below are sent to you during the experiment.
(a) For each pendulum, calculate the period
T
and the square of the period. Use a reasonable number of significant figures. Enter these results in the table above.
(b) On the axes below, plot the square of the period versus the length of the pendulum. Draw a best fit straight line for this data.
(c) Assuming that each pendulum undergoes small amplitude oscillations, from your fit determine the experimental value
g
_{exp}
of the acceleration due to gravity at this unknown location. Justify your answer.
(d) If the measurement apparatus allows a determination of
g
_{u}
that is accurate to within 4%, is your experimental value in agreement with the value 9.80 m/s
^{2}
? Justify your answer.
(e) Someone informs you that the experimental apparatus is in fact near Earth's surface, but that the experiment has been conducted inside an elevator with a constant acceleration
a
. Assuming that your experimental value
g
is exact, determine the magnitude and direction of the elevator's acceleration.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
friction
gravitational force (vector)
gravitational potential energy
Hooke's Law
impulse
kinetic energy
linear momentum
linear velocity and angular velocity
moment of inertia
net torque
Newton's 2nd Law
Newton's Law of Universal Gravitation
period and frequency
period of a simple pendulum
period of a spring
potential elastic energy
potential energy
power (dot product)
rate of change of momentum
rate of change of work
rotational kinetic energy
torque
uniform acceleration  displacement and instantaneous velocity
uniform acceleration  instantaneous position
uniform acceleration  instantaneous velocity
work (dot product)
Related Documents
Lab:
Labs 
A Physical Pendulum, The Parallel Axis Theorem and A Bit of Calculus
Resource Lesson:
RL 
Average Velocity  A Calculus Approach
RL 
Derivatives: Instantaneous vs Average Velocities
RL 
Thin Rods: Center of Mass
Review:
WS 
Drill: Mechanics
WS 
Drill: Waves and Sound
TB 
Schaum's 11th Edition
REV 
Course Objectives
REV 
Cumulative Review
REV 
Drill: Circular Motion
REV 
Drill: Common Variables
REV 
Drill: DC Circuits
REV 
Drill: Dynamics
REV 
Drill: Electrostatics
REV 
Drill: Kinematics
REV 
Drill: Magnetism
REV 
Drill: Metric System
REV 
Drill: Modern
REV 
Drill: Physical Optics
REV 
Drill: Projectiles
REV 
Drill: Refraction and Lenses
REV 
Drill: Rotary Motion
REV 
Drill: SHM
REV 
Drill: Thermodynamics
REV 
Drill: Work and Energy
REV 
Preregistration Survey
REV 
Sample NY Regents Review Questions
Worksheet:
AAPT 
1994 Physics Olympiad Screening Test (Part 1)
AAPT 
1994 Physics Olympiad Screening Test (Part 2)
AAPT 
1994 Physics Quiz Bowl (120)
AAPT 
1994 Physics Quiz Bowl (2140)
AAPT 
1995 Physics Olympiad Screening Test (Part 1)
AAPT 
1995 Physics Olympiad Screening Test (Part 2)
AAPT 
1995 Physics Quiz Bowl (120)
AAPT 
1995 Physics Quiz Bowl (Part 2)
AAPT 
1996 Physics Olympiad Screening Test (Part 1)
AAPT 
1996 Physics Olympiad Screening Test (Part 2)
AAPT 
1996 Physics Quiz Bowl (Part 1)
AAPT 
1996 Physics Quiz Bowl (Part 2)
AAPT 
1997 Physics Olympiad Screening Test (Part 1)
AAPT 
1997 Physics Olympiad Screening Test (Part 2)
AAPT 
1997 Physics Quiz Bowl (Part 1)
AAPT 
1997 Physics Quiz Bowl (Part 2)
AAPT 
1998 Physics Olympiad Screening Test (Part 1)
AAPT 
1998 Physics Olympiad Screening Test (Part 2)
AAPT 
1998 Physics Quiz Bowl (Part 1)
AAPT 
1998 Physics Quiz Bowl (Part 2)
AAPT 
1999 Physics Olympiad Screening Test (Part 1)
AAPT 
1999 Physics Olympiad Screening Test (Part 2)
AAPT 
1999 Physics Quiz Bowl (Part 1)
AAPT 
1999 Physics Quiz Bowl (Part 2)
AAPT 
2000 Physics Olympiad Screening Test (Part 2)
AAPT 
2000 Physics Olympiad Screening Test (Part 2)
AAPT 
2000 Physics Quiz Bowl (2140)
AAPT 
2000 Physics Quiz Bowl (Part 1)
AAPT 
2006 Physics Quiz Bowl (Part 1)
AAPT 
2006 Physics Quiz Bowl (Part 2)
AAPT 
2007 Physics Quiz Bowl (Part 1)
AAPT 
2007 Physics Quiz Bowl (Part 2)
AAPT 
2008 Physics Quiz Bowl (Part 2)
AAPT 
2008 PhysicsBowl (Part 1)
AAPT 
2015 net F = ma Contest
AAPT 
PhysicsBowl 2009 (Part 1)
AAPT 
PhysicsBowl 2009 (Part 2)
AAPT 
PhysicsBowl 2010 (Part 1)
AAPT 
PhysicsBowl 2010 (Part 2)
AAPT 
PhysicsBowl 2011 (Part 1)
AAPT 
PhysicsBowl 2011 (Part 2)
AAPT 
PhysicsBowl 2012 (Part 1)
AAPT 
PhysicsBowl 2012 (Part 2)
AAPT 
PhysicsBowl 2013 (Part 1)
AAPT 
PhysicsBowl 2013 (Part 2)
AAPT 
PhysicsBowl 2014 (Part 1)
AAPT 
PhysicsBowl 2014 (Part 2)
AAPT 
PhysicsBowl 2015 (Part 1)
AAPT 
PhysicsBowl 2015 (Part 2)
AAPT 
PhysicsBowl 2016 (Part 1)
AAPT 
PhysicsBowl 2016 (Part 2)
AAPT 
PhysicsBowl 2017 (Part 1)
AAPT 
PhysicsBowl 2017 (Part 2)
AAPT 
PhysicsBowl 2018 (Part 1)
AAPT 
PhysicsBowl 2018 (Part 2)
AAPT 
PhysicsBowl 2019 (Part 1)
AAPT 
PhysicsBowl 2019 (Part 2)
NY 
January 2006, Part 1
NY 
January 2006, Part 2
NY 
January 2006, Part 3
NY 
January 2007, Part 1
NY 
January 2007, Part 2
NY 
January 2007, Part 3
NY 
January 2008, Part 1
NY 
January 2008, Part 2
NY 
January 2008, Part 3
NY 
January 2008, Part 4
NY 
January 2009, Part 1
NY 
January 2009, Part 2
NY 
June 2006, Part 1
NY 
June 2006, Part 2
NY 
June 2006, Part 3
NY 
June 2007, Part 1
NY 
June 2007, Part 2
NY 
June 2007, Part 3
NY 
June 2008, Part 1
NY 
June 2008, Part 2
NY 
June 2008, Part 3
NY 
June 2008, Part 4
NY 
June 2009, Part 1
NY 
June 2009, Part 2
NY 
June 2010, Part 1
NY 
June 2010, Part 2
NY 
June 2010, Part 3
NY 
June 2011, Part 1
NY 
June 2011, Part 2
NY 
June 2011, Part 3
NY 
June 2012, Part 1
NY 
June 2012, Part 2
NY 
June 2012, Part 3
NY 
June 2013, Part 1
NY 
June 2013, Part 2
NY 
June 2013, Part 3
NY 
June 2014, Part 1
NY 
June 2014, Part 2
NY 
June 2014, Part 3
NY 
June 2015, Part 1
NY 
June 2015, Part 2
NY 
June 2015, Part 3
NY 
June 2016, Part 1
NY 
June 2016, Part 2
NY 
June 2016, Part 3
NY 
June 2017, Part 1
NY 
June 2017, Part 2
NY 
June 2017, Part 3
NY 
June 2018, Part 1
NY 
June 2018, Part 2
NY 
June 2018, Part 3
NY 
June 2019, Part 1
NY 
June 2019, Part 2
NY 
June 2019, Part 3
TB 
Antiderivatives and Kinematics Functions
TB 
Projectile Summary
TB 
Projectile Summary

MCAS 2004 Session 1

MCAS 2004 Session 2

MCAS 2005 Session 1

MCAS 2005 Session 2

MCAS 2006 Session 1

MCAS 2006 Session 2

MCAS 2007 Session 1

MCAS 2007 Session 2

MCAS 2008 Session 1

MCAS 2008 Session 2

MCAS 2009 Session 1

MCAS 2009 Session 2

MCAS 2010 Session 1

MCAS 2010 Session 2

MCAS 2011 Session 1

MCAS 2011 Session 2

MCAS 2012 Session 1

MCAS 2012 Session 2

MCAS 2013 Session 1

MCAS 2013 Session 2

MCAS 2014 Session 1

MCAS 2014 Session 2

MCAS 2015 Session 1

MCAS 2015 Session 2

MCAS 2016 Session 1

MCAS 2016 Session 2

MCAS 2017 Session 1

MCAS 2017 Session 2

MCAS 2018 Session 1

MCAS 2018 Session 2

MCAS 2019 Session 1

MCAS 2019 Session 2
CBETS
Copyright © 19702022
All rights reserved.
Used with
permission
Mainland High School
Daytona Beach, FL 32114