AP Free Response Question
2002 C2
Printer Friendly Version
The cart shown above is made of a block of mass
m
and four solid rubber tires each of mass
m/4
and radius
r
. Each tire may be considered to be a disk.
NOTE: A disk has rotational inertia
where
M
is the mass and
L
is the radius of the disk.
The cart is released from rest and rolls without slipping from the top of an inclined plane of height
h
. Express all algebraic answers in terms of the given quantities and fundamental constants.
Determine the total rotational inertial of all four tires.
Determine the speed of the cart when it reaches the bottom of the incline.
After rolling down the incline and across the horizontal surface, the cart collides with a bumper of negligible mass attached to an ideal spring, which has a spring constant
k
. Determine the distance
x
_{m}
the spring is compressed before the cart and bumper comes to rest.
Now assume that the bumper has a non negligible mass. After the collision with the bumper, the spring is compressed to a maximum distance of about 90% of the value of x
_{m}
in part (c). Give a reasonable explanation for this decrease.
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 © 19702023
All rights reserved.
Used with
permission
Mainland High School
Daytona Beach, FL 32114