AP Free Response Question
2010 C3
Printer Friendly Version
A skier of mass
m
will be pulled up a hill by a rope, as shown above. The magnitude of the acceleration of the skier as a function of time t can be modeled by the equations
where
a
_{max}
and
T
are constants. The hill is inclined at an angle
q
above the horizontal, and friction between the skis and the snow is negligible. Express your answers in terms of given quantities and fundamental constants.
(a) Derive an expression for the velocity of the skier as a function of time during the acceleration. Assume the skier starts from rest.
(b) Derive an expression for the work done by the net force on the skier from rest until terminal speed is reached.
(c) Determine the magnitude of the force exerted by the rope on the skier at terminal speed.
(d) Derive an expression for the total impulse imparted to the skier during the acceleration.
(e) Suppose that the magnitude of the acceleration is instead modeled as
for all t > 0 , where
a
_{max}
and T are the same as in the original model.
On the axes below, sketch the graphs of the force exerted by the rope on the skier for the two models, from t = 0 to a time t > T. Label the original model F
_{1}
and the new model F
_{2}
.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
elastic potential energy
friction
gravitational force (vector)
gravitational potential energy
gravitational potential energy
Hooke's Law
impulse
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 energy
power
power
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
work (dot product)
Related Documents
Lab:
Labs -
A Battering Ram
Labs -
A Photoelectric Effect Analogy
Labs -
A Physical Pendulum, The Parallel Axis Theorem and A Bit of Calculus
Labs -
Air Track Collisions
Labs -
Ballistic Pendulum
Labs -
Ballistic Pendulum: Muzzle Velocity
Labs -
Bouncing Steel Spheres
Labs -
Coefficient of Friction
Labs -
Coefficient of Friction
Labs -
Coefficient of Kinetic Friction (pulley, incline, block)
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conservation of Energy and Vertical Circles
Labs -
Conservation of Momentum
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Falling Coffee Filters
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Impulse
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
LabPro: Newton's 2nd Law
Labs -
Loop-the-Loop
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Ramps: Sliding vs Rolling
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rotational Inertia
Labs -
Rube Goldberg Challenge
Labs -
Spring Carts
Labs -
Static Equilibrium Lab
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: LabPro Data for Hooke's Law
Labs -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Ball Re-Bounding From a Wall
Labs -
Video Lab: Blowdart Colliding with Cart
Labs -
Video Lab: Cart Push #2 and #3
Labs -
Video LAB: Circular Motion
Labs -
Video Lab: Falling Coffee Filters
Labs -
Video Lab: M&M Collides with Pop Can
Labs -
Video Lab: Marble Collides with Ballistic Pendulum
Resource Lesson:
RL -
A Further Look at Impulse
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
APC: Work Notation
RL -
Average Velocity - A Calculus Approach
RL -
Conservation of Energy and Springs
RL -
Derivatives: Instantaneous vs Average Velocities
RL -
Energy Conservation in Simple Pendulums
RL -
Famous Discoveries: The Franck-Hertz Experiment
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Gravitational Energy Wells
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Linear Momentum
RL -
Mechanical Energy
RL -
Momentum and Energy
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Potential Energy Functions
RL -
Principal of Least Action
RL -
Properties of Friction
RL -
Rotational Dynamics: Pivoting Rods
RL -
Rotational Kinetic Energy
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Symmetries in Physics
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Thin Rods: Center of Mass
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
What is Mass?
RL -
Work
RL -
Work and Energy
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
Puppy Love
APP -
The Antelope
APP -
The Box Seat
APP -
The Jogger
APP -
The Pepsi Challenge
APP -
The Pet Rock
APP -
The Pool Game
APP -
The Raft
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Conservation of Energy
CP -
Conservation of Momentum
CP -
Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
CP -
Force and Weight
CP -
Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Mobiles: Rotational Equilibrium
CP -
Momentum
CP -
Momentum and Energy
CP -
Momentum and Kinetic Energy
CP -
Momentum Practice Problems
CP -
Momentum Systems and Conservation
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Power Production
CP -
Satellites: Circular and Elliptical
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
CP -
Work and Energy
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Cliffs
NT -
Elliptical Orbits
NT -
Escape Velocity
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Gravitation #2
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Momentum
NT -
Ramps
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Satellite Positions
NT -
Scale Reading
NT -
Settling
NT -
Skidding Distances
NT -
Spiral Tube
NT -
Tensile Strength
NT -
Terminal Velocity
NT -
Tug of War #1
NT -
Tug of War #2
NT -
Two-block Systems
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Calculating Force Components
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combining Kinematics and Dynamics
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Energy Methods: More Practice with Projectiles
WS -
Energy Methods: Projectiles
WS -
Energy/Work Vocabulary
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
net F = ma
WS -
Potential Energy Functions
WS -
Practice: Momentum and Energy #1
WS -
Practice: Momentum and Energy #2
WS -
Practice: Vertical Circular Motion
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Rotational Kinetic Energy
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: An Assortment of Situations
WS -
Work and Energy Practice: Forces at Angles
TB -
Antiderivatives and Kinematics Functions
TB -
Projectile Summary
TB -
Projectile Summary
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
CB-ETS
Copyright © 1970-2023
All rights reserved.
Used with
permission
Mainland High School
Daytona Beach, FL 32114