Resource Lesson
Conservation of Energy and Springs
Printer Friendly Version
When a spring is compressed, work is done on the spring by the external agent exerting the force. Suppose that this work is done by a moving object which strikes and sticks to a spring initially in its equilibrium position [position A] so that as the moving object loses kinetic energy (eventually coming to rest) it does work on the spring to compress it [position B]. We will not at this time continue our examination into when the spring later rebounds.
Numerically we would therefore set the magnitude of the kinetic energy lost by the object equal to the elastic potential energy gained by the spring. This will allow us to either solve for the maximum compression distance in the spring; or vice versa, if given the compression produced in the spring, solve for the original velocity of the colliding mass.
Horizontally Oscillating Springs
Now suppose that a spring is initially compressed and then released on a frictionless surface. It then oscillates with one end firmly attached to a base of support and a mass attached to its free end. As the mass vibrates back and forth, the energy in the system transforms between PE
_{e}
(at the endpoints of the oscillation) and KE (as the mass passes through equilibrium). Since the surface is frictionless no mechanical energy is lost to thermal energy as the mass slides back and forth over the surface.
The maximum kinetic energy occurs as the mass passes through equilibrium.
When a spring has been set into oscillatory motion, the equation used to calculate its period is
Remember that frequency and period are reciprocals: f = 1/T. The unit to measure frequency is hertz, or vibrations per second; while the unit to measure period is seconds, or seconds per vibration.
This formula is derived in the lesson on
Simple Harmonic Motion
.
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 -
Calculation of "g" Using Two Types of Pendulums
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conical Pendulums
Labs -
Conical Pendulums
Labs -
Conservation of Energy and Vertical Circles
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Introductory Simple Pendulums
Labs -
Kepler's 1st and 2nd Laws
Labs -
Loop-the-Loop
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Oscillating Springs
Labs -
Ramps: Sliding vs Rolling
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rotational Inertia
Labs -
Rube Goldberg Challenge
Labs -
Sand Springs
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Spring Carts
Labs -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Video LAB: A Gravitron
Labs -
Video Lab: Blowdart Colliding with Cart
Labs -
Video LAB: Circular Motion
Labs -
Video LAB: Looping Rollercoaster
Labs -
Video Lab: M&M Collides with Pop Can
Labs -
Video Lab: Marble Collides with Ballistic Pendulum
Labs -
Water Springs
Resource Lesson:
RL -
A Derivation of the Formulas for Centripetal Acceleration
RL -
APC: Work Notation
RL -
Centripetal Acceleration and Angular Motion
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Derivation: Period of a Simple Pendulum
RL -
Energy Conservation in Simple Pendulums
RL -
Gravitational Energy Wells
RL -
Kepler's Laws
RL -
LC Circuit
RL -
Magnetic Forces on Particles (Part II)
RL -
Mechanical Energy
RL -
Momentum and Energy
RL -
Period of a Pendulum
RL -
Potential Energy Functions
RL -
Principal of Least Action
RL -
Rotational Dynamics: Pivoting Rods
RL -
Rotational Kinematics
RL -
Rotational Kinetic Energy
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Springs and Blocks
RL -
Symmetries in Physics
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Thin Rods: Moment of Inertia
RL -
Uniform Circular Motion: Centripetal Forces
RL -
Universal Gravitation and Satellites
RL -
Vertical Circles and Non-Uniform Circular Motion
RL -
Work
RL -
Work and Energy
Review:
REV -
Review: Circular Motion and Universal Gravitation
Worksheet:
APP -
Big Al
APP -
Ring Around the Collar
APP -
The Jogger
APP -
The Pepsi Challenge
APP -
The Pet Rock
APP -
The Pool Game
APP -
The Satellite
APP -
The Spring Phling
APP -
Timex
CP -
Centripetal Acceleration
CP -
Centripetal Force
CP -
Conservation of Energy
CP -
Momentum and Energy
CP -
Momentum and Kinetic Energy
CP -
Power Production
CP -
Satellites: Circular and Elliptical
CP -
Work and Energy
NT -
Circular Orbits
NT -
Cliffs
NT -
Elliptical Orbits
NT -
Escape Velocity
NT -
Gravitation #2
NT -
Pendulum
NT -
Ramps
NT -
Rotating Disk
NT -
Satellite Positions
NT -
Spiral Tube
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 -
Basic Practice with Springs
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Energy Methods: More Practice with Projectiles
WS -
Energy Methods: Projectiles
WS -
Energy/Work Vocabulary
WS -
Force vs Displacement Graphs
WS -
Inertial Mass Lab Review Questions
WS -
Introduction to Springs
WS -
Kepler's Laws: Worksheet #1
WS -
Kepler's Laws: Worksheet #2
WS -
Kinematics Along With Work/Energy
WS -
More Practice with SHM Equations
WS -
Pendulum Lab Review
WS -
Pendulum Lab Review
WS -
Potential Energy Functions
WS -
Practice: Momentum and Energy #1
WS -
Practice: Momentum and Energy #2
WS -
Practice: SHM Equations
WS -
Practice: Uniform Circular Motion
WS -
Practice: Vertical Circular Motion
WS -
Rotational Kinetic Energy
WS -
SHM Properties
WS -
Static Springs: The Basics
WS -
Universal Gravitation and Satellites
WS -
Vertical Circular Motion #1
WS -
Work and Energy Practice: An Assortment of Situations
WS -
Work and Energy Practice: Forces at Angles
TB -
Centripetal Acceleration
TB -
Centripetal Force
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2018
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton