Resource Lesson
Energy Conservation in Simple Pendulums
Printer Friendly Version
Remember the formula used to calculate the gravitational potential energy of a mass given its mass and height above an arbitrary zero level is
PE
_{gravity}
= mgh
When a pendulum is pulled back from equilibrium through an angle θ, its height is calculated with the formula
h = L - L cos θ
where θ is the angular displacement
The formula used to calculate the kinetic energy of a massive particle is
KE = ½ mv
^{2}
In the absence of non-conservative forces, such as friction or applied, external forces, the mechanical energy in a system is conserved. That is
During the swing of a simple pendulum, when does the bob possess maximum PE?
During the swing of a simple pendulum, when does the bob possess maximum KE?
During the swing of a simple pendulum, what is the magnitude of the bob's maximum velocity?
Another way of looking at conservation of energy is with the following energy diagram. As you can see,
the "purple" curve represents the pendulum bob's KE which during each cycle begins with an initial value of zero, increases to a maximum value, and then returns to zero
the "green" curve represents the PE of the bob which begins each cycle at a maximum value, then becomes zero as the bob passes through its equilibrium position, and returns to its maximum value
the "brown" line represents the total energy of the pendulum bob that always remains constant
If a pendulum is initially released at an angle of 37º, at what angle will its PE and the KE be equal?
Refer to the following information for the next question.
At any intermediate position during the oscillation, the pendulum bob would have both PE and KE.
PE
_{max}
= PE
_{intermediate}
+ KE
_{intermediate}
= KE
_{max}
If the pendulum was released at point A, derive an expression for the pendulum's instantaneous velocity at point B, an intermediate position in its swing.
See the related lesson on vertical circles if you are asked to calculate the tension of the string during the pendulum's oscillation.
Remember that a pendulum is merely the bottom half of a vertical circle! These conservation of energy methods are the easiest way to determine an object's speed so that tensions can be calculated.
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 -
Conservation of Energy and Springs
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Derivation: Period of a Simple Pendulum
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 © 1997-2022
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton