Resource Lesson
Springs: Hooke's Law
Printer Friendly Version
In 1678, Robert Hooke announced the invention of the spring scale and the relationship for elastic materials that is now known as
Hooke's Law
. When an object is acted upon by a force, it can be compressed, stretched or bent. If when the force is removed, the object returns to its original shape, it is said to be elastic. Solids that do not return to their original configuration once they have been distorted are categorized as plastics.
Hooke discovered that not only are certain materials (steel bars, rods, wire, springs, diving boards, and rubber bands) elastic, but the stretch they experience is directly proportional to the load that they support.
Elastic media will stretch until the reach their elastic limit, or yield point. After that point, they exhibit plastic deformation and will never return to their original shape. Ductile materials stretch thinner and thinner, while brittle materials break without any plastic deformation. Eventually all will rupture at their breaking point.
To simplify our discussion, we are going to use springs as our example of an elastic medium. The formulas used to calculate the force required to stretch or compress an elastic medium with respect to its equilibrium position and its elasticity constant, k, are:
F
_{internal}
= - kx
force supplied by the spring to restore itself to equilibrium (Hooke's Law)
F
_{external}
= kx
force supplied by an external agent on the spring distorting it from equilibrium
This formula is only applicable to force acting on an ideal spring that has not surpassed its elastic limit. Note that the amount of force required by an external agent to stretch the spring depends on how far it has been displaced from its equilibrium position. That is, the force is not constant, it is
variable
.
When two or more springs are combined in
parallel
(side by side) so that any applied force must stretch both springs simultaneously, the spring constant for the combination will be
When two or springs are combined in
series
(one after another), an applied force may stretch one more than another. Recall a saying that a chain is only as "strong as its weakest link." The spring constant for the combination will be
Work done and energy stored
The formula used to calculate the work required to stretch the spring OR the amount of elastic potential energy subsequently stored in a spring is:
PE
_{e}
= ½kx
^{2}
This energy is calculated graphically as the area under a F vs x graph.
PE
_{e}
= Work done on the spring
= average force times distance
= area under the graph
= ½ bh
F is measured in newtons
= ½(x)(F)
x is measured in meters
= ½(x)(kx)
k is measured in nt/m
= ½ kx
^{2}
PE
_{e}
is measured in joules
Related Documents
Lab:
Labs -
Coefficient of Friction
Labs -
Coefficient of Friction
Labs -
Coefficient of Kinetic Friction (pulley, incline, block)
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Falling Coffee Filters
Labs -
Force Table - Force Vectors in Equilibrium
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 -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
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 -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Ball Re-Bounding From a Wall
Labs -
Video Lab: Falling Coffee Filters
Resource Lesson:
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Gravitational Energy Wells
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Properties of Friction
RL -
Springs and Blocks
RL -
Static Equilibrium
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
What is Mass?
RL -
Work and Energy
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
The Antelope
APP -
The Box Seat
APP -
The Jogger
CP -
Action-Reaction #1
CP -
Action-Reaction #2
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 -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
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 -
Calculating Force Components
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combining Kinematics and Dynamics
WS -
Distinguishing 2nd and 3rd Law Forces
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 -
Practice: Vertical Circular Motion
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: Forces at Angles
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2024
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton