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Experiment 205

Hookes Law

PHY11L / B3 / Group 2Janolino, Bryan Austin H.

Abstract

The experiment made use the

Hookes law apparatus in order to study the

elastic properties of the spring. And todetermine the total work done on the spring

when it is being stretch and also to

determine the force constant of the spring.

I. Introduction

Hooke's law is only a first orderlinear approximation to the real response of

springs and other elastic bodies to applied

forces. It must eventually fail once the

forces exceed some limit, since no materialcan be compressed beyond a certain

minimum size, or stretched beyond a

maximum size, without some permanentdeformation or change of state. In fact,

many materials will noticeably deviate from

Hooke's law well before those elastic limits

are reached.

On the other hand, Hooke's law is an

accurate approximation for most solidbodies, as long as the forces and

deformations are small enough. For this

reason, Hooke's law is extensively used inall branches of science and engineering, and

is the foundation of many disciplines such as

seismology, molecular mechanics and

acoustics. It is also the fundamentalprinciple behind the spring scale, the

manometer, and the balance wheel of the

mechanical clock.

II. Theory

Hooke's law is a principle of physicsthat states that the force Fneeded to extend

or compress a spring by some distance X isproportional to that distance. That is: F = k

X, where kis a constant factor characteristic

of the spring, its stiffness.

The deformation of an elastic

material obeys Hookes law which states

that Within the elastic limit of a body, the

deforming force is directly proportional tothe elongation of the body.

F = kxWhere:

Fdeforming force (N; dynes)

xdisplacement (m; cm)

kforce constant (N/m; dynes/cm)

Work is done when a spring is stretched.

The work done by a force when theelongation foes from xoto xf is given by the

equation

W = kx2

The degree of elasticity of a material is

called Modulus of Elasticity. For solidmaterials, the degree of elasticity is called

the Youngs Modulus of Elasticity. It is the

ratio of longitudinal stress to the resultantlongitudinal strain.

Y= S/

Where stress is the ratio an applied force per

unit area,

S = F/A

And strain is the relative change in the

bodys length, shape or size.

= e / L o

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Thus,

Y = FL o/ Ae

III. MethodologyA. Setup

B. Materials

1 set Hookes Law Apparatus 1 pc 4 N/m Spring 1 pc 8 N/m Spring

1 pc Mass Hanger

1 set Weights

C. Procedure

A. Setting up the Equipment

First, the group hanged the spring from thenotch on the support arm. Then connected

the Stretch indicator to the bottom of the

spring. Then the group adjusted the clampon the support rod until the indicator reading

is aligned at exactly zero. After aligning the

group connected the mass hanger to the

bottom of the stretch indicator.

B. Determining the Force Constant of the

Spring

As of Part 2 of the experiment, the group

placed the mass on the hanger and recorded

the change in displacement of the spring andthe weight of the hanging mass. Then the

group computed for the constant of the

spring using the equation F = kx . Thegroup repeated steps 1 -3 for another 3 trials

and add 10 grams of mass in each trial. After

doing the 3 more trials the group computed

for the average value of the force constant,they plotted a graph in which it included

Plot a force vs. displacement graph, after

graphing the group determined the slop ofthe line. The slope is then calculated after

that the group calculated the percentage

difference of the average value of the forceconstant and the slope of the line. They

repeated the said procedures using another

spring.

C. Determining the Work Done on the

Spring

The group then filled out table 2 using thedata gathered in Part B, then they computed

for the total work done in stretching the

spring using the equation:

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W = k (x2fx

2o)

Then after determining the work done instretching the spring, they computed for the

area under the graph of force vs.

displacement. Then they compared the totalwork done and the area under the graph offorce vs. displacement.

IV. References

General Physics 2 LaboratoryManual

Principles of Physics 9th

Edition byHalliday, Resnick and Walker

http://www.wikipedia.org