8/10/2019 E205.docx

1/3

EXPERIMENT 205HOOKES LAW

Manlapaz, Sarih S.Physics Department, Mapa Institute of Technology

ssmanlapaz@mymail.mapua.edu.ph

Abstract

Elasticity refers to a property by which an

object changes its length, shape or size underthe action of a deforming force and recovers itsoriginal configuration upon the removal of

force. The objectives of the study are that to

study the elastic properties of the spring, to

determine the force constant of the spring, toinvestigate the relationship between the

deforming force and amount the spring

stretches and to determine the total work done

on the spring when it is being stretched. Inperforming the experiment, we constantly

hanged weights on the Hookes law apparatusand measure the displacement it makes so thatwe can solve for the force constant, and the

work done.

I. Introduction

law ofelasticity discovered by the English

scientistRobert Hooke in 1660, which states

that, for relatively smalldeformations of anobject, thedisplacement or size of the

deformation is directly proportional to the

deforming force or load. Under theseconditions the object returns to its original

shape and size upon removal of the load.

Elastic behaviour of solids according toHookes law can be explained by the fact that

small displacements of their

constituentmolecules,atoms, orionsfrom

normal positions is also proportional to theforce that causes the displacement.

II. Theory

The shape of a body will distort when a force is

applied to it. Bodies which are elastic distort bycompression or tension, and return to their

original or equilibrium position when the

distorting force is removed (unless thedistorting force exceeds the elastic limit of the

material). Hooke's Law states that if the

distortion of an elastic body is not too large, the

force tending to restore the body to equilibrium

is proportional to the displacement of the bodyfrom equilibrium. Stated mathematically:

whereF is a restoring force, k is a constant of

proportionality and x is the distance the object

has been displaced from its equilibriumposition. From Newton's 2nd Law,

for a spring attached to a mass. The solution to

this equation is

where,

and is a phaseconstant, determined from initial conditions. A

mass hanging from a massless spring oscillates

about its equilibrium position with a period, T,

given by

However, if the spring is not massless, then mmust be replaced with m + amspwhere a equals

some fraction of the spring mass. Thus, in

general, the period of a spring/mass system can

by described by

equation (5) can be solve for m, so that

This is an equation of the form of y=mx+yo ,

where x =

and yo =amsp . Note that the

quantity (m + amsp) is known as the

http://www.britannica.com/EBchecked/topic/182035/elasticityhttp://www.britannica.com/EBchecked/topic/271280/Robert-Hookehttp://www.britannica.com/EBchecked/topic/155875/deformation-and-flowhttp://www.britannica.com/EBchecked/topic/165821/displacementhttp://www.britannica.com/EBchecked/topic/388236/moleculehttp://www.britannica.com/EBchecked/topic/41549/atomhttp://www.britannica.com/EBchecked/topic/292705/ionhttp://www.britannica.com/EBchecked/topic/292705/ionhttp://www.britannica.com/EBchecked/topic/41549/atomhttp://www.britannica.com/EBchecked/topic/388236/moleculehttp://www.britannica.com/EBchecked/topic/165821/displacementhttp://www.britannica.com/EBchecked/topic/155875/deformation-and-flowhttp://www.britannica.com/EBchecked/topic/271280/Robert-Hookehttp://www.britannica.com/EBchecked/topic/182035/elasticity

8/10/2019 E205.docx

2/3

equivalent mass of the system. For an ideal

Hookes law spring, a=

.

This experiment, aims to study the elasticproperties of the spring, it also aims to

determine the force constant of the springlikewise to investigate the relationship betweenthe deforming force and the amount the spring

stretches and lastly to determine the total work

done on the spring when it is being stretched.

III. Methodology

A. Setup

Fig. 1Experimental Setup (Part 1)

B. Materials

1 set Hookes Law Apparatus

1 pc 4 N/m Spring

1 pc 8 N/mSpring

1 pc Mass Hanger

1 set Weights

C. Procedure

Setting up the experiment, we hanged the

spring from the notch on the support armcarefully and connect the stretch indicator to

the bottom of the spring. Then, the clamp isadjusted on the support rod until the indicatorreading is aligned at exactly zero. Afterwards,

we connect the mass hanger to the bottom of

the stretch indicator and start doing the firstpart of the experiment which is the

determination of the force constant of the

spring.

First, we use the 8 N/m spring and a 10gram weight as our initial mass whereas, it is

placed on the hanger. From the reading of the

transparent scale plate, the change indisplacement of the spring was recorded andalso the value of first mass. Using equation (1),

we compute for the force constant of the spring.

We performed three trials but varying the massby adding 10 g in each trial. The average value

of the force constant was determined through

calculation and the graph of a force versus

displacement is alsodrawn in our data.

We find the slope of the line and finally

calculated the percentage difference of theaverage value of the force constant and the

lines slope. Applying the same procedures, we

used the other spring that is 4 N/m. For thecompletion of the experiment, we determined

the work done on the spring after gathering all

the required data and substituted it in the

equation,

Where xfis the displacement from trial 4 in the1st part of the experiment and xo=0.

We find the area under the graph of force

versus displacement and compared it to thetotal work done.

IV. Results and Discussion

8/10/2019 E205.docx

3/3

In the first part of the experiment, the forceconstant of the 4 N/m and 8 N/m spring is

determined by the quotient of the values from

force (product of mass and acceleration due to

gravity) and values of displacement (readingfrom transparent scale plate).(See table 1a & b)

Observing the data gathered from Table 1, wenoticed that for each spring, as the mass

increases, the force and displacement also

increases but produces a force constant that isquite close with the actual value of the spring.

Meaning, force and displacement are directly

proportional to each other.

The graph above perfectly illustrates therelationship between force and displacements

direct proportionality. The line graph is going

towards the upper right of the coordinate plane

and therefore has an increasing slope.The last part of the experiment was about the

determination of the work done on the spring

which is a pure computation.(See table 2)

V. Conclusion

The evident relationship between the force

applied and the force constant is that their

quotient would be equal to the distance

stretched by the spring.

A spring stretches because its structure is weak

enough to be pulled but this would create strain

on the spring that forces it to return to its

original form making it harder and harder to

stretch. The spring would be deformed if the

force applied was too much which would reachthe maximum strain that the material can have

then it goes to a point where the spring deforms

to reduce the strain.

This experiments objectives is to study the

springs elastic properties, determine its force

constant, investigate the relationship between

the deforming force and amount the spring

stretches, and determine the total work done on

the spring when it is being stretched or pulled.

After this experiment, our group was able todetermine the total work done on the spring

when it is being stretched with the use of the

equation (

). We were also able to

determines the true force constants of the two

springs. We also found out the relationship of

force and amount the spring stretches which

can be used to solve for the force constant by

manipulating the equations and turning them

into ( ).

Hooke's Law posses the idea that every spring

has a spring constant (stiffness of the spring)

and can be calculated by dividing the force

which pulls the spring by the spring

displacement.

VI. References

[1] Halliday, Fundamentals of Physics, 9th

edition.

[2]http://en.wikipedia.org/wiki/Hooke's_law

[3]http://www.brightstorm.com/science/physics

/oscillatory-motion/hooks-law

[4]http://www.physics247.com/physics-

tutorial/hookes-law.shtml

http://en.wikipedia.org/wiki/Hooke's_lawhttp://www.brightstorm.com/science/physics/oscillatory-motion/hooks-lawhttp://www.brightstorm.com/science/physics/oscillatory-motion/hooks-lawhttp://www.physics247.com/physics-tutorial/hookes-law.shtmlhttp://www.physics247.com/physics-tutorial/hookes-law.shtmlhttp://www.physics247.com/physics-tutorial/hookes-law.shtmlhttp://www.physics247.com/physics-tutorial/hookes-law.shtmlhttp://www.brightstorm.com/science/physics/oscillatory-motion/hooks-lawhttp://www.brightstorm.com/science/physics/oscillatory-motion/hooks-lawhttp://en.wikipedia.org/wiki/Hooke's_law