Nanyang Technological UniversityNATIONAL INSTITUTE OF EDUCATION

Singapore

Project Work in

P H Y S I C SPresented by:

RONALD P. DIANAParticipant, NIE-LEAP-CTP-2009

Presented to:

DR. AUGUSTINE TAN TUCK LEEProfessor, Physics Content and Pedagogy

November 2009

Background Information

BACKGROUND INFORMATION

Hooke’s law is a law of elasticity discovered by the

English scientist Robert Hooke in 1660, which states

that, for relatively small deformations of an object, the

displacement or size of the deformation is directly

proportional to the deforming force or load. Under these

conditions the object returns to its original shape and

size upon removal of the load.

The deforming force may be applied to a solid by

stretching, compressing, squeezing, bending, or twisting.

Mathematically, Hooke’s law states that the applied force

F equals a constant k times the displacement or change

in length x, or F = kx. The value of k depends not only on

the kind of elastic material under consideration but also

on its dimensions and shape.

Title

SPRING CONSTANT k OF A SINGLE SPRING AND TWO SPRINGS IN SERIES: A Comparative Study

Objectives

Objectives:

This study was conducted to:

1) verify the relationship between the amount of force and the elongation of a spring;

2) determine the value of the spring constant k from the gradient of the graph using:(a) a single spring; and (b) two springs in series

Resources

Resources:

Metal springs

Retort stand

Meter rule

Mass hanger

Set of masses

Pointer (can be improvised)

Physics books, journals, or magazines

Methodology

1) Using one metal spring, set up the apparatus as shown in the figure.

2) Place the mass hanger at the end of the spring and note the scale reading of the pointer. Record it as your initial length, lo.

3) Add 50 g mass one at a time to the hanger and record the new pointer reading, l, each time in the table provided.

4) Calculate the elongation of the spring, Δl.

5) Plot a graph of the mass against elongation.

6) Calculate the gradient from the graph.

7) Repeat steps 1-6 using two metal springs connected in series.

Results & Discussions

Mass, m(g)

Scale Reading, l(cm)

Elongation, Δl(cm)

1 2 3 Average

50 20.0 21.0 21.2 20.7 0.8

100 21.6 22.8 22.9 22.4 2.5

150 27.4 28.5 28.6 28.2 8.3

200 33.8 34.8 34.8 34.5 14.6

250 40.4 41.0 41.0 40.8 20.9

A. SINGLE SPRING:

Initial length, lo = 19.9 cm

0 5 10 15 20 250

50

100

150

200

250

300

m vs. Δl(single spring)

Mass, m(g)

Scale Reading, l(cm)

Elongation, Δl(cm)

1 2 3 Average

50 42.0 41.8 42.0 41.9 0.3

100 46.9 47.0 47.0 47.0 5.4

150 59.5 59.5 59.6 59.5 17.9

200 72.5 72.4 72.4 72.4 30.8

250 85.6 85.7 85.7 85.7 44.1

B. TWO (2) SPRINGS IN SERIES:

Initial length, lo = 41.6 cm

0 5 10 15 20 25 30 35 40 45 500

50

100

150

200

250

300

m vs. Δl(2 springs in series)

Conclusions & Recommendations

Conclusions:

Based on the results of the study, the following conclusions are drawn:

• as the amount of load is increased, the length of the metal spring also increases;

• using a single spring, the gradient of the graph is equivalent to the spring constant k; and

• using two springs connected in series, the gradient of the graph is equivalent to approximately k/2 or one-half of the spring constant.

Recommendations:

It is recommended that a similar study be conducted using three or more metal springs connected in series. Further, you can also try connecting the metal springs in parallel and see what happens to the spring constant k.

References

References:

Published Resources:

DISCOVER PHYSICS (GCE “O” Level Science)Chew, Charles, Chow Siew Foong, and Dr. Ho Boon TiongMarshall Cavendish Education, Singapore (2007)

PHYSICS MATTERS (GCE “O” Level)Chew, Charles, Chow Siew Foong, and Dr. Ho Boon TiongMarshall Cavendish Education, Singapore (2007)

INVESTIGATING PHYSICSPoh Liong Yong and Yau Ming ChinOxford University Press, Singapore (1998)

Online Resources:

http://en.wikipedia.org/wiki/Hooke%27s_lawhttp://asms.k12.ar.us/classes/physics/GENERAL/KENNETH/HOOKE.HTMhttp://webphysics.davidson.edu/applets/animator4/demo_hook.html

Acknowledgements

Many THANKS to:

•FP Office, for all the financial support during our stay and study here at Singapore…

•Dr. Augustine Tan, for providing all the knowledge and skills I need in this endeavor…

•Lionel, for unselfishly providing all the materials in the Physics laboratory...

•NIE Library and staff, for providing all the necessary references I needed…

•Google, for becoming a very powerful search engine to all my researches…

•My mom, Elizabeth, for all the love, moral support and prayers…

•The Almighty God, for bestowing upon me all these blessings.