Nanyang Technological University NATIONAL INSTITUTE OF EDUCATION Singapore Project Work in
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Transcript of Nanyang Technological University NATIONAL INSTITUTE OF EDUCATION Singapore Project Work in
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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
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Background Information
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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.
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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.
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Title
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SPRING CONSTANT k OF A SINGLE SPRING AND TWO SPRINGS IN SERIES: A Comparative Study
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Objectives
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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
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Resources
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Resources:
Metal springs
Retort stand
Meter rule
Mass hanger
Set of masses
Pointer (can be improvised)
Physics books, journals, or magazines
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Methodology
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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.
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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.
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4) Calculate the elongation of the spring, Δl.
5) Plot a graph of the mass against elongation.
6) Calculate the gradient from the graph.
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7) Repeat steps 1-6 using two metal springs connected in series.
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Results & Discussions
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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
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0 5 10 15 20 250
50
100
150
200
250
300
m vs. Δl(single spring)
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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
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0 5 10 15 20 25 30 35 40 45 500
50
100
150
200
250
300
m vs. Δl(2 springs in series)
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Conclusions & Recommendations
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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.
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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.
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References
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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
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Acknowledgements
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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.