1. Nanyang Technological University NATIONAL INSTITUTE OF EDUCATION Singapore Project Work in P H Y S I C S Presented by: RONALD P. DIANA Participant, NIE-LEAP-CTP-2009 Presented to: DR. AUGUSTINE TAN TUCK LEE Professor, Physics Content and Pedagogy November 2009

2. Background Information

3. 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.

4. 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.

5. Title

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

7. Objectives

8. 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

9. Resources

10. Resources: Metal springs Retort stand Meter rule Mass hanger Set of masses Pointer (can be improvised) Physics books, journals, or magazines

11. Methodology

12. 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, l o.

13. 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.

14. 4) Calculate the elongation of the spring, Δl. 5) Plot a graph of the mass against elongation. 6) Calculate the gradient from the graph.

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

16. Results & Discussions

17. Mass, m (g) Scale Reading, l (cm) Elongation, Δl (cm) 123Average 5020.021.021.220.7 0.8 10021.622.822.922.4 2.5 15027.428.528.628.2 8.3 20033.834.8 34.5 14.6 25040.441.0 40.8 20.9 A. SINGLE SPRING: Initial length, l o = 19.9 cm

19. Mass, m (g) Scale Reading, l (cm) Elongation, Δl (cm) 123Average 50 42.041.842.041.90.3 100 46.947.0 5.4 150 59.5 59.659.517.9 200 72.572.4 30.8 250 85.685.7 44.1 B. TWO (2) SPRINGS IN SERIES: Initial length, l o = 41.6 cm

21. Conclusions & Recommendations

22. 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.

23. 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.

24. References

25. References: Published Resources: DISCOVER PHYSICS (GCE “ O ” Level Science) Chew, Charles, Chow Siew Foong, and Dr. Ho Boon Tiong Marshall Cavendish Education, Singapore (2007) PHYSICS MATTERS (GCE “ O ” Level) Chew, Charles, Chow Siew Foong, and Dr. Ho Boon Tiong Marshall Cavendish Education, Singapore (2007) INVESTIGATING PHYSICS Poh Liong Yong and Yau Ming Chin Oxford University Press, Singapore (1998) Online Resources: http://en.wikipedia.org/wiki/Hooke%27s_law http://asms.k12.ar.us/classes/physics/GENERAL/KENNETH/HOOKE.HTM http://webphysics.davidson.edu/applets/animator4/demo_hook.html

26. Acknowledgements

27. 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.