Historical background: Hooke was never a person who did one thing at a time; indeed he seemed at his best when his mind was jumping from one idea to another. At the same time that he was working on the air pump he was also thinking about clocks and how they could be used in determining the longitude at sea. Realising the weakness of the pendulum clock in keeping time on a ship which was pitching and tossing, he wondered about the:-
... use of springs instead of gravity for making a body vibrates in any posture.
Rather than the balance wheel being controlled by a pendulum which in turn operated through gravity, he reasoned that controlling the balance wheel with a spring would have huge advantages for a portable timekeeper that one might carry around or one which would have to continue to keep the correct time on a ship. Beginning his experiments around 1658 he had made two significant steps by 1660, namely the use of a balance controlled by a spiral spring and an improved escapement called the anchor escapement. In 1660 he discovered an instance of Hooke's law while working on designs for the balance springs of clocks. However he only announced the general law of elasticity in his lecture of spring given in 1678.
Young’s modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. Sometimes referred to as the modulus of elasticity, Young’s modulus is equal to the longitudinal stress divided by the strain. Stress and strain may be described as follows in the case of a metal bar under tension. Thus Young’s modulus may be expressed mathematically as:
*where
This is a specific form of Hooke’s law of elasticity.
The equipments needed in the experiment are a spring; a number of weights which each of them is 100gram heavy; a meter ruler; a ring stand; clamps; notebook and pencil. They were placed as shown in the diagram.
To begin the investigation, the spring was attached to the ring stand. Next, two of the 100-gram loads were hung under the spring and the ruler was used to measure the extension of this spring. Subsequently, 2 more loads were added and the process of measurement was repeated. The number of loads was continuously increased until the total mass reached 1 kg. Between each time changing the weight, the results were recorded and then written down in the form of a table.
Diagram 1. The arrangement of apparatus (BHS Physics, 2002)
Table 1. Data collected from the experiment
Trend line k = 57.6 N/m
k max = 58.3 N/m
k min = 56.1 N/m
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Estimation of errors:
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Percentage of errors:
The experiment was done smoothly and carried out the precise results. The results show the obedience to Hooke’s law, which means the force applied is directly proportional to the displacement. The value of R2 is also close to 1, which implies that the trend line is very linear. During the experiment, astonishing situations did not arise, or no anomalous features of data found. However, the spring sometimes was unstable as it moved up and down, especially when the weight was just added, making it hard to check the extension. Therefore, the errors which occurred should be mainly due to parallax. The solution to this problem could be waiting for the spring to be stable, then do the measurement.
Introduction. http://www.roberthooke.org.uk/intro.htm
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It’s a spring thing. http://www.hookeslaw.com/hookeslaw.htm
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[5]Robert Hooke, Hooke's Law & the Watch Spring http://www1.umn.edu/ships/modules/phys/hooke/hooke.htm
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Physics 1 Dynamics Experiment How Does A Spring Scale Work? Hooke's Law
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