Hooke's law lab report. Hookes law and the investigation of spring constant k
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Hooke's law and the investigation of spring constant k * Aim To examine Hooke's law and to determine the value of spring constant k. * Introduction Robert Hooke (1635-1708) was born at Freshwater, Isle of Wight, son of John Hooke, curate at All Saints' Church . He was one of the most brilliant and versatile of seventeenth-century English scientists, who discovered the law of elasticity. Between 1658 and 1678 Robert Hooke worked on his invention of the watch-spring and developed his theory of elasticity, now known as Hooke's law. Hooke's law states that "the extension of a helical spring is directly proportional to the weight applied, provided the elastic limit of the spring is not exceeded."  However, the limitation of this law is if the spring is stretched beyond its elastic limit, meaning that there is a limit to a spring where if you stretch it too much it will deform, thus the spring will have a new spring constant.
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.
Extension e ±0.001(m) Mass (kg) Weight (N) 58 0.058 0.2 1.96 92 0.092 0.4 3.92 125 0.125 0.6 5.88 160 0.16 0.8 7.84 194 0.194 1 9.8 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 * * Estimation of errors: * Percentage of errors: * Discussion 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.
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