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Hooke's Law

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Introduction

Hooke’s law: determining k for a spring

Aim:

To investigate Hooke’s law for simple springs of rubber

Hypothesis:

The relationship between a load force and a light spring (F=k.x) was first determined by Robert Hooke in the 17th century.Where F is the force applied to the spring, k is the spring constant, and  x is the extension of the spring. Hooke’s law states that when an elastic material is subjected to a force, its extension (x) is proportional to the applied force. The value of k is constant for a particular spring.

Variables:

 Independent Controlled Dependent Different type of spring used (varied by using different springs) Weight of the mass attached (controlled by using only one mass) Spring constantExtension by the spring (measure by ruler)

Materials:

 Item Quantity Accuracy Spring with different stiffness 5 - Retort stand and clamp 1 - Meter rule or other measuring devices 1 ±0.005 m Mass hanger 1 - 50 gr masses 10 Δm ±0.05 gr balance 1 -

Methods:

1. First weigh and record the masses of each mass hanger and the masses
2. Record these in a suitable for reference during the activity

Middle

0.144

3

0.15

0.145

4

0.20

0.184

5

0.25

0.240

6

0.30

0.291

7

0.35

0.350

8

0.40

0.402

9

0.45

0.469

10

0.50

0.524

Table 3.6 Data of spring 5 extension

 Trial (n) Massm (kg) Suspended Lengthx2 (m)Δx2=±0.0005m 1 0.05 0.179 2 0.10 0.196 3 0.15 0.221 4 0.20 0.246 5 0.25 0.274 6 0.30 0.301 7 0.35 0.328 8 0.40 0.355 9 0.45 0.381 10 0.50 0.412

Data processing:

k= (Δm/Δx) x g

Table 4.1 Data of spring 1 extension

 Trial(n) Massm (kg) Pulling forceF (N) Suspended Lengthx2 (m)Δx2=±0.0005m 1 0.05 0.49 0.140 2 0.10 0.98 0.141 3 0.15 1.47 0.145 4 0.20 1.96 0.177 5 0.25 2.45 0.235 6 0.30 2.94 0.289 7 0.35 3.43 0.346 8 0.40 3.92 0.401 9 0.45 4.41 0.465 10 0.50 4.90 0.533 Spring’s constant: Table4.2 Data of spring 2 extension

 Trial(n) Massm (kg) Pulling forceF (N) Suspended Lengthx2 (m)Δx2=±0.0005m 1 0.05 0.49 0.158 2 0.10 0.98 0.158 3 0.15 1.47 0.172 4 0.20 1.96 0.236 5 0.25 2.45 0.292 6 0.30 2.94 0.367 7 0.35 3.43 0.426 8 0.40 3.92 0.487 9 0.45 4.41 0.558 10 0.50 4.90 0.635 Spring’s constant: Table4.

Conclusion

th spring that is very stiff (18.679) and on the other hand in 3rd spring that is the least stiff (3.584).

The difficulties encountered in conducting this experiment is when measuring the extension of the spring, as the spring tend to swings when the mass is attached and this can affect the result of the experiment. In addition, the extension of the spring occasionally hits the floor when the number of mass is increased and this affected the results. This difficulty has been solved by using a retort stand and clamp, which give an increase the stretch of the spring but still easily adjusted.

In conclusion, it could be said that the experiment is successful in verifying value of the spring constant. Both the Hooke's law and the graph give similar result, thus proving the hypothesis. My suggestion to improve the experiment is to carefully measure the extension of the spring despite the variation of the spring. This is best dealt with by carefully observed the spring until it places perfectly so that there will be no further movements that may lead to the mistake in calculating the exact extension of the spring.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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