Experiment 2:Hooke’s Law
Experiment by: Group 37
Tshepiso Mokwena: 50456245
Ephriam Kyere: 45274452
Mpumelelo Nkabinde:35107707
Kganya Velempini:53365690
Isaac Manamela:52601196
Neo Khanyile:52431320
Nkateko Vuma:48053635
Supervisor
Dr. Peter O:
(23 May 2024)
Contents
Abstract
ii
Introduction
1
Aim
3
Apparatus
4
Method
4
Analysis
7
Conclusion
8
Questions and Answers:
9
i
Abstract
Hooke’s Law is a fundamental principle in mechanics and materials
science, which states that the force required to extend or compress a
spring by some distance is proportional to that distance. This linear
relationship is typically expressed as:
F = kx, where F is the force applied to the spring,
x is the displacement of the spring from its equilibrium position,
and
k is the spring constant, a measure of the stiffness of the spring.
Hooke’s Law is named after the 17th-century British physicist Robert
Hooke, who first formulated the principle in 1660.
This law is crucial for understanding elastic behavior in materials
and has broad applications in engineering, physics, and everyday life.
It forms the basis for the study of harmonic oscillators, which are
systems that experience restoring forces proportional to the displacement from equilibrium, and is instrumental in analyzing stress and
strain in materials.
One significant application of Hooke’s Law is in the design of mechanical systems that rely on spring-like components, such as vehicle
suspension systems, which absorb shocks and maintain contact with
the road. Additionally, Hooke’s Law is essential in the field of seismology, where it helps model the elastic properties of Earth’s materials
ii
during seismic events.
Recent research has extended Hooke’s Law to non-linear regimes
and complex materials, examining how deviations from linearity can
inform us about the material properties under large deformations.
Advances in computational methods and experimental techniques
have also enabled more precise measurements and applications of
Hooke’s Law in various scientific and engineering domains.
Understanding Hooke’s Law and its implications allows for the
development of more robust materials and systems, enhancing performance and safety across multiple industries. This abstract aims
to provide a comprehensive overview of Hooke’s Law, its theoretical foundation, practical applications, and ongoing research developments. (1)
iii
Introduction
Introduction Hooke’s Law is a cornerstone of classical mechanics and
materials science, postulating that the force needed to extend or compress a spring is directly proportional to the displacement from its
equilibrium position. Formally, this relationship is expressed as
F = −kx,
where F represents the applied force,
x denotes the displacement,
and
k is the spring constant, indicative of the stiffness of the spring.
This principle was first articulated by Robert Hooke in 1660 and
later published in 1678 in his work ”Lectures de Potentia Restitutiva,
or of Spring Explaining the Power of Springing Bodies” (7).
The simplicity and elegance of Hooke’s Law lie in its linearity,
making it a fundamental concept for studying the behavior of elastic
materials. It is foundational to the understanding of harmonic oscillators, systems that experience restoring forces proportional to their
displacement. This law is essential for analyzing stress and strain relationships in various materials, facilitating the design and evaluation
of structures and mechanical systems (2) (5).
Hooke’s Law’s applications are vast and varied, encompassing both
everyday scenarios and advanced engineering systems. For instance,
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vehicle suspension systems, which rely on spring mechanics to absorb shocks and ensure smooth motion, are directly designed using
principles derived from Hooke’s Law. In seismology, the law aids in
modeling the elastic properties of the Earth’s materials, enhancing
the understanding of seismic wave propagation and the behavior of
geological materials under stress (4).
Beyond these classical applications, modern research continues to
explore the limits and extensions of Hooke’s Law. Investigations into
non-linear elasticity and the behavior of materials under large deformations provide deeper insights into material properties and their
practical implications. Advances in computational methods and experimental techniques have significantly enhanced the precision with
which Hooke’s Law can be applied and tested in various scientific and
engineering contexts (3).
This introduction aims to set the stage for a comprehensive exploration of Hooke’s Law, delving into its theoretical underpinnings,
practical applications, and ongoing research developments that continue to expand its relevance in both classical and contemporary scientific inquiries.
2
Aim
To determine a spring-constant (k). This will be done through investigating Hooke’s law by attaching weights to a spring and observing how the displacement of the spring changes with the number of
weights attached to the spring (8)
3
Apparatus
1. 5x 100g mass(brass)
2. 1x Spring
3. 1x Stand with heavy base
4. 1x Transparent Scale with mm resolution
5. 1x Brightly colored stretch indicator
6. 1x Wire
Method:
1. Connect one end of the spring to the stand or support structure.
Ensure that it is securely fixed in place.(8)
2. Attach a wire hook to the free end of the spring. The wire hook
will serve as a platform for attaching the copper weights.(8)
3. Identify the position where the wire hook is at rest (with no additional weight attached). This is your zero displacement position;
mark this position on the spring or record its location.(8)
4. Hang the first copper weight on the wire hook and observe the
displacement of the spring from its rest position due to the weight
using the brightly colored stretch indicator.(8)
4
5. Repeat for Additional Weights:(8)
-Add the remaining copper weights, one by one, to the wire hook.(8)
-After attaching each weight, mark the new displacement of the spring.(8)
-Continue until all five copper weights are attached, resulting in six
measurements of displacement (including the zero position).(8)
6. Along with each displacement measurement, record the cumulative weight of the copper weights attached to the spring.(8)
5
Results
Restoring Force vs. Displacement
Restoring Force (N)
0
−2
−4
0
1
2
3
4
5
Displacement (m)
6
Figure 1: Restoring Force vs. Displacement
6
7
·10−2
Analysis.
Our experiment shows that Hooke’s Law works. We found that as
we pull the spring more (extension), it pulls back harder (force), just
like Hooke’s Law says. But this only works up to a certain point (the
elastic limit).
We did have some issues though. We might not have measured
the spring’s stretch perfectly, and we assumed the spring was perfect
with no friction or weight, which isn’t totally accurate.
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Conclusion.
In the end, our experiment showed that Hooke’s Law is correct and
we figured out the spring’s constant (how stiff it is). In the future, we
could test what happens when we stretch the spring past its elastic
limit (when it doesn’t bounce back).
8
Questions and Answers:
1. Is your data nicely described by the Eq. F(x)=mx+c? If not,
what is the reason for the discrepancy.
Answer:
Yes,
2. What is the value of the spring constant and its error, use the
standard scientific way of presenting a measurement and its error.
Answer:
3. What can be determined from the graph of force against extension?
Answer: The slope of the graph represents the spring constant, k,
which is a measure of the stiffness of the spring. It indicates how
much force is needed to produce a certain amount of extension. (6)
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Bibliography
[1] Atanackovic, T. M., Guran, A., Atanackovic, T. M. and Guran,
A. (2000), ‘Hooke’s law’, Theory of elasticity for scientists and
engineers pp. 85–111.
[2] Beer, F. P., Johnston, E. R., DeWolf, J. T. and Mazurek, D. F.
(2017), Mechanics of Materials, McGraw-Hill Education.
[3] Cioroianu, A. R., Harkness, P. and Connell, S. D. (2018), ‘Nonlinear elasticity: Theory and applications’, Journal of Physics D:
Applied Physics 51(48), 485302.
[4] Fitzpatrick, R. (2008), ‘Advanced calculus and its applications
to the engineering and physical sciences’, Cengage Learning .
[5] Gross, D., Hauger, W., Schröder, J., Wall, W. A. and Rajapakse,
C. (2004), ‘Engineering mechanics: Dynamics’, Springer Science
& Business Media 2.
[6] Halliday, D., Resnick, R. and Walker, J. (2017), Fundamentals
of Physics, 10th edn, John Wiley & Sons.
[7] Hooke, R. (1678), Lectures de Potentia Restitutiva, or of Spring
Explaining the Power of Springing Bodies, Royal Society.
[8] Prof Medupe, R. and Mr Nhlapo, M. (2021), First Year Physics
Laboratory Manual, NORTH WEST UNIVERSITY.
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