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PHYS204 Physics Lab 2 - Hooke's Law and Force Constants

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Course
PHYS204 (PHYS204)

Institution
Athabasca University (AU )

In this experiment you will study the stretching response of a rubber band (or a spring) and compare the observed behaviour with the predictions of Hooke’s Law.

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Uploaded on April 7, 2023
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PHYS204 – Physics for Scientists and Engineers I

Lab Manual V2.0

Experiment 2: Force Constant

, Experiment 3: Force Constant

INTRODUCTION

The purpose of this lab is to investigate and analyze the response of varying weights on a rubber band, to
compare these observations with Hooke’s Law, and to ultimately calculate a ‘k’ constant.

A 17th century physicist named Robert Hooke developed the theory that the amount or distance that a
spring is compressed or stretched is proportional to the force required to do so. Hooke’s law can be
applied to any elastic object, as long as compression and the stretching can be expressed by a single
positive or negative number, and can be observed with the plucking of a guitar string or the stress placed
on a steel beam.

Hooke’s law is stated as 𝐅⃑𝐬 = 𝐤𝐱 (with units N/m/m), where ⃑F⃑s is the applied force, the ‘x’ is the
displacement of the elastic from its original resting spot (state of equilibrium), and the ‘k’ is a constant
that is particular to each type of spring or elastic material, and describes the stiffness, dimensions, and
shape of the material. The stiffer the material, the larger the ‘k’ value.

This formula indicates that the applied force is proportional to the displacement that the elastic material
will experience. Thus, every time the force is doubled, the displacement is doubled.

Hooke’s law can also be stated as 𝐅⃑𝐬 = −𝐤𝐱, where the applied force is now the ‘restoring force’,
indicated with the negative sign because this force acts in the opposite direction of the displacement.
Hooke’s law also changes slightly when applied to masses hanging from springs or elastics. The gravitation
force, 𝐦𝐠⃑⃑, has to be accounted for, and so 𝐅⃑𝐬 = −𝐤𝐱 becomes 𝐦𝐠 ⃑⃑ = −𝐤𝐱.

One note to keep in mind is that elastic materials have their limits. Many materials, in reality, will
irreversibly deform (at their elastic limit) or break (at their yield point) if too much force is applied.

PROCEDURE

To begin this experiment, follow the steps below:

1. Gather together 2-3 rubber bands that are approximately 20 cm long, 10 identical coins, a small
resealable bag to hold the coins, a measuring tool, a camera, and a computer/laptop with Logger Pro.

Fig.1. – Experiment Tools

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