Physics Lab Report: Hooke’s Law

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Table of Contents

Introduction
Objectives
Materials
Preliminary Set Up and Questions
Procedure
Data Tables
Analysis
Conclusion
Appendixes
Reference

Introduction

When a string or an elastic material is pulled, it extends in proportion to the force exerted until the elastic limit is exceeded. In response to the pulling force, a restoring force is equal to the compression or extension force. The direction of force, that is, compression or stretching force determines the sign on the equation.

In essence, the restoring force is equal and in opposite direction to the force exerted on the elastic material.

F=kx- (i)
F=-kx- (ii)

The first equation represents extension/stretching, while the second equation represents compression. These equations are only valid for as long as the force exerted does not exceed the material’s elastic limit (Mazur, 2014). In the equations above, F represents the force exerted, k is the spring constant given in N/M, and x is the extension or compression given by the difference between the new and original lengths of the material.

Objectives

To experimentally determine the relationship between the force exerted on a spring and the extension or compression produced
To determine the spring constant from graphical data

Materials

A vertically-hanging spring	Different masses
A ruler

Preliminary Set Up and Questions

Different elastic materials have different spring constants, implying that they react differently to forces exerted on them. Again, one may not easily tell the value of a material’s spring constant since many are not labeled. For this reason, an experiment on Hooke’s law enables one to generate mass vs. extension/compression change and plot a graph. The graph’s slope can then be calculated to give the spring constant. The three main elements studied in this experiment are mass, force, spring constant, and extension.

Element	Description	SI unit
mass	Is defined as how heavy a given material is. It is the amount of matter in an object.	Kg
force	Force is the weight of an object due to gravitational acceleration. It is given by the product of mass and the average gravitational acceleration.	N
Spring constant	The spring constant defines the spring’s resistance to change.	N/M²
Extension/compression	The difference between the original and new length.	m

Procedure

Hang the spring on a vertical plane
Measure its initial length
Hang one mass
Record the new length
Calculate the difference between the initial and new lengths
Repeat the procedure with different masses while recording the new lengths
Record the extension by subtracting the new length from the initial in each measurement
Plot a graph of the extension, x, versus the mass
Calculate the spring constant from the slope of the graph

Data Tables

First trial
M1	0.2
M2	0.1
X1	0.06
X2	0.12
Second trial
M1	0.2
M2	0.07
X1	0.06
X2	0.18
Third trial
M1	0.2
M2	0.2
X1	0.06
X2	0.06

x	m
0.06	0.2
0.12	0.1
0.18	0.07

Analysis

The data collected and the graph above show a linear relationship between the mass and the extension. Three different masses were used: 0.07. 0.1, and 0.5 Kg and the relative extensions measured. The straight line shows a linear relationship implying that the spring constant was not exceeded, that is, the masses were lighter than that required to completely cause a deformation. The spring constant is calculated as the slope of the graph as shown below:

F=kx
F=mg

In this experiment, the gravitational acceleration, g was used as 10 N/Kg

From the above equation, the spring constant can be derived from the equation for force.

K=df/dx
K=10. (0.2-0.1)/(0.06-0.12)=0.1/0.-06= -1.667

The spring constant k=1.667N/m²

Since the value is a constant for a particular spring, it has no negative values. In the first two trials, different masses were used to show the variation between mass and extension. The third trial was used as a control experiment in which the same mass was used twice to show that no change in extension would occur unless an extra weight was added. In essence, although one experiment would give sufficient results, the three trials were important to confirm the application of Hooke’s law. In the above equation, the gravitational acceleration was a constant value of 10N/Kg. For this reason, the varying factors were only the mass and extension.

Conclusion

Hooke’s law is one of the fundamental principles in physics that defines the relationship between mass exerted and the extension/compression of an elastic material. Mass is the quantity of matter in an object, given in Kg. Every free object is acted on by the gravitational force of acceleration, giving its weight. According to Hooke’s law, whenever weight is exerted on a vertically hanging spring, it extends. The extension is directly proportional to the force exerted, in the case of a pulling force. If a compression force is used, then the spring shrinks in size in a measure proportional to the force. The direction of the restoring force is always opposite to the force acting on the spring. In this experiment, three different masses were used in three trials, and the data was recorded for graphical representation. The graph shows a linear relationship between mass and extension, with its slope giving the spring’s constant.

Appendixes

Basic definitions

Hooke’s law

A law that states that extension is directly proportional to the applied force

Mass

Quantity of matter

Extension

The difference in the length after application of weight on a spring

Equations

F=kx
K=df/dx
F=force exerted on the spring, K=spring constant, x= the extension

Reference

Mazur, E. (2014). Principles and practice of physics. Addison-Wesley Professional.

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