Hookes Law- to determine the spring constant of a metal spring

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IB Physics Investigation – Mechanics

Title: Hooke’s Law- to determine the spring constant of a metal spring

  1. BACKGROUND/ INTRODUCTION

A branch of the mechanical energy, elastic potential energy is one of the fundamental base energy concepts that is very commonly used in the modern technology. Elastic potential energy deals with the elasticity of an object (e.g. to what extent a string can be stretched?), and it’s used in a wide range of everyday life situations; such as in the process of decelerating an airplane landing on an aircraft ship. And the type of strings used there, is regarded to the spring constant of that string, in which it may or may not be able to stop an airplane within a certain distance.

Under investigation of Hook’s Law, the aim of this experiment is to determine different spring constants of some springs, and that is done by measuring how far a spring stretches when a certain amount of mass added. In order to find the spring constant, we investigate it by rearranging energy formulas and basic knowledge:

  • The general formula for Energy is , where  is force and  is displacement.
  • The formula for Elastic Potential Energy is , where  is
  •  the spring constant and  is

the extension of the spring.

  • The relation between the two formulas is that  (displacement) is equal to  (extension) since both have the same units (measured in meters). Therefore, we can state that
  • The area under the a Force-Extension () graph gives the work done on the spring and therefore, the Elastic Potential Energy (). Since it’s the area of a triangle, then
  • From the graph, we know that , then . Therefore if we substitute this into the first formula () we get  and that is equal to
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From this information we can extract that , the spring constant can be found as follows:

  1. Measure the force and extension of the spring
  2. Plot a  graph
  3. Find the slop of the graph, which is , the spring constant

  1. QUESTION

What is the role of the spring constant in the relationship of force and extension and how can it be determined?        

  1. HYPOTHESIS

The independent variable of this experiment is Mass (the number of masses added) and the dependent variable is Extension (the extension of the spring). The control variables ...

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