# Applying Hooke's Law: Make Your Own Spring Scale

Difficulty | |

Time Required | Very Short (≤ 1 day) |

Prerequisites | None |

Material Availability | Readily available |

Cost | Low ($20 - $50) |

Safety | Minor injury possible |

## Abstract

Hooke's law says that the opposing force of a spring is directly proportional to the amount by which the spring is stretched. How accurately Hooke's law describe the behavior of real springs? Can springs be used to make accurate scales for weighing objects? Spring into action and find out for yourself with this project.## Objective

The goal of this project is to investigate Hooke's law and see how a spring can be used to weigh objects.

## Credits

Andrew Olson, Ph.D., Science Buddies

Sources

This project is based on:

- Stanbrough, J.L., 2006. "Dynamics: Hooke's Law Experiment," Batesville High School, Batesville, IN [accessed June 13, 2007] http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Newton3/Labs/SpringScale.html.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.Last edit date: 2013-02-16

## Introduction

Under some conditions, a spring has an interesting property that was discovered by the physicist Robert Hooke. The property is described by an equation now known as Hooke's law. Hooke's law says that the restoring force (*F*) produced by the spring is proportional to the distance by which the spring has been lengthened (*x*). In equation form, Hooke's law looks like:

*F*= −

*kx*.

*F*) of the spring is equal to the spring constant (

*k*, a measure of the stiffness of the spring) times the distance (

*x*) that the spring has been stretched. The minus sign says that the force is exerted in the opposite direction of the stretching. In other words, if you stretch the spring out, the spring force is pulling back in the other direction.

As anyone who has stretched a Slinky® a bit too much knows, if you pull the spring *too* far, Hooke's law no longer applies. The part of the spring that is stretched too much doesn't spring back any more, because the stretching went beyond the *elastic limit* of the spring material. When this happens, the spring usually ends up with a visible kink where the excessive stretching occurred. So there are certainly some conditions where Hooke's law doesn't apply.

This experiment is to test whether Hooke's law accurately describes the stretching of a spring over some range. Can you calibrate a spring and then use it to weigh objects of unknown mass? Try it for yourself and find out.

## Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:

- Physics of springs
- Hooke's law
- Spring constant
- Elastic limit
- Force of gravity

Questions

- What happens when a spring is extended beyond its elastic limit?

## Bibliography

- Here is a brief introduction to Hooke's Law:

Krowne, A., 2005. "Hooke's Law," PlanetPhysics.org [accessed June 13, 2007] http://planetphysics.org/encyclopedia/HookesLaw.html. - You might also be interested in the Science Buddies resource, Stress, Strain and Strength.
- For more advanced students, this high school physics tutorial on Newton's second law of motion can help you understand how to convert from units of mass (hanging from the spring) to units of force (mass × acceleration due to gravity):

Henderson, T., 2004. "Newton's Second Law," The Physics Classroom, Glenbrook South High School, Glenview, Illinois [accessed June 13, 2007] http://www.glenbrook.k12.il.us/gbssci/Phys/Class/newtlaws/u2l3a.html. - This project is based on:

Stanbrough, J.L., 2006. "Dynamics: Hooke's Law Experiment," Batesville High School, Batesville, IN [accessed June 13, 2007] http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Newton3/Labs/SpringScale.html.

## Materials and Equipment

To do this experiment you will need the following materials and equipment:

- Several springs with different lengths, diameters, and stiffness
- Weights to hang from springs, here are some tips:
- You can use metal weights, or hang a container from the spring and fill it with glass beads, water, or sand
- The appropriate weight to be used with each spring depends on the stiffness of spring, you'll have to use your best judgment

- Sturdy support from which to hang the springs, for example:
- Wood
- Sturdy cup hook
- Clamp
- Screw the cup hook into one end of the piece of wood
- Clamp the other end of the wood to a table or workbench
- Hang the spring from the cup hook
- The clamp and wood will both need to be strong enough to support the weights you intend to hang from your springs

- Kitchen scale for measuring actual mass of weights used
- Metric ruler

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Experimental Procedure

- Do your background research so that you are knowledgeable about the terms, concepts, and questions, above.
- For each spring, do the following steps:
- Hang the spring from a sturdily-mounted hook.
- Measure the length of the spring with no weight hanging from it. Always measure between the same two points on the spring (you may even want to mark them).
- Hang a weight from the spring, and wait for it to settle.
- Again measure the length of the spring.
- Measure the mass of the weight, using the kitchen scale.
- Repeat for a series of different weights.
- Remove the weight from the spring, and check to make sure that the spring returns to its initial length.
- Do at least three trials for each spring.

- Keep track of your results in a table like this one:
Weight

(g)Length of spring

(cm)Average

(cm)Change in length

(cm)Trial #1 Trial #2 Trial #3 0 — 5 10 20 40 0 — - To calculate the change in length, subtract the average length of the spring with no weight (0 g) from the averaged measured length for each of the other weights.
- For each spring, make a graph of the change in length of the spring (in cm, y-axis) vs. the mass of the weight hanging from the spring (in g, x-axis).
- More advanced students should graph the change in length of the spring (in cm, y-axis) vs. the force on the spring (in newtons, x-axis). The force on the spring in newtons can be obtained by multiplying the mass (in kg) by the acceleration due to gravity: 9.8 m/s
^{2}. Remember that to convert g to kg, you have to divide by 1000. - From your graph, does it appear that your spring is following Hooke's Law?
- What is the spring constant (
*k*) for each spring? - With the help of the matching graph, can you use your spring to measure the weight of another object? Check how accurate your measurement is by weighing the object on the kitchen scale.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Variations

- For a more advanced experiment using a spring-based mechanical model of the human knee, see the Science Buddies project Deep Knee Bends: Measuring Knee Stress with a Mechanical Model.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Ask an Expert

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