**Key concepts**

springs

Elasticity

Weight

Distance

**introduction**

Have you ever played with a Slinky, used a pinball machine, written with a click pen, or ridden in a car? If so, then you have used a spring! Springs are in machines all around us and have many useful functions. In this activity, you will learn another interesting use of a spring – making a scale to weigh objects.

**Background**

Springs are usually metal spirals. They have the useful property that they are very extensible – the scientific term for this is *elastic*. If you crush a spring or pull on it and then release it, it will return to its original shape. There are limits to this behavior, however. If you pull (or push) too much, you risk causing the spring to protrude. *Elastic limit*. After this point, there will be a permanent change – or deformation – in the spring, and it will not fully return to its original shape.

Fortunately, the elastic behavior of a spring is defined by a well-known equation called Hooke’s Law, which states that the restoring force of a spring (the force with which the spring pushes or pulls to return to its original length ) is proportional to the distance the spring has been stretched (or compressed) from its original length. This law is expressed mathematically by F = kx, where *F* is the force, *X* is the change in spring length and *k* is a number called the spring constant, which is different for springs of different sizes or materials. For a given spring, however, *k* stays the same as long as you stay within the elastic limit of the spring. This makes Hooke’s Law useful because if you can measure the force or the change in length, you can use the spring constant to calculate the other value.

You might think of a scale as something you stand on or place objects on, measuring mass *to push* down on it. But you can also weigh objects from a hanging scale, in which the mass *drawn* above. In this project, you will make a simple spring scale by hanging weights on a spring. First you need to calibrate the scale using known weights, but after that you can measure the weight of an unknown object by hanging it on the spring and measuring how far the spring stretches.

**Materials**

- A spring (You can find a selection of springs at a hardware store or get one by disassembling a click pen or toys, with permission of course. Have an adult help you take a pen or toy apart if necessary .)
- Paper clips
- Small plastic bucket or paper or plastic cup with a string tied through holes near the top to form a handle
- Items to use as weights, such as coins (The weight of the items you use will depend on the strength of your spring.)
- Kitchen scale
- Rule
- Paper and pencil or pen
- Various small custom-made household items

**Procedure**

- Play with your spring using your hands to get a feel for its strength. How much pressure does it take to compress it? How much do you have to pull on it to stretch it? Be careful not to push or pull on it enough to exceed its elastic limit and permanently deform it, but this should give you a good idea of how heavy your weights should be.
- Hang your spring vertically on one of the paper clips by hooking the second coil of the spring with one end of the paper clip. (You may want to bend the end of the paper clip a bit to make it easier to hook the spring.) You can hold the paper clip with your hand or hang it on something like a hook, if available.
- Use the ruler to measure the length of the spring without any weight hanging from it. Write down that number.
- Now use a second paper clip, coiled onto the second spool from the bottom, to hang your bucket or mug on the bottom of the spring.
- Add some weights (like coins) to the bucket or mug. Add enough weight so that the spring will stretch a bit and you can measure a change in length. The exact amount you need to add to see a change will depend on your jurisdiction. Be careful not to add too much weight to the point of stretching the spring beyond its elastic limit and permanently deforming it.
*How does the spring stretch when you add weight?* - Measure the new length of the spring and write down that number.
- Remove the bucket or cup from the spring and weigh it, including the weights, using the kitchen scale. Write this number next to the distance you just measured.
- Repeat this process and add a few more weights to the bucket or mug. Note the new spring length and the new weight.
- Repeat the measurement several times until you have a few data points. Be careful not to add too much weight and to permanently stretch the spring.
*What happens to the distance as you continue to add weight?* - Now try to determine the weight of another object
*without*using your kitchen scale.*Can you do this using the data from the experiment you just did?* - Hang the object on your spring and measure how far the spring extends. Then compare this distance with the distances you recorded in your experiment and find the corresponding weight. (This will be easier if you have a chart; see the first “extra” below.)
*How much does the object weigh according to your data? Now measure it on the kitchen scale: how far away were you?* - Repeat this process with a few more items and compare the weights you are looking for using your spring scale with what you are measuring with your kitchen scale.
*How accurate is your scale? If it’s good enough, maybe you can save it to use in the kitchen or for other activities!* **Additional:**Graph your data, with the distance on the*X*axis and weight on the*Yes*axis. This will make it easier to determine the weight of other objects.*Is your graph a straight line?***Additional:**Using Hooke’s law and your data, can you calculate the spring constant,*k*, for your spring? Index:*k*is the slope of a graph of force versus distance.**Additional:**What if you stretch the spring beyond its elastic limit, but continue activity testing?**Additional:**Can you figure out how to do the same activity by pushing on the spring (compression) instead of pulling on it (tension)? Tip: It can be difficult because the spring will suddenly deform or bend in half. You can prevent this by limiting the movement of the spring in some way (for example, placing it inside the body of a click pen or other cylinder).

**Observations and results**

While the exact weights and distances you measure depend on the individual spring, in general you should see that any spring follows Hooke’s Law in its elastic limit. This means that the relationship between weight and distance is linear – if you double the weight, the amount of spring stretch will double. For example, let’s say your spring has an unstretched length of 10 centimeters. When you add a certain amount of weight, it stretches up to 11 centimeters (a change of one centimeter from its unstretched length). When you add double that weight, it should stretch up to 12 centimeters (a change of two centimeters from its unstretched length).

Once you’ve collected a few data points, this allows you to easily “find” the weight of a new object just by using a ruler to measure the change in spring length. This is how real spring scales work: the springs are calibrated so that when stretched by a certain amount, it corresponds to a known weight. This fails, however, if you stretch a spring beyond its elastic limit. This will cause a permanent change in the shape of the spring, so it will not revert to its original length and your measurements will no longer be valid.

**More to explore**

How Does a Spring Scale Work ?, from Batesville High School, by Jerry Stanbrough

Applying Hooke’s Law: Create Your Own Spring Scale, from Science Buddies

Science activities for all ages, by Science Buddies

*This activity is offered in partnership with Science Buddies*