Written by Ben Finio and Science Buddies

**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 made use of a spring! Springs are in machines all around us and have many useful purposes. In this activity you will learn another cool use for a spring: making a scale to weigh objects.

**Background**

Springs are usually spirals made out of metal. They have the useful property that they are very stretchy—the scientific term for this is

*elastic*. If you squish a spring or pull on it, then let go, it will bounce back to its original shape. There are limits to this behavior, however. If you pull (or push) too much, you might take the spring past its

*elastic limit*. After that point, there will be some permanent change—or deformation—in the spring, and it will not fully recover its original shape.

Luckily, 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 (how hard the spring pushes or pulls to get back 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 as F = kx, where

*F*is force,

*x*is the spring’s change in 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*remains the same as long as you stay within the spring's elastic limit. This makes Hooke's law useful because if you can measure either the force or change in length, you can use the spring constant to calculate the other value.

You might think of a scale as something that you stand—or place objects—on, measuring mass

*pushing*down on it. But you can also weigh objects from a hanging scale, in which mass

*pulls*on it. In this project you will make a simple spring scale by hanging weights from a spring. First you have to calibrate the scale using known weights, but after that you can measure the weight of an unknown object by hanging it from 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 some toys—with permission, of course. Ask an adult to help you take apart a pen or toy if necessary.)
- Paper clips
- Small plastic bucket or a paper or plastic cup with string tied through holes near the top to form a handle
- Objects to use as weights, such as coins (The weight of the objects you use will depend on how strong your spring is.)
- Kitchen scale
- Ruler
- Paper and pencil or pen
- Various small household objects to measure

**Procedure**

- Play with your spring using your hands to get a sense for how strong it is. How hard do you have to push on it to compress it? How hard do you have to pull on it to stretch it out? Be careful not to push or pull on it so hard that you go past its elastic limit and permanently deform it, but this should give you a good idea of how heavy your weights should to be.
- Hang your spring vertically from one of the paper clips by hooking the second coil of the spring with an end of the paper clip. (You might want to bend the end of the paper clip out a bit to make it easier to hook the spring.) You can hold the paper clip with your hand—or clip it on to something such as a hook, if available.
- Use the ruler to measure the length of the spring with no weight hanging from it. Write this number down.
- Now, use a second paper clip, looped onto the second-from-the-bottom coil, to hang your bucket or cup from the bottom of the spring.
- Add a few weights (such as coins) to the bucket or cup. Add enough weight that the spring stretches out a bit and you can measure a change in length. Exactly how much you need to add to see a change will depend on your spring. Be careful not to add so much weight that you stretch the spring past its elastic limit and permanently deform it. How does the spring stretch as you add weight?
- Measure the new length of the spring and write this number down.
- Remove the bucket or cup from the spring and weigh it, including the weights, using the kitchen scale. Write this number down next to the distance you just measured.
- Repeat this process and add a few more weights to the bucket or cup. Write down the new length of the spring and the new weight.
- Repeat the measurement a few more times until you have a few data points. Be careful not to add too much weight and permanently stretch the spring. What happens to the distance as you keep adding weight?
- Now, try to figure out the weight of another object without using your kitchen scale. Can you do it using the data from the experiment you just did?
- Hang the object from your spring and measure how far the spring stretches. Then, compare this distance with the distances you recorded during your experiment and look up the corresponding weight. (This will be easier if you have a graph; see first "extra" below.) How much does the object weigh according to your data? Now measure it on the kitchen scale—how close were you?
- Repeat this process with a few more objects and compare the weights you look up using your spring scale with what you measure with your kitchen scale. How accurate is your scale? If it's good enough, perhaps you can keep it around for use in the kitchen or for other activities!
**Extra:**Make a graph of your data, with distance on the x axis and weight on the y axis. This will make it easier to determine the weight of other objects. Is your graph a straight line?**Extra:**Using Hooke's law and your data, can you calculate the spring constant, k, for your spring? Hint: k is the slope of a graph of force versus distance.**Extra:**What happens if you stretch the spring past its elastic limit, but continue the activity trials?**Extra:**Can you figure out how to do the same activity by pushing on the spring (compression) instead of pulling on it (tension)? Hint: This may be difficult because the spring will buckle or suddenly bend in half. You can prevent this by constraining the spring's motion somehow (such as putting it inside the body of a click pen or other cylinder).

**Observations and results**

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

Once you have collected a few data points, this allows you to easily "look up" the weight of a new object simply by using a ruler to measure the change in the spring’s length. This is how real spring scales work—the springs are calibrated so that when they are stretched by a certain amount, it corresponds to a known weight. This fails, however, if you stretch a spring beyond its elastic limit. That will cause some permanent change in the spring's shape, so it will not return to its original length and your measurements are no longer valid.

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