Science

You Need to Weigh Some Water. All You’ve Got Is a Paper Clip

OK, so you might need a couple other supplies, but your best option is to do what MacGyver would do: Turn it into a scale.
water
Photograph: MirageC/Getty Images

Let's suppose you need to measure the mass of some water, and you want to construct a scale to do it. But you are in a normal house filled with normal stuff. There’s no fancy scientific equipment. Can you do it with a common household item?

I think this is indeed possible, and I'm going to try to do it—with a paper clip.

OK, but why? This started with my work as the technical consultant for the CBS show MacGyver. My job was to check the scientific plausibility of different hacks and sometimes suggest ways that MacGyver could get out of a tricky situation. One of MacGyver's favorite things to use was a paper clip—so I figured I would see how many things I could make from them.

So far, I've made some cool paper clip-based gadgets.

It's just fun making complicated objects from basic parts—it's the MacGyver way.

Now for the scale. This might seem simple, but there's going to be some graphing involved, such that this might be more appropriate as a blog post instead of a video. Let's do it.

Remember, the goal here is to measure the mass of some water. Since we are on the surface of the Earth, there is a constant relationship between mass and weight—so we are technically going to measure the water’s weight. What's the difference between mass and weight? Here is my full explanation, but the short answer is that mass is the amount of matter (protons, neutrons, electrons) a thing is made of, and weight is the gravitational force exerted on that object by the Earth.

So how do you measure weight? It turns out that most of our measurement tools are actually for measuring distance. (It's true—check it out.) In this case, we can determine the weight (and thus the mass) of something by measuring the deflection of a paper clip, or how much it bends. If you have straightened a paper clip out into a long wire, the more you push on one end, the more it bends. However, when it’s curled up into its normal paper clip shape, it is much more difficult to fold. This is very similar to the force required to stretch a spring, which is much harder to deform than a straight wire. However, for an ideal spring, the stretch distance is linearly proportional to the stretching force, and that might not be true with a bending paper clip.

So the idea is that if we flatten out our paper clip, we can turn it into a lever arm that will help us weigh our water.

Let's build this thing. Here is what I have.

Photograph: Rhett Allain

This, of course, starts with a flattened paper clip. It does take some practice getting the thing straight, but at least paper clips are fairly cheap and abundant. This straight clip is held onto the top of a wooden block with some tape, such that the majority of the paper clip sticks out horizontally. This will be the lever arm. It doesn't actually matter how much of it sticks out from the wood, but it has to stay constant, without sliding back and forth. I also put a tiny little bend at the end of the clip so that I could hang a string on it without it slipping off.

The next important part of this balance is the mass holder. I'm using a lightweight plastic cup. This cup has some tape with a string to attach it to the paper clip arm. Another paper clip is mounted on the top lip of the cup. This is just a marker to measure the position of the cup and thus the deflection of the supporting arm. Finally, I have attached a vertical ruler to the wall. This will be used to measure the paper clip arm’s deflection. You can build one of these too—be creative and make some changes. The key is to use the stuff that you find around you in the office or at home or wherever.

Now we need to calibrate this measuring device. Sure, the paper clip arm will bend more when more mass is added to the cup—but we need to know the relationship between deflection and mass. For this, I need some known mass units. In sticking with my "use what you can find" rule, I'm going to use pennies. If you use pennies made after 1982, they have a mass very close to 2.5 grams. These post-’82 pennies have a zinc core and are a little bit lighter than older pennies, which were mostly copper. Yes, there will be some variation from penny to penny based on wear and dirt, but overall this should work fine.

So, here's what I'm going to do: I will record the position of the paper clip marker on the cup with respect to the mounted ruler. This will take into account the mass of the cup and string. Since I’m just going to measure the amount the paper clip bends, I will just “zero” it with the mass of the cup so that it doesn’t matter. Only the change in mass due to extra stuff inside the cup will count as a measurement.

Next, I’ll add some pennies and record the new position. I will keep doing this until I have enough data to make a graph. Here's what I get.

Photograph: Rhett Allain

I don't know if there is a linear relationship between the mass and the displacement—that's why I need to make a graph. Here's what that looks like.

That's actually fairly linear, and I'm pleasantly surprised. Fitting a linear function to this data, I get:

Illustration: Rhett Allain

This is your basic slope-intercept form of a line, but it's also very useful. This is an equation such that I could put in any mass (m) and it would tell me the position (y) of the cup hanging on the paper clip. Of course, I want this the other way around. I want to determine the mass for a particular cup position. I can solve the above equation for the mass and I get:

Illustration: Rhett Allain

Here is how this is going to work: Put something in the empty cup and read the y-position of the paper clip pointer. Now take this value and subtract 8.786 and then divide that number by 0.03085. Boom! That's the mass of the stuff in the cup.

OK, let's try it out with water. I'm going to pour some into the cup and measure the mass.

Photograph: Rhett Allain

The position of the pointer is 11.5 centimeters. Plugging this into my mass equation, I get 87.97 grams. Now, let's check it. If I put the same cup of water on a digital balance (I just happen to have one nearby), I get a mass of ... 74.54 grams. OK, OK, that's not the same. But we are comparing an expensive digital balance to one I built with some paper clips. I think it's pretty close. I mean, you have to start somewhere, right?

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