Apr. 08, 2011

Science Dad on Weight, Mass, and Density

by Vince Harriman

Click to enlarge images

Which sponge has more mass?

Beckett's bike has a slow leak in the back tire, so every time we go for a ride we need to pump it up. This has led to many interesting conversations for us about mass, weight, and density, so I though we could do some simple projects to help understand the difference between mass and weight and how density factors in.

I decided to start with the easiest concept, density. When the tire is flat the density (pressure) of the air inside the tire is the same as the density of the air around it. Every time Beckett pushes down on the bike pump he is forcing air into the tire. This makes sense -- if you force more air in, there will be more particles of air in the tire than the air around it. But since air is invisible and air (and its mass) is still a slightly intangible concept for kids, we headed to kitchen. I had Beckett pull out a dry, compressed sponge and a sponge that was also dry but had already been used. Which one has more molecules in it? Of course they are basically the same, but when dry and compressed, the unused sponge has a much higher density. The bike tires are the same -- when half inflated, the tires feel squishy. Fully inflated (the air is compressed inside) they feel hard like the dry sponge. Changing the density of an object does not change its mass. Its volume changes, but not its weight or mass.

But what is mass and what is weight? We often use mass and weight interchangeably, but they are not the same. Mass can be tricky to define and understand, since there are special circumstances which require mass to be defined very very specifically (light particles, sub-atomic particles, objects moving at or near the speed of light all come to mind.) For our purposes, mass is a measure of how much 'stuff' is in an object, how many atoms or molecules.

The tricky part is that we measure mass in kilograms and grams -- which most people understand as units of weight. Weight is a measure of how the force of gravity is acting on an object. And gravity can be variable even here on planet Earth. We can take a box of chocolate cookies with a mass of 500 grams to the top of a high mountain and it will weigh less than it does at sea level, while the number of molecules (and calories, alas) will stay the same. If we put the cookies on the International Space Station, they will weigh next to nothing, but still contain 500 grams of chocolate cookie goodness (and yes, calories) in space!

This large yoga block weighs next to nothing

To illustrate these concepts, Beckett and I weighed a couple of objects we found around the house. We started with one of Science Mom's (she's also Yoga Mom) yoga blocks. Bigger than a standard household brick, it barely weighs a thing, which makes it great for yoga. Easy to carry around, you can drop it on your toe and you can put your knee or elbow on it without it hurting. We also weighed a brick.

So how much mass does a yoga block have? Not much, which is a function of both its density and the molecules that make it up. The number of molecules present in the yoga block is low, and I am personally guessing that molecules that make up the yoga block are less massive than the molecules that make up a brick. But take a look at the brick -- it weighs almost five pounds! Now why are we using weight to estimate mass, when I started the post by saying not to do that?

Well, since the yoga block and the brick are both being weighed in exactly the same spot, where they experience exactly the same gravity, we can assume the force acting on them to give them weight is the same, and a little simple math would let us remove gravity from the weight equations leaving just mass. We could weigh them both on the moon and derive mathematically the same result -- the gravity on the moon is only 1/6 that of Earth's gravity, so the brick would weigh under a pound and the yoga block would really weigh very little, but we would still learn about their relative masses.

So, mass is the amount of matter in an object, which does not change even if the force of gravity changes. Density (or pressure for gasses and liquids) is a measure of how tightly packed those molecules are. And weight is a measure of how the force of gravity is acting on an object.

A standard brick

There are lots of great experiments that can illustrate this:

First, with a very accurate scale you can measure the difference between an uninflated and over-inflated ball. Just be sure to use only one ball for your experiment, because manufacturing differences in two balls can be as much as the air weighs. Deflate any sturdy large ball and weigh it, then slightly over inflate it and weigh it again.

Second, to measure density, you can try our sponge experiment. If you can't find compressed sponges, you can compress your own. Or you can get a sponge soaking wet and compare it to a damp sponge. Which sponge has more mass and molecules? How is a soaking wet sponge different in density than a damp sponge?

To understand density -- and have a break from science and a snack -- pop some popcorn. Start by weighing a certain amount -- say 1/4 cup popcorn kernels, or a single microwave popcorn bag. Weigh them in the bowl you will put the popped popcorn in -- this is known as 'tare' weight and makes it easier to be accurate. Then with the help of your parents, pop the popcorn. Put it back in the bowl and weigh everything again (including the bag if you used a microwave.) Is there any difference? If there is, what could account for the difference? Did you notice any steam leaving the popper or the bag? Where was all that steam in the kernels?

To understand that weight is a function of force, find a bathroom scale that has a live reading. Step on to the scale and stand very still. This will give you an accurate measure of both your weight and mass. Now extend as tall as you can then quickly fall into a crouch and watch your weight as you hit bottom. If you have a spring loaded scale you can even jump on it (with your parent's permission). Your mass in motion gains 'weight' with the energy of movement.

Finally, a fun gravity experiment, all the way from Galileo. Legend has it that he dropped balls from the Tower of Pisa to figure out how the laws of gravity work. First, take a piece of paper and a book. Hold one in each hand and drop them at the same time. The book will slam to the floor and the paper will float slowly and gently down. The paper is slower because air slows it down -- it has a lot of resistance. Next, hold the paper and book vertically and drop them. The paper falls a lot faster now, right? Try some other things -- remember our paper airplane experiment that was all about aerodynamics? Fold a sheet of paper into an airplane, point it straight at the ground and drop it at the same time as the book. Almost even now? Finally, cut a piece of paper just slightly smaller than the size of the book. Place it flat on top of the book and with two hands carefully drop the book so that it falls flat. The paper stays put on the book and falls at exactly the same speed! With no air resistance to slow it, the flat piece of paper falls as quickly as the book!

About Vince Harriman



