# Mass

#### Prerequisites

In our pages on the physical content of Newton's Laws, we've talked about how an interaction between two objects can change the motion of one (or both) of them.  If a hammer hits a bowling ball it can start the ball rolling, speed up or slow down the ball if it's already moving, or change the direction of the ball's motion. We describe the interaction between the hammer and the ball as a force (though we have not specified how to measure it).  But it's not clear if we have properly separated what the hammer does to the ball from the ball's response.

## Thought experiment 3: The double bowling ball

We thought about hitting a bowling ball with a hammer (in the section on Inertia).  But suppose we took multiple bowling balls, drilled holes through them, and then bolted them together as shown below.

Do you think that if we gave the same hit to a double (or triple) bowling ball that their velocity would change the same way as when we hit the single ball?

A natural expectation (and one that is borne out by careful experiments) is that when we hit the double bowling ball we would only get 1/2 the velocity that we got when we hit the single ball — and when we hit the triple ball we would only get 1/3 of the velocity of the single ball.

This suggests the following conceptual idea:

When one object exerts a force on another, that force is shared over all parts of the structure of the object.

## Quantifying mass

What this now suggests is that we have to find some way to quantify the "parts" of an object.  For the examples above, the "number of bowling balls" is a good measure.  So if we just count the number of bowling balls in the object we will get what we refer to as the mass of the object (in bowling ball units).

This is our third dimensionality (along with length and time) -- a property of the physical world that we will model mathematically as a (positive) number.  Of course not all objects are made up of bowling balls.  So instead of that, we use a rectangular object -- the standard kilogram (kept at the National Institute of Standards and Technology). It really isn't so different from counting the number of bowling balls!

Joe Redish 9/13/11

Article 343