What is up with the spherical cow? (original) (raw)

If you hang around physicists for a significant amount of time, someone is going to bring up the spherical cow. What is this thing? This came up recently in class since it is mentioned in the Matter and Interactions textbook (Chaby and Sherwood).

Maybe I can give a quick explanation of this. Suppose I am in a room and I throw a pencil. Why? No worries, I just did. Sometimes I do random things. However, suppose I also want to model the motion of this projectile pencil. What do I do? Some things I could consider:

• Should I consider it to be a flexible object? If so, when I throw it will oscillate and flex.
• As a semi-rigid object, I still need to consider it rotation in three different directions. This turns out to be non trivial.
• What about air resistance?
• What about variations in the density of the air in the room?
• Is the gravitational field in the room constant? What about the gravitational interaction between the pencil and that massive desk over there?
• Does the pencil have any excess charge that would produce and electrostatic interaction with other objects or an electromagnetic interaction with the Earth's magnetic field?

That should be enough for you to get the idea that this could be a complicated problem. But what if I just want to get a value for the initial velocity based on the horizontal distance it travels? In that case I could just ignore all the above stuff. Yes, it would be wrong but I could get a pretty good answer. Really what I would be doing is reducing the complicated problem to the following:

• A point mass.
• Only the gravitational interaction with a constant gravitational field.

This makes the problem quite doable. In physics (and science) we try to make models. They don't have to be perfect models, in fact they never are. We just want models that work. If I assume the pencil is a point mass, that model works pretty well.

Back to the spherical cow. I don't know the origins of this joke, but this is the one I always remember.

There is this dairy with cows and everything. The dairy farmer wants to increase his production of milk. To do this, she hires three consultants - an engineer, a psychologist, and a physicist.

After a week, the engineer comes back with a report. He said: "If you want to increase milk production, you need to get bigger milk pumps and bigger tubes to suck the milk through."

Next came the psychologist. He said: "You nee to make the cows produce more milk. One way to do this is to make them calm and happy. Happy cows produce happy milk. Paint the milking stalls green. This will make the cows think of grass and happy fields. They will be happy."

Finally, the physicist came to present her ideas. She said: "Assume the cow is a sphere...."

Get it?