Snow is all the buzz right now. Actually, I think I might like the term "SnOMG" better than last year's word: "snowmageddon". Anyway, Lifehacker even had a nice post about making a great snowball. Their tips are essentially - make it denser. But why?
Everyone knows that higher density snow balls work better, but how about a little physics to show this. Let me aim for a super-basic explanation. When you throw a snowball, there are essentially two forces on the ball while in air. No, one of them is not the "force of the throw". Once you let go of the snowball, you no longer exert a force on it (unless you are a jedi). So, suppose you throw two snowballs. Snowball A is tightly packed (the kind where you use your hands to sort of melt it). Snowball B has the same size and shape, but it is lightly packed. The only difference between snowball A and B is the mass. Just for fun, let me say that snowball A has twice the mass of snowball B. If I were to throw them at the same speed (which I will get to in a second), then I could represent the forces on these two balls with this diagram:
First, let me say that the dot-line arrow is just there to represent the velocity. It is not a force. There is no force of motion. Ok, what about the two forces then? First, there is gravity. On the surface of the Earth, the gravitational force is an interaction between that object and the Earth. It is a force that is directed down and is proportional to the mass. Snowball A has a gravitational force twice that of snowball B (thus the longer gravitational force arrow).
The other force is the force of snowball interacting with the air. This is commonly called the air resistance force. In the usual model, it depends on the speed of the object and the type of object (size and shape). It also depends on the density of the air, but that doesn't really change in this case. The direction of the air resistance force is always in the opposite direction as the velocity. To get a 'feel' for air resistance, try this simple experiment. Safely stick your hand out the window of a moving car. You can feel the air pushing on your hand. The faster the car goes, the more the air pushes. What if you change the size of your hand by making a fist - force changes. There, you are now an air resistance expert.
What do forces do to the snowball? Forces change the velocity of an object. Take a snowball and drop it instead of throwing it. Right when you let go, its velocity is zero and the only force acting on the snowball is gravity (since it is not moving). What does this gravitational force do? It makes the velocity change in the direction of that force. This means it speeds up going down. The key is the forces CHANGE motion.
If there were no air, the motion of the two snowballs would be the same. This is because the amount of change in velocity for an object is proportional the magnitude of the force acting on it, but inversely proportional to its mass. More massive objects have a much smaller change in velocity compared to the same force on a less massive object. This can be summarize with the all-too-familiar expression from Newton's second law:
A couple of notes:
- I bet you thought I was going to write something like F = ma, didn't you? That is how it is traditionally been stated, but I like it in the above form better. Although I often say that "forces cause acceleration", this isn't the best thing. Really, there is a correlation between force and acceleration. We model this with the above expression. Which came first, the chicken or the egg? It doesn't matter. If it does matter, Dr. Tyree's philosophy class is just down the hall (right next to Dr. Jones' archeology class).
- What are those arrows over the force and the acceleration variables? Those arrows mean that acceleration and force are different types of variables. These are called vectors. That means that for force and acceleration, direction matters. Mass is another type of quantity - a scalar. It has no direction. Maybe at this point the difference between these two doesn't matter, but I just like to be consistent.
- I wrote F with a "net" subscript. This means that you need to look at the sum of the forces acting on an object, not just one. If I push to the right on a book with a force of 10 Newtons, and you push with the same force to the left - the forces add up to the zero vector. In this case, the book would have the same acceleration as a book with no forces acting on it.
Back to the snowballs. The only difference between these two (at the instant shown) is the gravitational force and the mass. But here is the deal, although they have the same air resistance force, this means a smaller change in velocity for the heaver snowball (A). The result is that the heavier ball will be able to travel farther. The lighter one will slow down (assuming it stays intact).
But what about the throw? Wouldn't a person be able to get the lower mass snowball going faster? Well, that might be true. However, the human arm can only go so fast. Take your arm and pretend to throw a ball. Your hand is going as fast as it can. Decreasing the mass isn't going to get you much.
There you go. The physics of snowballs.
