Sunday, January 19, 2014

Second Law

You have a spool of rope laying on it's side. The rope is passing under the central axle and to the right toward you. You pull slowly on the rope directly to the right. What will happen? Will the spool roll away from you to the left, or toward you to the right?


Despite the common intuition that such pulling will cause the spool to spin counterclockwise and roll to the left, in fact it will roll to the right (and wind up the rope you are pulling). Try it.

One way to think of why this must be true is through Newton's Second Law of Motion. Newton's second law is one of the most simply stated yet powerfully predictive ideas in physics. It is:

F = M * A

Where F is the force exerted on an object. This is a vector, so it is a direction and a magnitude.
M is the mass of the object.
And A is how the object accelerates, also a vector.

This means that if you pull on the spool to the right (F), and nothing else is pushing or pulling on it*, the acceleration vector (A) must be in the same direction and just scaled by the mass, M.

*Gravity is pulling it down, but the ground is pushing it up just the same, and our pulling is not at all in the same direction, so it shouldn't affect anything. Also friction is pushing left, but by its nature friction can't be greater than our force, F. Since we're just talking about the direction and not magnitude of the motion, it's fine to ignore it.

Thursday, January 9, 2014

Momentum

We previously talked about conservation of energy - an idea that is a very powerful way of understanding the world. However, actually auditing every form of energy and trying to find out how much goes to what form can be very difficult. Sometimes it helps to apply another, similar rule: Conservation of momentum.

Momentum is a thing’s mass x velocity

Like energy, momentum remains constant unless acted on my some extended outside force. Let’s look at a famously bad example from Lethal Weapon. When Riggs, the protagonist, starts to get too close to the truth, one of the villains drives by and shoots him. In the movie, the blast propels Riggs off his feet, into the air and through a window. Conservation of momentum gives us a simple way to see how plausible this is. Let’s compare things right before and after impact. Before, you have Riggs standing still and the cluster of shotgun pellets flying toward him. After, you have Riggs with the cluster of pellets embedded in his bullet-proof vest moving at some speed we’d like to figure out. 


Before:
Riggs’ momentum = (150 lbs) x (0 mph) = 0 lb-mph
Shot’s momentum = (0.05 lbs) x (820 mph) = 41 lb-mph

After:
41 lb-mph = (150.05 lbs) x V
V = 0.3 mph

That’s pretty close to a giant tortoise pace; ten times slower than average human walking pace. He may stagger, but he definitely will not go flying through the air.

Saturday, January 4, 2014

Body English

Perhaps you've heard of "putting english on" a ball to cause it's path to curve (See the Magnus Effect). What about this is English? Especially since it seems to be almost exclusively an American term. The English don't refer to it as english; they call it "side."

There are two possible explanations I like:
1. The first relatively widespread and dramatic ball curvature Americans were exposed to was thorough English pool sharks in the 19th century.
2. It comes from the French word "anglais," which refers both to the geometry concept and to the Angles who were early settlers of England (think Anglo-Saxon).   

The earliest example of the term in print seems to be by Mark Twain in The Innocents Abroad:
"the cues were so crooked that in making a shot you had to allow for the curve or you would infallibly put the "English" on the wrong side of the ball"



A similar sounding, but separate term is Body English. This describes the physical gestures the athlete may perform after releasing the ball to encourage it to follow the desired path. Our President demonstrates above.

This may be an expansion of the term above, in that both seek the same result though different means, or it may come independently from one's gestures being a kind of body language, or body English.