Friday, Feb 8, 2008

Collected Abstract Reasoning Problem set. I will grade on the first 5 correct, additional correct problems will earn extra credit.

Showed video of objects dropped in vacuum (remove air from tube, and also dropped on the airless Moon). If no air, they fall at the same rate.

Discussed a model of air resistance - knocking aside molecules of air. Air resistance depends on speed and cross-sectional area - increasing either of these increases the number of air molecules you knock aside in a given time. If you drop a book and a piece of paper, the book reaches the ground first but it also has the greater force of air resistance acting on it (even though the EFFECT of air resistance is more noticeable with the paper) since the book knocks aside more air molecules in the same amount of time. Galileo was able to separate air resistance from the effects of gravity.

Worked some examples with average speed = total distance/total time interval. You have to use the equation.

Talked about rates, how some quantity changes with time. Speed is the rate at which distance is covered. Worked examples of v = d/t. Introduced Seattle example.

Showed using the example of hourly wage and pay raises that the two are different.
A person earns $9/hr. If every year he gets a raise of $3/hr, after 1 year he is earning $12/hr. This is the pay rate. The rate at which the pay rate increased was $9/hr/year - a rate of a rate.

Acceleration is a rate of a rate. It is the rate at which velocity changes.
a = (vf -vi)/t or vf = vi + a*t
Note that final amount = initial amount + rate * time
Worked some examples of changing speed while driving. Answers had units of miles/hr/min. There are two units of time since acceleration is a rate of a rate.

If the acceleration is in the direction of the velocity, the object speeds up.
If the acceleration is opposite the direction of the velocity, the object slows down.
Showed example of tossing ball into air. It slows down on the way up and speeds up on the way down.

Near the surface of the Earth, the acceleration of gravity is about 10 m/s/s (approx to 9.8 m/s/s). This means that for every second of fall (neglecting air resistance) the object picks up 10 m/s of speed every second on the way down and loses 10 m/s of speed for every second on the way up.

Worked examples of how fast an object is falling after a given time when dropped.
Worked examples of how fast an object is moving after a given time if thrown into the air.

IF THE ACCELERATION IS CONSTANT (as it is near the surface of the Earth), then we can write d = vavg * time where the average velocity is just, vavg = (vi + vf)/t

Used this "sus it out" technique to calculate how far an object falls in a given time.

Finished by showing that the "d" in that equation is actually displacement (distance from starting point and in what direction) and NOT actual distance traveled. If you throw a ball up into the air, you can use d = vavg * t to find how far above or below the starting point the ball is after a given time, which is not always the same as the total distance traveled.

Homework due Monday - do WebAssign assignment WA Chapter 2 part 1. The cutoff time is Sunday night at 10 pm.

If Monday is warm (above 50 deg F), and sunny, we will shoot rockets. Be prepared to go outside to do the Rocket Lab 1.