Day 5

Friday, January 18, 2008

Announcements:

There is an information session for the INSPIRE program next Tuesday and Wednesday from 7-8 pm in Phillips 265. INSPIRE is a volunteer organization designed to improved science education in North Carolina. UNC students are matched with local science teachers to assist in elementary, middle, and high school classes. Check it out!
Responses to yesterday's Minute Paper.

Assignments:

Answer the recommended conceptual exercises and problems for Chapter 3 (listed at the bottom of the daily schedule), and check your understanding by looking at the answers in the back of the textbook.

Class Discussion:

Chapter 2 - Atoms

Discuss: In Fig. 2.12, the length scales range from 10^25 m down to 10^-25 m, with human size (~1 m) right in the middle. Is this just chance, or is there a reasonable explanation for this occurrence?
Question: What is the age of a typical student in seconds?
Discuss: Suppose someone offers you a billion one-dollar bills if you are willing to first count them. Should you accept this offer?
Estimate the number of molecules in a drop of water.
If the nucleus of a hydrogen atom were the size of a baseball, how far away would the electron typically be?
Why is ice less dense than water? (Hint: see figures 2.2 and 2.7 in the textbook.)

Units of measure and common conversion factors

All of physics is based on empirical (experienced or experimental) evidence, which requires measurements to be made. These measurements must be standardized and sufficiently precise in order to make comparisons with other scientists so that a meaningful discussion can be made as to whether a theory is or is not supported by experimental findings.

Qualities of good measurement standards
US National Institute of Standards and Technology
Bureau International des Poids et Mesures

SI Unit notation and dimensions:
[length] = m    1 m ~ 3.3 ft
[mass] = kg    1 kg ~ 2.2 lbs.
[time] = s

Becoming familiar with mks units:
· Distance from floor to waist of your instructor: ~ 1 m
· Length of forearm (fingers to elbow): ~ 0.5 m, 18 in
· Width of your smallest fingernail: ~ 1 cm
· Thickness of a single page from your physics textbook: ~0.01 cm
· Mass of your physics textbook (in kg), weight in pounds (lb): ~1 kg
· Mass of a nickel coin (in grams): 5.00 g
· Your heart rate (in Hz): ~1 Hz
· Slow walking speed: ~ 1 m/s = 2 mph
· Highway speed: ~ 60 mph = 30 m/s
· Number of seconds in a year: ~ pi*10^7 (by coincidence)
Why is it wrong to show extra digits when reporting numbers?

Example: Number of water molecules in a drop of water = 6.02 x 10²³ (wrong for 2 reasons)
Number of water molecules in a drop of water = 3 x 10²¹ (correct magnitude and sig. figs.)

Fermi-problem: How many trees are there in the state of North Carolina?

A) 10⁶ = 1 million
B) 10⁸ = 100 million
C) 10¹⁰ = 10 billion - BEST ESTIMATE
D) 10¹² = 1 trillion
Solution: NC is about 300 mi by 200 mi, = 6 x 10⁴ sq. mi. Estimating that about half of the state is wooded, and that the average distance between trees is about 10 feet, there are about 528 trees in a linear mile, or 500 x 500 = 3 x 10⁵ trees per sq. mi. Therefore, there are about 18 x 10⁹ or ~10¹⁰ = 10 billion trees in the state. (Note: Different assumptions about the tree density may vary this estimate by as much as a factor of 100, so a reasonable range of answers to this question is 100 million to 1 trillion trees.)

Another Fermi problem: Estimate the weight of the air in this room (Density of air is about 1.21 kg/m3)

Scaling problems:
    1D (linear) things scale ~ x
    2D (flat) things scale ~x^2
    3D (spherical or cubic) things scale ~x^3

Scaling Problem: If the nucleus of an atom (Hydrogen for example) were the size of a basketball, how far away would an electron typically be?

Answer: The size of an atom is about 1 Angstrom = 0.1 nm, while the nucleus is only 1 fm = 10^-15 m. The ratio of the atomic diameter to the nucleus diameter is threfore 10⁵, so an electron is typically about 100,000 nuclear diameters from the nucleus (using the Bohr model of the atom). If the nucleus were the size of a basketball (~ 0.3 m), then the electron would typically be 3 x 10⁴ m or 30 km away!

Another scaling problem – A friend from the art school has asked for your expert opinion. She is considering making a large UNC ram that would sit on a platform designed to support a maximum of 1000 lbs. She has already made a 1/5 scale model that weighs 20 lbs. If the full-scale sculpture is made from the same kind of concrete as the smaller model, how much will the finished product weigh? What advice can you give her? Answer: weight ~ mass ~ volume for same density, so full size will be about 5³ = 125x heavier than the 1/5 (length) scale model. Therefore, the full size mascot will weigh 125(20 lbs) = 2500 lbs. Your friend should put the ram on a diet!