Response to student question from Friday:
Why is it wrong to show extra digits when reporting numbers?Fermi-problem: How many trees are there in the state of North Carolina?
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.)
A) 106 = 1 millionAnother Fermi problem: Estimate the weight of the air in this room (Density of air is about 1.21 kg/m3)
B) 108 = 100 million
C) 1010 = 10 billion - BEST ESTIMATE
D) 1012 = 1 trillionSolution: 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.)
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!Trigonometry mneumonic: SOH-CAH-TOA
Exercise: What are the angles inside a 3-4-5 triangle?
Assignments:
· Read Chapter 2 in your textbook
· WebAssign HW1a and HW1b are due Wednesday
· Register on WebAssign if you have not done so already