Wednesday, May 11, 2011

Announcements:

• Be sure to attend one of  three sessions offered for the physics concepts survey in Phillips 215.  Remember to bring your laptop computer or write your answers on a scrap piece of paper and enter them online at your earliest convenience: www.unc.edu/~brogshan
• 9:45 - 10:15
• 11:30 - 12:00
• 1:00 - 1:30
• The first Supplemental Instruction (SI) session will be held today at 5:00 pm. Meet in this room (Phillips 215).
• Fill out a Student Survey if you did not do so yesterday.
• Labs begin tomorrow (Thursday) in Phillips 206.
• There seems to be some confusion about the access code for Mastering Physics.  In order to register for MP, you will need to purchase an access code from the Mastering Physics website (or from the campus bookstore if they have more codes).  The scratch-off code in your textbook is only for the Student Companion Website, not for Mastering Physics.
• Since the Intro to Mastering Physics homework is only for practice, there is no penalty for submitting this assignment late.
• Graded homework assignments (e.g. HW1) submitted after the due date will receive a 10% deduction for each day late, down to a minimum of 50% (half credit).
• Based on survey responses, this class may require more time than you expected (see below).

Expected time requirements for this course:

Activity	Hrs/wk
class time 5(1.5 hr/day)	7.5
Homework/study: 3(class time)	22.5
Lab time: 2(2 hr/lab)	4
Lab prep/report: 2(3 hrs/lab)	6
TOTAL	40

Assignments:

• Submit HW1 by midnight tonight.
• Read Chapter 2 in your textbook and submit HW2 by midnight tomorrow.
• Read error analysis section in your lab book and take Measurement Uncertainty Quiz before going to lab.

CHAPTER 1:  Intro to Physics (continued from Day 1)

Fermi problem:  Estimate the number of molecules in a drop of water.

Answer:  1 drop ~ 0.1 mL(1 g/mL)/(20 g/mL) = 0.005 mol = 3 x 10²¹ water molecules/drop
Wrong:    Number of molecules in a drop of water = 6.02 x 10²³  (wrong for 2 reasons)

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
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.)

Powers of 10 video

Table of powers of 10 and metric prefixes.

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

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!

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

RWP1 – pizza problem

CHAPTER 2: Motion in One Dimension

Position is the location of an object relative to some point in space.
Displacement (a vector) is the change in position of an object: final position - initial position
Distance is the total length traversed by an object.
Average speed = distance/elapsed time
Average velocity = displacement/elapsed time
(Instantaneous) velocity:  v = dx/dt
Speed (a scalar) is the magnitude of the velocity (a vector)
Average acceleration = change in velocity/change in time
(Instantaneous) acceleration:  a = dv/dt
The magnitude of the acceleration does not have a special name.
The change in acceleration is called a "jerk" = da/dt

Equations of motion for constant acceleration: (see Table 2-4 on p.34)
Note:  These equations come from integrating and the definitions of velocity and acceleration

Example:  Walk forward 3 m and back 3 m in 6 seconds.  What are the above quantities?

Exercise:  A car accelerates from 0 to 30 m/s in 6 seconds
 - Sketch the position versus time graph
 - Sketch the velocity versus time graph
 - Sketch the acceleration versus time graph