Extra Credit Assignment #2 Posted: April 10, 2008

Due: April 20, 2008, 3pm

The purpose of this assignment is to allow students to demonstrate their understanding of various abstract and applied physics topics. Because of the nature of this assignment, it will be graded fairly strictly--pay close attention to the Notes below. Assignments which are not completed as required will not be evaluated.

NOTES:

The Extra Credit Assignment consists of five problems, to be completed outside of class.

This assignment is Extra Credit and not required. This assignment is intended to provide students with the opportunity to review

some of the material we've covered, and not all students need the same amount of review. Students will be eligible to receive credit on problems completed according to the table below.

Your Current Test Average

Review Problems You Are Eligible to Complete

0 - 69% Problems #1 - 5 70 - 79% Problems #2 - 5 80 - 89% Problems #3 - 5

90 - 100% Problems #4 - 5 The total points earned by a student on this assignment will be determined by the

instructor based on a number of factors, including number of problems completed, difficulty of problem, and overall quality of assignments submitted by students.

You may work on the problems with other people--in fact, this is encouraged--but each person must complete his or her own assignment to be turned in. Even when numeric answers to problems are the same, solutions from different students must be written independently, and differently, and developed and explained in each student's own words.

The assignment must have a separate cover sheet that includes your Name, Date, Course and Period, and Name of Assignment. Staple this cover sheet to the front of the problems that you've solved.

Each response must be hand-written on a separate piece of paper, which must include:

a) Your name and the problem number at the top of the page. b) The original question written out in full. c) Your solution, hand-written, with all work shown in detail. d) Drawings, diagrams, or graphs with labels may (and should!) be used to explain

your solution more clearly. e) Written explanations (blurbs, in English) explaining important steps in your

solution. f) The final answer, with a box around it. See below for an example. If this seems like an awful lot of work, it is!

Remember that this is Extra Credit: you're trying to impress the instructor with how well you can do. If in doubt, do a little more than you think you

should, rather than trying to get by with less, and losing points on the problem.

The assignment will be available online on Friday, April 10 on the Internet at http://www.crashwhite.com/ap

The instructor will be available to answer questions about the assignment on a limited basis: before school, after school, and possibly by e-mail (rwhite@crashwhite.com). The instructor will not be able to help you if you leave all of your work until the night before the assignment is due.

Your completed assignment must be turned in directly to the instructor anytime before 3:00 PM on Friday, April 18. Absolutely NO late work will be accepted for this assignment.

EXAMPLE PROBLEM AND SOLUTION:

SAMPLE PROBLEM:

In "The Matrix," Neo is given a test by Morpheus, who asks him to leap from the top of one building to another. Assume the buildings are each 100m tall, and 15m apart. Neo runs and leaps from the first building with a velocity of 5.00 m/s at an angle of 36.9 degrees (toward the second building).

a. Will he make it to the next building? b. Where exactly will Neo land? (Assume no air friction in this problem.)

Problems! 1. World Keeps Turning

a. Assume, for fun, that all the human occupants of the earth line up and stand along the equator. What is the earth's angular momentum at this time? (Make sure you clearly identify the values and assumptions that you're making in solving this problem.) b. If each one of the billions of people lined up at the equator were to take one giant step to the east at 1.00 m/s, what would this do to the rotation of the earth? Specifically, would the rotation of the earth change by a significant amount? Support your answer mathematically.

2. A Collision

NOTE: The following problem requires the ability to do regressions on data using a graphing Calculator or suitably sophisticated spreadsheet software. If you don't know how to do a regression, hook up with someone who can and learn. Once you do part (a) in this problem, the rest of it is easy!

Sulley (m=120.0kg) is practicing for scaring kids, and throws himself down on the ground. (Consider him as a particle.) During the time that he is colliding with the floor, the following data is collected:

time (seconds) Fnet acting on monster (Newtons) 0 0 0.05 600 0.075 875 0.09 950 0.11 950 0.125 875 0.15 600 0.20 0

a. Perform a Quartic (a polynomial expression of the form At4 + Bt3 + Ct2 + Dt + E) regression analysis on this data and determine a time-based function for the net

Force acting on the monster during the impact with the floor. b. Using your function and an appropriate integral, determine the Impulse on Sulley during this collision. c. At t=0.2 seconds, Sulley comes to a halt. Determine his change in velocity during the impact. d. Determine Sulley's average acceleration during the impact. e. Determine the average net Force on Sulley over the entire 0.2 seconds. f. Determine the maximum net Force on him during the 0.2 second time period.

3. Trajectory of Distraction

In the movie Mission Impossible: III, Zhen launches softball-sized projectiles from a "pitching machine"-style device. Assume the machine gives each 200-g ball an initial Kinetic energy of 97.9 J:

a. What is the initial velocity of the ball, in m/s? b. What is the initial velocity of the ball, in miles/hour? c. If the ball is launched at an angle of 65° above the horizontal:

i. What is the maximum height it reaches? ii. How far away--horizontally--does the ball land, if its landing point is 15 meters above the launch elevation?

d. For the previous problems, we've assumed the ball isn't rotating. If, during the launch, the ball is given a rotational speed of 20 revolutions/second, and the ball has a radius of 6.00 cm:

i. What is the ball's moment of inertia? ii. How much rotational kinetic energy does the ball have? iii. How far away--horizontally--does the ball land now, assuming the launching machine still gives it a total of 97.9 J of Kinetic energy?

4. CalTech Fountain

a. Go to the fountain at CalTech that is due west of the Beckman Auditorium. b. Have someone take a digital picture of you standing near the fountain. c. Using a printout of this digital photo and any measurements that you have taken at the fountain, calculate the velocity of the water as it leaves the jets.

5. Tom Cruise's Center of Mass

In the original movie "Mission: Impossible," Ethan is lowered down into a vault. The rigging to support him needs to be attached at his horizontal center of mass. Assume Ethan's body is symmetrical in the y and z axes, has a uniform density of ρ=1000 kg/m3, and can be considered as two parts with dimensions shown here: SOLUTION:

If the left end of the diagram is x=0 m, where along the x-axis is the center of mass of Tom's body?