Extra Credit #2

Begins: Feb 28, 2018

Due: Friday, March 9, 2018, 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.


  1. The Extra Credit Assignment consists of five problems, to be completed outside of class.
  2. This assignment is Extra Credit and not required.
  3. 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 AverageReview 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
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. The assignment will be available online on Monday, February 29, on the Internet at http://www.crashwhite.com/apphysics
  9. 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.
  10. Your completed assignment must be turned in directly to the instructor anytime before 3:00 PM on Wednesday, March 9. Absolutely NO late work will be accepted for this assignment.



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.)


1. World Keeps Turning

  1. 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.)
  2. 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)
  1. 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.
  2. Using your function and an appropriate integral, determine the Impulse on Sulley during this collision.
  3. At t=0.2 seconds, Sulley comes to a halt. Determine his change in velocity during the impact.
  4. Determine Sulley's average acceleration during the impact.
  5. Determine the average net Force on Sulley over the entire 0.2 seconds.
  6. Determine the maximum net Force on him during the 0.2 second time period.

3. Free Throw

The "free throw" in basketball is one of the most important parts of the sport, particularly at the end of a match when fouls play an important role.

  1. What is the diameter of a standard NBA basketball?
    You don't need to get too technical here. If a range of masses and sizes are acceptable, identify specific values that you can use in your analysis. Identify the source of your information.
  2. What is the mass of this standard baskeball?
    1. What is the overall weight of the ball?
    2. What is the weight of the air inside the ball? (Hint: identify inflation pressure and work from there.)
    3. What is the weight of the thin, spherical, rubber "shell" of the basketball?
  3. What is the overall moment of inertia for the basketball?
  4. Download this video (shot at 30 frames per second).
  5. Based on values that you measure/estimate in the video and provide in your answer, what is the translational velocity of the ball as it leaves Kaitlyn's hands?
  6. Now that you've determined the linear velocity of the ball at its launch...
    1. Estimate the rotational velocity of the ball as it leaves Kaitlyn's hands.
      Be sure to explain how you got this value.
    2. Calculate the rotational kinetic energy of the ball.
    3. Calculate the total Work Kaitlyn did to launch the ball toward the basket.

4. CalTech Fountain

  1. Go to the fountain at CalTech that is due west of the Beckman Auditorium.
  2. Have someone take a digital picture of you standing near the fountain. Take additional photos as necessary to help justify your data/estimates.
  3. 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. Please refrain from actually entering the water in the fountain, wading in it, etc. Although you might find the idea entertaining—and valuable from a data collection standpoint—the last thing you, I, or Poly needs is a call from Caltech regarding your behavior. Thanks! :)

5. Select one of these two problems

a. Tom Cruise's Center of Mass

In the original movie "Mission: Impossible," Ethan Hunt 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:

Extra Credit 3D

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

b. The Chain

A chain of length L is laid out stationary and in a straight line on the ground. The coefficient of kinetic friction between the chain and the surface is µk. Without lifting it up, a student grasps the chain at the left end and begins to drag it back along the chain's length. (Note that in the beginning, there will only be a small part of the chain that has been doubled back and is in motion along the ground, whereas toward the end most of the chain will be moving.)

  1. Draw an appropriate coordinate axis for this situation with the chain positioned as it will be after some arbitrary period of time.
  2. Assuming the mass M of the chain is uniformly distributed over the length of the chain, derive an expression for the work friction does over the interval required to get the entire chain in motion
  3. If the force applied by the kid is twice the frictional force applied, how fast will the chain be moving by the time the entire chain is in motion?
  4. A second chain with a linear mass density of λ = kx replaces the original chain. Repeat Parts (a) and (b) for that situation, assuming the kid has grabbed the lighter end of the chain in this case.