Extra Credit #1

Begins Oct 16, 2017

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:

  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 Test Average (incl. Ch 5-6 test)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
  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) Salient details from the original question written out as appropriate.
    c) Your solution, hand-written in blue or black ink, with all work shown in detail.
    d) Drawings, diagrams, or graphs with labels must 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, at the risk of losing points on your solution.
  8. The assignment will be available online on Monday, Oct 16 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. 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 Monday, October 23, 2017.

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.)

EXTRA CREDIT PROBLEMS

1. Volleyball Serve

Watch the video of Becca Hanel serving a volleyball. Using time data taken from the video (which runs at 30 frames per second) and reasonable distance/length estimations, calculate the initial velocity of the ball as it is served.

Carefully explain and document your reasoning, in words and calculations.

2. Motorcycle's Coefficient of Friction

In the 2012 MotoGP race in Silverstone England, TV coverage provided data for some motorcycles' position on the racetrack and speed at that location (see video clip). By taking some screenshots, searching on Google Maps for the racetrack, and using Adobe Photoshop layers, I was able to do some additional graphical analysis (shown here).

Based on information gained from these preliminary analyses, determine the coefficient of static friction between the motorcycle's tires and the road.

Carefully explain and document your reasoning, in words and calculations, and comment on how reasonable you think your results are.

3. Polytechnic Drinking Fountain

  1. Take a digital picture which clearly shows a drinking fountain at Polytechnic, your face, the water's full trajectory as it leaves the fountain's spout, and at least part of a vertically oriented meter stick. By printing this picture and using the meterstick as a scale, you can make various length measurements (horizontal and vertical) to help you solve the other parts of this problem. It's appropriate for you to draw on the photo any lines or guides that will indicate measurements you made using the photo.
  2. using these measurements (and not a protractor), calculate the x and y components of the water's velocity at the point where the water leaves the fountain.
  3. calculate the amount of time it takes for the water to reach its highest point.
  4. Determine the angle (relative to the horizontal) of the initial velocity at the point where the water leaves the fountain nozzle by two different methods, and calculate the percent difference between the two values.
    Method 1: Measure the angle on the photograph using a protractor.

    Method 2: Calculate the angle based on your answers to part b.
  5. Develop an equation to describe the water's trajectory (x and y coordinates) as a function of time.

4. Friction on a Jet Sled

Lovely Grizzelda, Poly’s super-star physics student, has built a jet sled. Its power supply provides a force equal to 5 times the weight of the sled. Problem is, the rails upon which the sled travels provides a frictional force that is directly proportional to the sled’s velocity.

  1. Derive an expression for the sled’s maximum speed. It is OK if this includes an undefined constant.
  2. Derive an expression for the sled’s velocity as a function of time, assume it starts from rest. Put the final solution in terms of your answer in Part a.
  3. Use the relationship derived in Part b to determine the velocity of the sled at: i.) t = 0; and ii.) t = infinity.
  4. Derive an expression for the sled’s position as a function of time, assuming it starts at the origin.
  5. Use the relationship you derived in Part d to determine the coordinate of the sled at t = 0.
  6. You are given a graph of the velocity as a function of time, but the graph is not complete. Assuming the mass of the sled is 600 kg, use the information provided to determine the value of the “undefined constant” alluded to in Part a
 

5. Kaylee Goes Skydiving

Kaylee (m = 60.0 kg) decides to go skydiving, and wants to solve some physics problems along the way.

  1. What is the force of gravity in Newtons acting on Kaylee just before the plane takes off (at the surface of the earth)? (The acceleration due to gravity in the Los Angeles area is approximately 9.796 m/s2. Calculate to four sig figs.)
  2. According to Newton's Law of Universal Gravitation, what is the force of gravity in Newtons acting on Kaylee at the jump height of 14,000 feet? (Calculate to four sig figs.) What is the percent difference between her weight at the two different heights?
  3. The density of the atmosphere varies with altitude. Perform some research that will allow you to determine a function that describes the density of the atmosphere as a function of altitude for the Troposphere, that portion of the atmosphere through which Kaylee is performing her skydive. (Be sure to cite your source URL if accessing a webpage, and the date that page was accessed.)

    Note that if you can't find a function that will work for you, you can take data from this page and create your own exponential function using a regression.

  4. Kaylee jumps from the plane at a height of 14,000 feet with an initial vertical velocity of 0, where the air density has been determined above. The Resistive force of fluid friction on her as she falls is described by the equation:

    R = (1/2) DρAv2
    where
    • D = drag coefficient, a dimensionless quantity determined empirically
    • ρ = density of air
    • A = cross-sectional area (of surface exposed to air)
    • v = instantaneous velocity

    Assuming some amount of air friction R is acting on Kaylee as she falls, draw a free-body diagram of her before she has reached terminal velocity.
  5. Based on your research, identify a reasonable estimate for her drag coefficient and a reasonable estimate of her cross-sectional area.
  6. Assume that at one point, Kaylee has a downward velocity of 25.0 m/s at a height of 3,000.0 meters. Based on your calculations, identify the magnitude and direction of her acceleration at that instant.
  7. [Challenging] We'd like to calculate Kaylee's velocity as she falls, but we have an issue: the net force acting on her (including drag) determines her acceleration, which determines her velocity, which affects the net force acting on her, which determines her acceleration, which determines her velocity, which...

    Use Euler's method, along with a spreadsheet analysis, to determine one of two values:

    1. Kaylee's terminal velocity before she pulls the parachute, or
    2. Kaylee's velocity just before she hits the ground (not having pulled the parachute).

    Please note that Kaylee did safely land with a parachute when she performed this experiment!

    For information on how to solve this problem, you might consult any of the relevant explanations on YouTube. My favorite is this one from Flipping Physics.

    The spreadsheet you use to solve this problem should include clear titles and documenting cells, and shared/emailed to your instructor, as well as being printed and included with your paper solution.