assignments

Homework 1

• On Units: Problems 5, 27, 45, 52, and 54 from Chapter 1 of UP
• Correlations and Curve-Fitting: This problem is rather open-ended. Come up with an idea for two variables which you think might be correlated, then go gather some data to find out. For example, you could ask for the height and weight of 15 friends (under the assumption that, on average, taller people weigh a bit more.) Or you could ask 15 folks how many semesters they have been at Marlboro and how many classes they have taken in the science building (on the assumption that the longer people have been here, the more science classes they will have taken.) Don't feel that you are limited to asking people questions! You could measure the length and width of a random sample of leaves from your favorite tree (on the assumption that they grow in both height and width as they mature.) So... think of something like this, and then go actually get some data (at least 15 data point pairs, please.) Then put your data in an Excel spreadsheet and do the following: calculate the mean and standard deviation for each of the two quantities; make a graph of the data (which should visually suggest whether or not there is really a trend or correlation); perform a "curve fit" to find an equation which fits the data reasonably well. What can you say about the uncertainty on any constants that appear in your curve-fit equation?

Homework 2

• These problems are based on the in-class lab activities. Please turn in nicely-written, readable solutions. Show your work and explain (in complete sentences!) what you are doing and why.
  • How does the period of a pendulum depend upon the mass of the bob? Show your data from class, and discuss/analyze its implications.
  • How does the period of a pendulum depend on the amplitude of the swing? What role (if any) does air resistance play here? Again, show your data from class and provide empirical support for your claims.
  • How does the period of a pendulum relate to its length? Show the data and the formula you found from curve-fitting (being, of course, careful to report such things as units and uncertainties.)
  • There is a tire-swing behind the science building (just outside of Out of the Way.) Figure how long it is, but not by measuring its length directly. Instead, go there with an assistant, and time the period of oscillation while your assistant swings. Then solve for the length (and your uncertainty in length) by using the formula you posited in the previous problem. Note that this involves extrapolating your law outside of the range in which you tested it. Does the result seem reasonable? We'll compare results in class on Friday.

Homework 3

• This week's assignment should again be in the form of a lab report, and should address the following topics.
  • Show your H vs L data from class. Analyze this data by performing a curve fit and finding an equation that summarizes the data. Be sure to specify the units and uncertainty of any parameters that show up in your formula.
  • Using your new equation relating H to L find an equation relating the height H (from which the ball dropped) to the time t (the time it takes for the mass to drop to the ground). The method for doing this is outlined in this week's lab handout. It involves combining your new H v L equation with the equation you got last week for the relation between a pendulum's length and period. No new data taking is necessary for this step -- only some algebra and some clear thinking. I do want to see all of your work, but the final answer should consist of an equation relating H to t, and a specification of the value(s) (with units and uncertainty!) of any parameters in the H-t equation.
  • What can you infer from this new H v t equation? Does the dropped mass fall at a constant speed? Why or why not? How can you tell?
  • In the spirit of last week's measuring of the length of the tire swing, measure the height of the balcony above the south-facing entrance to the Rice Library (say, from the top of the handrail to the ground just below). Do this by dropping something (appropriate) over the edge and timing (with a digital watch or something) how long it takes to his the ground (and then using your new equation relating H to t to find the height). Please work with a partner or find a helper so there is someone below warning innocent passers-by about the falling objects. In short, don't drop anything on anyone's head! As always, do your best to report an uncertainty on your answer for the height of the balcony.

Homework 4

• Problems based on Chapter 2 of Understanding Physics. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Problem 5
  • Problem 16 Also sketch a position vs. time graph for this problem.
  • Problem 21
  • Problem 24
  • Problem 50

Homework 5

• Problems based on Chapter 3 of Understanding Physics. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Problem 10
  • Problem 18
  • Problem 32 (Make sure to draw and properly label graphs of position, velocity, and acceleration vs time)
  • A fully loaded freight train moving at top speed rams into a hovering mosquito. Clearly the force exerted by the train on the mosquito (SPLAT!) is huge compared to the force the mosquito exerts on the train. Is this a violation of Newton's Third Law? Why or why not?
  • Consider this statement: "Newton's second law says that the net force on an object is proportional to its acceleration. So if two equal-magnitude forces act in opposite direction, and if no other forces are acting, the acceleration has to be zero, and hence the object must be at rest." Do you agree or disagree? If you agree, explain why it's a good statement and give a real-life example to support it. If you disagree, explain what's wrong with it and give a real-life counterexample.
• Again, there may also be a short write up due based on a simple lab run on Wednesday. More information about this later.

Homework 5 Problems

• I just added this "assignment" on the page so I could separate out the lab report grade from your problem set grades.

Homework 6

• Problems based on Monday's lab activity and UP Chapter 4. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Write up your results from Monday's lab activity. Explain what you did, show the results (in graphical form where appropriate), and then explain your empirical basis for the 6 formulas mentioned in the lab activity guide. Summarize by explaining whether/how the vertical and horizontal motions of a projectile object affect one another. This should all be done in the style of earlier lab write ups.
  • After carefully studying the entire chapter, pick one problem from the end of UP Chapter 4 which you think is interesting. Solve it, and write up the solution. Be prepared also to share your question/solution with others in class on Thursday.

Homework 7

• Problems based on UP Chapter 5. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Problem 1 -- 'Rifle and Bullet'
  • Problem 17 -- 'Airplane and Decoy'
  • Problem 57 -- 'Stone on a String'
  • EXTRA CREDIT -- A cannon launches a ball with initial speed v_o at an angle θ above the horizontal. However, the ground is not level. Rather, the cannon is shot up a hill which itself makes some other angle α with respect to the horizontal. Develop a formula (like the one from Wednesday's class) for the Range of the ball in terms of v_o,α,θ, and g .

Homework 8

• Problems based on UP Chapter 6. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Problem 6 -- 'Three Astronauts'
  • Problem 13 -- 'Baseball Player'
  • Problem 17 -- 'Hockey Puck'
  • Problem 24 -- 'Pig on a Slide'
• And two more not in the book
  • The coefficient of static friction between a vinyl record and a penny is about 0.2. If the record is rotating at 45 rev/min, what is the furthest distance from the center the penny can sit and stay there, i.e., rotate around with the record without being flung off?
  • For each of your trials in this week's in class labs please: draw an accurate free body diagram, derive the coefficient of friction (static or kinetic depending on trial), and discuss your results. It is not necessary to write a full lab report (though it won't hurt your grade if you do!) but I do expect the Free Body Diagrams to be neatly drawn and the discussion to be well thought out, clear, and complete.

Homework 9

• Problems based on UP Chapter 6. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Problem 31 -- 'Body A-Body B'
  • Problem 42 -- which will require doing Problem 14 as well. In addition to answering the questions posed by the book, tell me what coefficient of kinetic friction would be required to allow a storm with 150mph winds to move the same 20kg stone.
  • Problem 57 -- 'Pencil Box'
  • Problem 69 -- 'Puck on Table'
  • Problem 76 -- 'Pushing the Second Block'

• Also there will be a small lab on Wednesday with a write up similar to last week's lab writeup. (Worth 10 points, but with an additional 5 points possible if you write it up as a full lab report).

Homework 10

• Problems based on UP Chapter 7. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
  • Problem 13 -- 'Rebounding Ball'
  • Problem 16 -- 'Softball'
  • Problem 25 -- 'Meteor Impact'
  • Problem 45 -- 'Two Vehicles'
  • Problem 61 -- 'Game of Pool'

• Again, there will be a smallish lab on Wednesday with another small write up. And there will be some sort of extra credit piece to be explained in class on Wednesday.

Homework 11

• Problems based on UP Chapters 8 and 9. Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
• Chapter 8
  • Problem 8.9 -- 'Ammonia'
  • Problem 8.10 -- 'Metal Cube'
  • Problem 8.27 -- 'Shell Explodes'
  • Problem 8.32 -- 'A Certain Nucleus'
  • Problem 8.43 -- 'Suspicious Package'
• Chapter 9
  • Problem 9.9 -- 'Freight Car'
  • Problem 9.17 -- 'Luge Rider'

• No lab write up this week. Possibly some hard extra credit problems.

Homework 12

• Please turn in nicely-written, readable solutions. Show your work and explain (in English words, sentences, etc.) what you are doing and why.
• Review Questions First:
  • Problem 5.20 -- 'Volleyball'
  • Problem 6.80 -- 'Expert Witness'
  • Problem 8.46 -- 'Car on a Boat'
  • Problem 9.48 -- 'Average Rate of Work'
  • Freshman Curve -- Model "Freshman Curve" on South Road as part of a circle of radius R = 100 m. Suppose it is rather slippery and icy and the coefficient of kinetic friction between your car's tires and the road is μ_k = 0.1 . Of course, you are driving quite safely, and are thus crawling along at a speed of v = 8m / s . (a) If you just keep going at a constant speed, will you make it around the turn without sliding out into a tree/ditch? (b) Suppose that, just as you're entering the curve, you get a bit nervous and gently apply the brakes. Suppose in particular that you brake as to reduce your speed at a rate of 0.8m / s² . Explain what happens and why. (Hint: what does the acceleration vector look like after you step on the brakes?) (c) State, for the record, the general lesson about winter driving that this illustrates.
• Chapter 10 Questions
  • Problem 10.6 -- 'Loop-the-loop'
  • Problem 10.26 -- 'Tarzan'
  • Problem 10.35 -- 'Ice Mound' Tricky one!
  • Problem 10.95 -- 'Puck on Table'

Final Exam

• Date and Times to be announced