This page contains notes and hints for the homework assignments.

The purpose of the homework assignments is to focus your study of the topics we cover in the course.  Your task is to make sure that you know how to solve the homework problems that are due each class.  Homework assignments are available on the Wiley electronic homework system as explained in class.  The links for the various sections are given below.

There will also be a number of unannounced homework quizzes in class.  These quizzes will test whether you can solve problems similar to the homework problems that are due on that day.  These quizzes will provide both you and your instructor with early feedback if you are not "getting" one or more of the concepts.  It will then be up to you to seek help from office hours, drop-in tutoring, and other resources that are available to you.

Please see the Syllabus for more information about homework quizzes and your homework grade. 

ABOUT SIGNIFICANT DIGITS

ABOUT REGULAR AND CHALLENGE PROBLEMS

ABOUT REVIEW PROBLEMS

Review Problems for Exam #1

Review Problems for Exam #2

Review Problems for Exam #3

SIGNIFICANT DIGITS

In Physics I, numerical uncertainty is represented by the number of significant digits.  The significant digits are the digits used to represent a number except for any zeroes used to place the decimal point.  For example, the number 0.0001 has one significant digit (the "1") because the other digits simply indicate the location of the decimal point.  If a number contains an unnecessary 0, it is assumed to be significant.  For example, the final zero in 0.00010 is significant.  If a whole number ends in a decimal point, all digits are significant.  Otherwise, any final zeroes are not significant.  All digits in the mantissa of a number expressed in scientific notation are significant.  Unless otherwise indicated, the uncertainty in a number is plus or minus one digit in the last significant place.

Generally speaking, the number of significant digits in the answer to a problem should be the same as the number used to specify the problem.  In most cases in our textbook, this will be two or three digits.

However, counting significant digits is only the beginning of wisdom in assessing the uncertainty in a number.  In some cases, significant digits can be misleading.  For example, the numbers 0.100 and 0.999 have the same number of significant digits (three), but the uncertainty in the first number - expressed as a percentage - is approximately ten times the uncertainty in the second number.

Approximating numerical uncertainty using significant digits works best when multiplying and dividing numbers.  When adding and subtracting numbers, significant digits can be gained or lost.  One common example of this occurs when two numbers that are close to each other are subtracted.  In that case, it is easy to lose significance.  For example, subtracting 0.998 from 0.999 leaves 0.001 and loses two significant digits in the process.

Another area of difficulty you may encounter is accuracy lost due to premature rounding of intermediate values that you calculate on your way to the final answer.  If you have a calculator that allows you to store numbers in memory, a good strategy is to keep all intermediate calculations to full precision and then round the final answer to the correct number of significant digits.

Since Physics I is not a course on error analysis, we will not be grading the numerical accuracy of your answers.  Numerical answers in the electronic homework are graded as correct if they are within 2%.  The most important things are the principles of physics you used to get the answers to the homework problems, not the precise numbers.

Each homework assignment has Regular Problems and a number of Challenge Problems, typically two or three.  The Challenge Problems are marked with asterisks ("*").  The problems are generally listed in order of difficulty.  If you expect to get an "A" in the course, you should understand how to do most of the Challenge Problems if not all of them.

There are three sets of optional Review Problems, one for each unit exam.  Each set contains ten problems of varying difficulty, from easy to challenge.  The purpose of these problems is to help you focus on the material that will be covered on each exam.  These are to be written on paper, clearly showing how you got the answers, and handed in just before taking the exam.  It is totally up to you whether you do all, some, or none of the problems.

Review Problems for Exam #1
Chapter 2 - 62 page 34. (a) -8.0 m/s² (b) 20. m/s
Chapter 4 - 50 page 80. 14.3º 
Chapter 4 - 66 page 81. (4.00,6.00) m  The acceleration of the particle has a magnitude = v²/r, where v is the speed of the particle and r is its distance from the center of the circle; the direction of acceleration points toward the center of the circle and is at a right angle to the direction of its velocity.
Chapter 5 - 59 page 112. (a) 0.735 m/s² (b) down (c) 20.8 N
Chapter 5 - 67 page 113. (a) 8.0 m/s (b) +X direction
Chapter 6 - 60 page 136. (a) 0.40 N (b) 1.9 s  The acceleration of the bob has a magnitude = v²/r, where v is the speed of the bob and r is its distance from the center of the circle; the direction of acceleration points toward the center of the circle.  To figure out what the magnitude of acceleration is, consider the following principles of physics: (a) The acceleration and net force point in the same direction. (b) What are the forces on the bob?  (Hint: There are two; "centrifugal" force is not one of them.)  (c) The bob's acceleration in the vertical direction = 0.  (d) Net force is related to acceleration by Newton's Second Law; there is one equation for the horizontal direction and another for the vertical direction.  (e) The period of the motion is the time it takes for the bob to go around the circle once.  (Think speed = distance/time.)
Chapter 9 - 22 page 231. 48º
Chapter 9 - 30 page 232. (a) 30. i kg m/s (b) 37.5 i kg m/s (c) 6.0 i m/s
Chapter 9 - 53 page 234. (a) 721.4 m/s (b) 937.4 m/s
Chapter 9 - 103 page 238. We will see this problem again in the review for Exam #2.  For now, we will make it simpler by giving you the final velocity of ball #1, which is -2 i m/s.  In the answer, "sqrt(3)" means the square root of 3.  You can do this problem without a calculator.  Hint: Use symmetry to help solve the problem.
    (a) 4 sqrt(3) m/s (b) ? (c) ? (d) ? (e) 2 m/s (f) 180º

Review Problems for Exam #2
Chapter 7 - 30 page 162. (a) 15.6 J (b) 15.6 J (c) 0 J (d) -14.4 J
Chapter 7 - 39 page 162. (a) 42 J (b) 30 J (c) 12 J (d) 6.5 m/s (e) 5.5 m/s (f) 3.5 m/s (all +X)
Chapter 8 - 31 page 192. (a) 0.347 m (b) 1.69 m/s
Chapter 8 - 62 page 194. The force of friction is 1/2 mg.  H = 3/4 d
Chapter 9 - 80 page 236. (a) 7.11 m/s (b) greater (c) less (d) less
Chapter 9 - 103 page 238. We saw this problem in the review for Exam #1.  Now, we are ready to do it from the beginning.  Assume that the collision is elastic, but you cannot assume you know the final velocity of ball #1 until you find it.  In the answer, "sqrt(3)" means the square root of 3.  You can do this problem without a calculator.  Hint: Use symmetry to help solve the problem.
    (a) 4 sqrt(3) m/s (b) ? (c) ? (d) ? (e) 2 m/s (f) 180º
Chapter 10 - 55 page 269. (a) 0.0600 m/s² (b) 4.87 N (c) 4.54 N (d) 1.20 rad/s² (e) 1.39 x 10^-2 kg m²
Chapter 10 - 110 page 274. (a) 3.3 J (b) 2.9 J
Chapter 11 - 31 page 299. (a) 0 (b) 22.6 kg m²/s into page (c) 7.84 N m into page (d) same as (c)
Chapter 11 - 63 page 302. (a) 0.18 m (b) clockwise

Review Problems for Exam #3
Chapter 13 - 81 page 357. d = 2.5 x 10⁴ km The value of g is 9.8 m/s² on the surface of Earth, and the radius of Earth is 6370 km.
Chapter 21 - 60 page 579. (a) 6.16 x 10^-24 N (b) +208°
Chapter 22 - 11 page 599. (a) 1.38 x 10^-10 N/C (b) 180°
Chapter 22 - 16 page 599. +/- 67.6°
Chapter 22 - 50 page 602. (1.532 x 10⁶ i - 0.434 x 10⁶ j) m/s
Chapter 24 - 45 page 650. (a) 60,000 V (b) -780,000 V (c) 2.5 J (d) increases (e&f) same
Chapter 24 - 71 page 652. (a) 1.75 cm (b) 8.4 x 10⁵ m/s (c) 2.1 x 10^-17 N (d) +X (e) 1.6 x 10^-17 N (f) -X 
Chapter 28 - 6 page 758. (a) Vx = -3500 m/s (b) Vy = 7000 m/s
Chapter 28 - 26 page 759. 2.09 x 10^-22 J
Chapter 28 - 24 page 759. (a) 5.00 x 10⁶ m/s (b) 7.12 mm (c) 8.94 ns

Welcome to Physics I at RPI for Fall 2007!

We post important announcements here, at the bottom of each page.  All of the information you need to know about the course is posted on this site.  Add it to your list of “favorite sites” (I know, I know...) and check often.

If you are using Microsoft Windows Vista, you need to upgrade to LoggerPro 3.5. Follow this link for instructions.

If you are having trouble connecting your laptop to the LabPro device when you attach the USB cable, check this possible workaround.

You can download copies of the first exam and its solutions, the second exam and its solutions, and the third exam and its solutions.

There will be Supplemental Instruction for Physics 1 by Asantha Kempitiya Mondays and Thursdays 8-10pm in DCC 235.  (This is a change from the original location.)

The optional review for exam 3 will be held Tuesday, Nov. 27, from 6:00 to 7:30 pm, in DCC 308.