Physics 116a02: Homework for Spring 2008

Professor Charles F. Maguire

Homework Submission via MasteringPhysics on the Internet

Like the other introductory physics courses, Physics 116 uses the MasteringPhysics Internet service for automated submission and grading of homeworks. You were asked to register into this system for this course. Typically, there will be at least one assignment due per week. The first two assignments shown below give first a practice introduction to the system, and then a later graded assignment.

You would be wise to remember that Internet outages do occur. So leaving your homework submission to almost the last minute can have you frozen out, since late homeworks will not be accepted.

Help Desk Facility for Physics 116a Started

There will be a Help Desk facility dedicated to this course. This Help Desk consists of 4 TAs in an office who can answer your questions about the homework assignments, or anything covered in class. Here is the link for the current schedule for the Help Desk facility. The facility stared on Monday, January 14, with the 1:30 PM session. This facility is being shared with Prof. Ramayya's Section 1 class.

Physics 116a One Hour Tutorial Sessions in the Physics 118a Lab course

Because of the very large enrollment in Physics 116a this semester, the Department is initiating one hour tutorial sessions in the Physics 118a labs. The plan is that Prof. Ramayya and I will provide a tutorial topic to the Physics 118a lab TAs. These TAs will then discuss that tutorial topic during the lab, which may include working out some simple problems. This plan means that Prof. Ramayya and I are coordinating our lecture schedules as much as feasible, given that Section 1 is MWF, and Section 2 is TR.

Current Homework Assignments from MasteringPhysics

Introduction to MasteringPhysics (was due January 11 before 11 PM)



Chapter 1: Units, Physical Quantities, and Vectors (was due January 15 before 9 AM)
Average grade 86.4%, median completion time 2 hours 59 minutes



Chapter 2: Acceleration and Free-Fall (was due January 22 before 9 AM)
Average grade 89.4%, median completion time 3 hours 47 minutes
Responses to some of the most repeated comments on this assignment

• Problem 2.31 is well designed but poorly implemented. Getting the correct answer to two digits for the acceleration at say the 7 second time required that one be able to estimate fairly exactly the times when the speed started to increase and when the speed stopped increasing. It would have been better if those two times corresponded to an actual grid point on the time axis instead of being part-way between two time grid points.
  
  
• Problem 2.84 required that you realize that you first had to calculate the distance, call it d, that the instructor fell in the first 3 seconds. This is easy enough (d = gt = 3g) since the instructor started to fall with zero initial speed (unless she was pushed). Then the sound of her initial yell would travel a total distance of h + (h-d) in 3 seconds at a constant speed of 340 meters/second. This will enable you to calculate the h distance, where h is the height of the cliff. Lastly, you can calculate her speed at the bottom of the cliff from the third kinematic equation since you know the initial speed (=0 m/s), the acceleration g, and the distance traveled h.
  
  
• Problem 2.94 doesn't have a numerical answer, but an algebraically derived answer in terms of H0, h, and g. I believe that the solution given in the problem does not correspond to how the problem is actually stated. As in problem 2.84, you can get the speed of the apple when it first touches the grass by knowing how far the the apple has dropped. As stated in the problem, that distance seems to be H0 (the textbook uses just H). However, the MasteringPhysics solution corresponds to a drop distances of H0 - h. I will send an e-mail to the MasteringPhysics representative about this discrepancy.
  
  Then you are told the apple slows down with constant deceleration until it has 0 speed just as it hits the ground. From the previous calculation you know the initial speed, you know that the apple has traveled a distance h, and you know that the final speed is 0. So again, using the third kinematic equation, you can figure out the acceleration of the apple while it is traveling this amount of distance h. It is possible that you were a bit confused by the fact that gravity is still acting accelerating the apple downward. However, there was another force acting (and you will learn about forces in Chapter 4) which produced an even greater acceleration in the opposite direction. So there was a net acceleration upwards which slowed down the particle. In fact this upwards acceleration acts just like air resistance, but with greater effect since it slows down the apple to zero speed.
  
  

Chapter 3: Two Dimensional Motion (was due January 29 before 9 AM) Extra hints for assignment 4
Average grade 86.4%, median completion time 2 hours 56 minutes


• The solution for problem 3.89 will be posted here after 9 AM on January 29.
  PDF file or Mathematica source file
  
  As explained in the class lecture, you do not have to know Mathematica to solve this problem. Part A is a two simultaneous equations (trajectory equation and linear equation) algebraic manipulation. Part B requires taking a derivative of a two term expression, and then simplifying the derivative result with trigonometric identities. The simplified derivative result has a cos(theta + 2phi) factor, and it will be equal to zero when theta + 2phi = pi/2.
  

Chapter 4: Newton's Laws of Motion (was due February 5 before 9 AM) Extra hints for assignment 5
Average grade 87.1%, median completion time 2 hours 34 minutes


The solutions for problem 4.38 and 4.54 will be posted here after 9 AM on February 5.
Problem 4.38
Problem 4.54


There were also some comments about the addition or subtraction of two (three) force vectors, from the Newton's 1st and 2nd Laws tutorial. Very simply, if one has a vector of magnitude A and another vector of magnitude B, then the maximum magnitude of their addition is A+B, and the minimum magnitude of their addition is the absolute value |A - B|. The maximum occurs when the vectors have the same direction, while the minimum occurs when the vectors are oppositely directed. If you think about it, the limits for the subtraction of two vectors are the same, depending on their relative directions. So only forces of exactly equal magnitude can be combined to give zero net force, which in turn means zero net acceleration. The answers for the "at rest" and "at constant velocity" questions are the same, since no acceleration means a constant velocity (including zero velocity "at rest") for the mass.

You can extend the analysis to three forces. If you have two forces of 2 Newtons each, then the maximum of their addition is 4 Newtons. If there is a third force of 5 Newtons, this force cannot be canceled out by the pair of 2 Newton forces. On the other hand, a pair of two 200 Newton forces can easily add up to a 5 Newton result, which can be canceled out by a third force of 5 Newtons, leading to an object with no acceleration.

Chapter 5: Applications of Newton's Laws of Motion (was due February 12 before 9 AM) Extra hints for assignment 6
Average grade 86.0%, median completion time 2 hours 54 minutes



Chapter 6: Work and Kinetic Energy (is due February 19 before 9 AM) Extra hints for assignment 7
Average grade 87.5%, median completion time 2 hours 25 minutes



Chapter 7: Potential Energy (was due February 19 before 9 AM) Extra hints for assignment 8
Average grade 82.7%, median completion time 1 hours 53 minutes



Chapter 8: Momentum and collisions (was due February 26 at 9 AM, according to the survey results) Extra hints for assignment 9
Average grade 85.4%, median completion time 1 hours 59 minutes



Chapter 9: Kinematics of Rotation (was due March 13 at 9 AM, includes two-day extension for Alternative Spring Break service) Extra hints for assignment 10
Average grade 82.2%, median completion time 3 hours 25 minutes



Chapter 10: Torques and Rotational Acceleration (was due March 18 at 9 AM) Extra hints for assignment 11
Average grade 77.7%, median completion time 2 hours 27 minutes
Illustration for solving problem 10.83
Explanation for solving problem 10.83


Chapter 11: Rotational Equilibrium; Chapter 12: Universal Gravity (is due March 25 at 9 AM) Extra hints for assignment 12

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This page was last updated on March 22, 2008