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# Winter 2017 Physics 41 - Mechanics - Problem Set 1 Dimensional Analysis; Kinematics in One Dimension Written parts (1 and 2) are due by 6:, Jan. 13,...

number 2!!! 45 m before traffic light. Reaction time: .5 sec for brake.

Winter 2017 Physics 41 – Mechanics Problem Set 1 Dimensional Analysis; Kinematics in One Dimension Written parts (1 and 2) are due by 6:15 p.m. Fri., Jan. 13, uploaded to gradescope. The MasteringPhysics portion (item 3) is due online by 6:15 p.m. Fri., Jan. 13. Read “To The Student” (pages ix - x) and review Chapter 1 (skipping 1.10 Products of Vectors, for now) and Chapter 2 in the textbook by Young & Freedman. Practice Problems in Young & Freedman (good problems to do in a study group): Ch. 1: 1.9, 1.10, 1.49; Ch. 2: 2.3, 2.8, 2.13. Practice Tutorials are available through MasteringPhysics; see item 3 on next page. You can use HINTS in these MasteringPhysics tutorials to help develop conceptual un- derstanding of the material and problem-solving strategies. Practice problems will not be graded. However, if you are not already very familiar with any topic covered in the ﬁrst week, then do the relevant practice tutorials in Mas- teringPhysics and practice problems in Young & Freedman before tackling the assigned problems. Answers to odd-numbered problems are in the back of the textbook. In working through problems, do not substitute numerical values for variables until the very end of the problem. This has several advantages: some variables may cancel, making the dependence of the result on each variable more apparent and simplifying calculations; you are less likely to make transcription errors; you can check special cases and limiting behavior. Remember that variables have dimensions (not units); numerical values have associated units . Therefore, never include units with the symbol for the variable, but always include units (e.g., m, kg, s) with any numerical value assigned to a variable that has dimensions. Check that units cancel appropriately when multiplying numerical values. Points will be deducted if units are not included with numerical values, even in intermediate steps. An important aspect of solving “real world” problems is identifying necessary information and recognizing when information is not relevant. In this course, you may be given information that you ﬁnd is not needed for the problem you are asked to solve. In other cases you may ﬁnd that you need some information that is not given in the problem, such as readily available numerical values for quantities. E.g., if you need the value of g on the Moon, just google “what is g on the moon?” and you will get the result! Always show your work and justify your response with an equation or concise explanation. 1. In a movie, the director wants to depict the toppling of a sequoia tree which is 50 m high. Instead of ﬁlming a real sequoia tree being cut down, a scaled-down model of the tree and its surroundings is made. The model tree is 1 m high and has the same density as a real sequoia. A recording is made of the model tree falling over; however, upon viewing the recording, the director notices that it does not look realistic. (a) Use dimensional analysis (i.e., the technique we used in Lecture 1) to determine a formula – up to a dimensionless constant – for the estimated time it takes for a tree of height h and mass m to fall to the ground (ie. lie horizontally). Assume the 1
density of the tree is uniform and given by ρ , and feel free to make any simplifying assumptions that you feel are warranted. You may also assume that the tree has a slight tilt away from being perfectly vertical when it is cut. (b) To make the ﬁlm look realistic, should the recording of the model tree be sped up or slowed down? By what factor should the speed of the ﬁlm be changed? 2. You are driving down El Camino Real at 10 m/s, and your car is 45 m from an intersection when the traﬃc light turns red. Assume that your reaction time is 0.50 s before hitting the brakes and that your car slows down with a constant magnitude of acceleration after hitting the brakes. (a) How far are you from the intersection when you begin to apply the brakes? (b) What magnitude of acceleration will bring you to rest right at the intersection? (c) How long does it take you to stop after the light turns red? (d) Make a graph of x versus t for your car. Assume the light turns red at t = 0, and also let x = 0 denote your position when the light turns red. (Be sure to label the axes with variables and units, and include a scale.) 3. Complete “Assignment 1: Intro to MasteringPhysics” through the MasteringPhysics (MP) website at www.masteringphysics.com . Follow the instructions in the syllabus on Canvas to register for MP (the course ID is PH41YLEE2017). The purpose of this ﬁrst MP assignment is to introduce you to the details of the MasteringPhysics online tutoring system. Your grade for the MP portion of this problem set is based on completing the ten required exercises, not on the correctness of responses – but make sure that you learn how to enter responses correctly to save frustration later! In the MasteringPhysics assignment list, you will also ﬁnd practice tutorials for Chap- ters 1 and 2 in Young & Freedman. We strongly recommend that you use this op- portunity to review any concepts in the Ch. 1 and 2 practice tutorials with which you are not completely comfortable since these concepts are essential background for this course. Then move on to the Ch. 2 practice tutorials – kinematics in one dimension. 2

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