Massachusetts Institute of Technology - Physics DepartmentPhysics - 8.01 Assignment #1 September 8, 1999.It is strongly recommended that you read about a subject before it is covered in lectures.Lecture Date Material Covered Reading from Ohanian#1 Wed 9/8 Powers of Ten - Units - Dimensions Prelude, page 1–18Measurements - Uncertainties Ch. 1, page 1–20Dimensional Analysis - Scaling Arguments Take Notes#2 Fri 9/10 1D Kinematics - Speed - Velocity - Acceleration Page 25–43#3 Mon 9/13 Vectors - Dot Products - Cross Products Page 53–683D Kinematics Page 74–81Watch videos on PIVoT (e.g. keywords:vector multiplication,dot product, etc. andlook at the Simulation)#4 Wed 9/15 3D Kinematics Page 74–84Falling Reference Frames Page 86–90Due Wednesday, Sept 15, before 4 PM in 4-339B. Solutions will be available on Sept 17.1.1 Estimates and Uncertainties – Ohanian page 21, ques tion 1.1.2 Fundamental Units – page 21, question 14.1.3 How to measure the thickness of one sheet of paper to a high degree of accuracy?a) With a ruler, measure as accurately as you can the thickness (in mm) of your temporaryfive-chapter copy of Ohanian (excluding the yellow front and back cover).b) What is the approximate uncertainty (often called error) in your measurement (in mm)?c) What is the percentage uncertainty (often called relative uncertainty or relative error) in yourmeasurement under a)?d) Deduce from your answer under a) the thickness of one sheet of paper (in microns).e) What is the uncertainty in the thickness of one sheet of paper (in microns)?f) What is the p erc entage uncertainty in your result of the thickness of one sheet?g) Differe nt students may find very different values for the thickness (even if we take the uncer-tainty in their measureme nts into account). Why is that expected?1.4 Relative UncertaintiesThere is a very large difference in the relative uncertainties of the measurements of (i) the length ofthe student measured in lectures on 9/8, and (ii) the thickness of the femurs shown in lectures (se ethe data on the 8.01 Home Page). What is the relative uncertainty (in %) for the student’s length,and what for a typical value of the thickness of the bones? Why are the two so very different?1.5 Distant Quasar – page 22, problem 8.http://dir.yahoo.com/Science/Astronomy/Astrophysics/Stellar Phenomena/Quasars/1.6 Distances on Earth – page 22, problem 10.1.7 Atoms in your Body – page 23, problem 26.1.8 Astronomical Distances – page 23, problem 29.http://einstein.stcloudstate.edu/Dome/clicks/au.html1.9 Mean Density of Stars - page 24, problems 37 and 38.http://search.yahoo.com/bin/search?p=neutron+stars1.10 Position, Velocity, Speed, and Acceleration.The position, x (in m), of an object that moves along a straight line is changing with time, t (insec), as follows:x = +16 − 12t + 2t2a) Make a plot of the position x vs. time from t = 0 to t = +6.b) Make a plot of the velocity, v (in m/sec), vs. time from t = 0 to t = +6.c) Make a plot of the acceleration, a (in m/sec2), vs. time from t = 0 to t = +6.d) What is the velocity at t = 0, +2, and +4?e) What is the acceleration at t = 0, +2, and +4?f) When is the velocity zero, and what then is the x position of the object?g) What is the average velocity between t = −1 and t = +3?h) What is the average velocity between t = 0 and t = +6?i) What is the average speed between t = 0 and t = +6?j) At what time does the object reverses its direction?1.11 Car Crash and Seat Belts – page 49, problem 35.1.12 Brain Teaser - Returning to the same Point on Earth.A person starts walking at point A on earth. She walks 10 km to the south, stops, then walks 10km to the east, stops, then 10 km to the north, and she is back at point A where s he started. Findall points on the surface of the earth that will meet this condition. Don’t miss any, there are aninfinite number of them!1.13 Human Femur.Look at http://www.wcape.school.za/subject/biology/skeleton/femur.htm. You will see a humanfemur on a scale roughly 2:1.a) What is the ratio d/l as defined in class (look at our plot on the 8.01 home page)? The ratiod/l is independent of the scale. You will not b e able to measure the average value of d asdefined in class. This, however would make a difference of at most 10%.b) What is the average value of d/l of the data in our plot? This value is substantially higherthan the value under a).c) C an you come up with reasons why that may be the case. Frankly, I am somewhat at a loss.Since humans walk on two legs, I had expected the value of d/l for humans, if anything, to behigher, not lower, than the average value for the mammals in our plot as they walk on fourlegs.REMEMBER!8.01 Home Page http://www.mit.edu/˜8.01/Fall99/There are 26 recitation sections. If you want to change, f or whatever reason, please go tothe physics education office
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