Winter 2017
Physics 41 –
Mechanics
–
Problem Set 1
Dimensional Analysis; Kinematics in One Dimension
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Written parts (1 and 2) are due by 6:15 p.m. Fri., Jan. 13, uploaded to gradescope.
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The MasteringPhysics portion (item 3) is due online by 6:15 p.m. Fri., Jan. 13.
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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.
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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.
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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.
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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.
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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.
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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.
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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!
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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