Review for Test 1 – This is a sample, not a complete review. It is meant to give you indications
of what you need to go over.
1) Find the x and y components of 𝐺⃑ = 50 m/s @ 23 degrees S of W.
2) What elements are present on a good graph?
3) If you are given a set of data, write a step by step process that you would use to
a) find the relationship between the data points
b) straighten the curve
c) find the constant of proportionality
4) Name three scalar quantities and three vector quantities.
5) What is the difference between precision and accuracy?
6) What is valid error? How do you quantify the significance of error? How do you mitigate
error?
7) Make the following conversions
a) 40 km = ___________ cm
b) 34 µm = ________ m
c) 2.3 x 10-2 Mm = __________ mm
d) 8.2 x 102 cm = _________ nm
8) For each of the below, use dimensional anaysis to find the units of K.
A measured in gurgs
B measured in dips
C measured in toks/dips
D measured in toks squared
𝐵𝐾
𝐴𝐵
a) 𝐴 = 𝐷
c) 𝐷 = 𝐾𝐶
6𝐾𝐷
b) CA = KD
d) 𝐴2 = 𝐵
9) Given the following three vectors:
M = 50 m @ 60 degrees N of W
N = 100 m North
P = 85 m @ 15 degrees S of E
Graphically and mathematically add these vectors in order M + N + P.
What would happen if the vectors were added in R = P + N + M?
10) If B α H2, if
a) I double H, what happens to B?
b) I take 1/9 H, what happens to B?
c) I want B to triple, what must be done to H?
11) What is the difference between causation and correlation?
12) Why is a foot an acceptable but not ideal basis for a system of length measurement?
13) What is the difference between vectors drawn consecutively vs. concurrently? When would
you do each?
14) What is the difference between a fundamental quantity and a derived quantity? Can you
name examples of each?
Answer Key
𝑚
𝑚
1. |𝐺⃑𝑥 | = |𝐺⃑ | cos 𝜃𝐺 = 50 𝑠 cos 23 = 46.0 𝑠
𝑚
𝑚
. |𝐺⃑𝑦 | = |𝐺⃑ | sin 𝜃𝐺 = 50 sin 23 = 19.5
𝑠
Not drawn to scale…
Assuming normal compass rose
𝑠
2. Good graph
- Title in the format Dependent vs Independent
- Axes with a scale that is even and extends the trend over the entire space. Labels of the variable
with units.
- circles around experimental points
- You have considered if (0,0) should be a point
- Best fit lines/curves
3. a) plot the points and use your knowledge of the shapes of graphs to make a guess as to the
type of relationship
b) Steps:
1) Guess the relationship and write the expected proportionality
2) Make a new data column that takes the INDEPENDENT DATA and does the name of the
relationship to the independent data. Remember you will do this operation to the units too. So if
the original data was a time column in seconds and your guess was a squared relationship, your
new column would be time squared in seconds squared.
3) Plot the new points on a properly labeled graph
4) If the trend is linear, you guessed right on the proportionality. If you guessed wrong, the trend
will still be some sort of curve. Guess again and go back to step 2
c) the constant of proportionality is always the slope of the straightened line. Include units!
4) Vectors – force, velocity, displacement, weight, acceleration, momentum, and others…
Scalars – volume, speed, distances, density, mass, time, and others…
5) Accuracy talks about how closely a data set compares to a known. Precision is about how
closely the data of the data set compares to the other members of the data set. When there is no
known value, a closely clustered set of results can be used to establish confidence in that
unknown value.
6) Valid error is unavoidable error due to the tools used (measurement error caused by the
precision of the measuring device) or the procedures used (systemic error)
Quantifying the significance of this error can come from comparing the size of the absolute
precision error of the measuring device (+ or – the smallest gradation or reaction time for a
stopwatch) to the size of the measurements OR by comparing the variation in a data set to the
size of the average.
Error can be mitigated by taking multiple trials to detect the presence of and reduce the
significance of outliers. A larger sample size can be used (such as measuring the time for 10
occurrences of an event rather than one). This reduces the significance of the inherent error of
the tool. Note that this doesn’t reduce the actual AMOUNT of error present. A different tool can
be used with a more precise scale.
7. a) 40 km = 4.0 x 106 cm
c) 2.3 x 10-2 Mm = 2.3 x 107 mm
8. a) [𝑘] =
𝑔𝑢𝑟𝑔 𝑡𝑜𝑘 2
b) 34 µm = 3.4 x 10-5 m
d) 8.2 x 102 cm = 8.2 x 109 nm
𝑔𝑢𝑟𝑔
b) [𝑘] = 𝑑𝑖𝑝 𝑡𝑜𝑘
𝑑𝑖𝑝
9. Drawing is below.
Let’s make North and East +
Find the components of non-axial vectors:
⃑⃑⃑𝑥 | = |𝑀
⃑⃑⃑| cos 𝜃𝑀 = 50𝑚 cos 60 = 25 𝑚
|𝑀
⃑⃑⃑𝑦 | = |𝑀
⃑⃑⃑| sin 𝜃𝑀 = 50𝑚 sin 60 = 43.3 𝑚
|𝑀
|𝑃⃑⃑𝑥 | = |𝑃⃑⃑| cos 𝜃𝑃 = 85 𝑚 cos 15 = 82.1 𝑚
|𝑃⃑⃑𝑦 | = |𝑃⃑⃑| sin 𝜃𝑃 = 85 𝑚 sin 15 = 22.0 𝑚
Make the table
X
y
M
-25 m
+43.3 m
N
0
+ 100 m
P
+82.1 m
- 22 m
R
57.1 m
+ 121.3 m
2
2
|𝑅⃑⃑ | = |𝑅⃑⃑𝑥 | + |𝑅⃑⃑𝑦 |
2
2
|𝑅⃑⃑ | = |57.1 𝑚|2 + |121.3 𝑚|2
⃑⃑⃑⃑⃑⃑
|𝑅| = 134.1 m
⃑⃑⃑⃑⃑
|𝑅
𝑦|
⃑⃑⃑⃑⃑𝑥 |
|𝑅
121.3 𝑚
𝑡𝑎𝑛 𝜃𝑅 =
57.1 𝑚
𝜃𝑅 = 64.8
⃑⃑⃑⃑⃑⃑
|𝑅| = 134.1 𝑚 @ 64.8 𝑁 𝑜𝑓 𝐸
𝑡𝑎𝑛 𝜃𝑅 =
c) [𝑘] =
𝑔𝑢𝑟𝑔 𝑑𝑖𝑝𝑠2
𝑡𝑜𝑘𝑠3
d) [𝑘] =
𝑔𝑢𝑟𝑔 2 𝑑𝑖𝑝
𝑡𝑜𝑘 2
10. a) 2H = > squared relationship => (2)2B => 4B
b) 1/9 H => 1/81 B
c) If I want B to triple, I need to ask, what squared equals tripled? Which is √3. So if I multiply
H by √3
11. Causation means a change in one variable always causes a specific type of change in another
variable. Correlation means that when one variable changes, often it is observed that another
variable changes.
12. It is acceptable because as long as people agree on the meaning, we can still use the foot to
compare values and communicate effectively with each other. This basis is fairly arbitrary and
more arbitrary than some other choices we could have made since the concept of a foot changed
over time due to political and social factors. A more stable basis is a better basis.
13. Concurrently means drawn from the same point. Often this is done to get a good physical
representation for what is occurring.
Consecutively means the vectors are draw one after the other. This is used to do vector addition.
14. Fundamental quantities are not composed of other quantities (length, time, mass, etc).
Derived units are mathematical combinations of fundamental quantities (speed, area, density,
acceleration, etc)
This review isn’t everything but a representative sample. For example, there is nothing here
about using dimensional analysis to prove the potential validity of an equation. Missing is a
discussion of observation, conclusion, hypothesis, theory and a law. SO, this is guideline to point
you to things you need to review and not a comprehensive review.