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Answer keys
EAS 1600 Lab 1 (Clicker)
Math and Science Tune-up
Note: Students can receive partial credit for the graphs/dimensional analysis.
For questions 1-7, match the correct formula (from the list A-I below) to the physical entity, and
enter the corresponding letter to CLICKER. To enter the letter, press any letter key (A-D, T, F)
and then use scroll up/down key (∧ and∨) to get to the letter corresponding to your answer. (1 pt.
each)
Question 1. Area (sphere) = _____ 4π ⋅ R 2 _______ D
Question 2. Area (circle) = _____ π ⋅ R 2 _______ C
4
Question 3. Volume (sphere) = _____ π ⋅ R 3 _____G
3
Question 4. Velocity = ____
d
________I
t
Question 5. Weight = ____ m ⋅ g ______B
Question 6. Kinetic Energy = ____
Question 7. Density = ____
m ⋅ v2
______F
2
m
______E
V
For questions 8-14, choose the correct MKS unit ( that is meters m, kilograms kg and
seconds s) for the physical entity, and enter the corresponding letter to CLICKER. To enter
the letter, press any letter key and then use scroll up/down (∧ and∨) to get to the needed
letter. (1 pt. each)
Question 8. Area (circle) is measured in ____ m 2 ______B
Question 9. Area (sphere) is measured in _____ m 2 _____B
Question 10. Velocity is measured in _____
m
_____E
s
Question 11. Volume (sphere) is measured in ____ m 3 ______C
Question 12. Weight is measured in ___
kg ⋅ m
_______F
s2
Question 13. Density is measured in ____
kg
______G
m3
Question 14. Kinetic Energy is measured in
____
kg ⋅ m 2
______I
s2
For questions 15-20, enter the correct multiplier to CLICKER. Example: for G (Giga-) the
multiplier is 1000000000. For numbers smaller than 1, enter 0 before decimal point, e.g.
0.00001 (1 pt. each)
Question 15. Multiplier for k (kilo-) is ____1000______
Question 16. Multiplier for M (mega-) is ____1000000______
Question 17. Multiplier for h (hecto-) is __100________
Question 18. Multiplier for c (centi-) is ____0.01______
Question 19. Multiplier for m (milli-) is _____0.001_____
Question 20. Assume some variable is measured in unit G . Then µ G (micro-G) is
___1000_______ times smaller than mG (milli-G). Enter the number into your Clicker.
For questions 21-23, enter the answer in the requested units into CLICKER. (1 pt. each)
Question 21. 2.8 g/cm3 = ______2800________kg/m3
Question 22. 6.3 km/h = ______1.75_______m/s
Question 23.
0.002 km2 = _______2000_______m2
2
Section 2. Density.
Question 24. A golden-colored cube is handed to you. The person wants you to
buy it for $200, saying that is a gold nugget. You immediately pulled out your
cell phone, go online and find that gold density is 19.3 g/cm3. You measure the
cube and find that it is 3 cm on each side, and weighs 135 g. What is the cube
density? Enter the answer into Clicker in units of g/cm3. (3 pts.) Answer: 5
Question 25. Is the cube in the above question made of gold? Enter “Y” for yes or “N” for
no into your Clicker. (2 pts.) Answer: “N”
Question 26. The ship on the image to the right weighs
67000 tons (1 ton = 1000 kg). Assuming the density of the
seawater is ~1.04 g/cm3, what is the amount of water
displaced by this ship in m3 ? Enter your answer into your
Clicker. (3 pts.) Answer: 64423
Section 3. Plots and Excel®.
Please See the File : Graphs-keys.xls (10 points for correct printed graph)
Question 27. Using your trend-line, predict what CO2 concentration will be in 2020. Enter
the number (in ppm) into your clicker. (5 pts.) Answer: 402.9 ppm.
Section 4. Trigonometry.
For questions 28-31, choose the mathematical expression that correctly defines the
trigonometric function using the sides of the right-angle triangle shown in Figure 1. Enter the
corresponding letter (A through G in the list below) to Clicker. (1 pt. each)
3
A. C/A
B. A/B
C.
A2 + B 2
D. C/B
E. B/C
F. A/C
Figure 1.
G. B/A
Question 28. Sine(ϕ) = ____ side opposite/hypotenuse = B/C _____E
Question 29. Cosine(ϕ) = _____ side adjacent/hypotenuse = A/C ____F
Question 30. Tangent(ϕ) = ____ side opposite/side adjacent = B/A ______G
Question 31. Side C expressed in terms of A and B:
C = A2 + B 2
C
Question 32. Calculate the sine of 13.7°. Enter the answer into CLICKER to the 4th digit
after the decimal point. (1 pt.)
Answer: ~ 0.2368
Question 33. Calculate the cosine of π/2 rad. Enter the answer into CLICKER to the 4th
digit after the decimal point. (1 pt.)
Answer: < 0.0001
Question 34. Enter into CLICKER the result of the following reaction:
CO + O → _ CO2__
To enter the answer to CLICKER, use a letters and numbers, e.g. enter N2 as N2. (2 pts.)
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Question 35. Balance the following equation (Ethylene combustion):
____2____NH3 + ____2____ O2 → ___1____N2O+ ____3___H2O.
(first coefficient)
(second coefficient)
(third coefficient)
(fourth coefficient)
Enter the coefficients of this equation into CLICKER as one number, e.g. if the coefficients
(from first to fourth) are 2, 4, 5, 2 then enter 2452 as your answer. (5 pts will be in
Clicker.) 2213
Section 6. Time-Distance-Velocity
For questions 36-33, solve the following time-distance-velocity problem. Two railroad
stations are 380 km apart. The first train leaves station A at a speed of 80 km/h, bound for
station B. At the same time another train leaves Station A at a speed of 64 km/h, bound for
station B.
Question 36. What is the time delay between the arrival of first and second train to the station
B? Enter the answer (in hours) into Clicker (4 pts.)
v1, t1 = velocity and time for train 1; v2, t2 = velocity and time for train 2
t1 =
t2 =
d
v1
d
v2
= 380/80 = 4.75 hours
= 380/64 = 5.94 hours
Δt = 5.94-4.75=1.19 hours
Question 37. How far will the trains be from station A when the delay between trains is 1
hour? Enter the answer (in km) into Clicker. (4 pts.)
t2- t1=1 hour, d=unknown distance. t1 =
d
v1
; t2 =
d
v2
, then
d
-
d
v2 v1
=1
dv1/v1v2 - dv2/v1v2 =1 ; dv1- dv2 =1* v1v2 ; d(v1- v2)= 1*v1v2 ;
finally d= v1v2/(v1- v2)=80*64/(80-64) = 320 km
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Section 7. Significant Digits
Question 38: 6,482.76388 rounded to the nearest hundredth is:
6,482.76
Question 39: 0.874 rounded to the nearest tenth is: 0.9
Question 40: 87,456.261 rounded to the nearest tenth is: 87,456.3
Section 8. Scientific notation
Question 41.
write 56 7000 in normalized scientific E-notation
5.67E5
Question 42.
write 690 000 000 in normalized scientific E-notation
6.9E8
Question 43.
express 5.34 ×10-2 as a standard decimal umber
Question 44.
express 87.586 × 100 as a standard decimal number
0.0534
87.586
The following problems are non-CLICKER problems:
Problem 1. Pressure is defined as force per unit area. Newton’s Second Law tells us that
force is mass multiplied by acceleration, while acceleration is the first time derivative of
velocity (or the second time derivative of distance). Therefore the units of acceleration are
m/s2 . A unit of force has the dimensions of kg⋅m/s2, and a unit of pressure has the
dimensions of kg⋅m/s2⋅m2 or kg/m⋅s2. The basic unit of pressure is Pascal (Pa, 1Pa = 1
kg/m⋅s2). Atmospheric pressure is normally recorded in hecto-Pascals (hPa). 1 hPa = 100
Pa.
Now the problem: the gas constant for dry air is 287 m2/s2⋅K (here K stands for
degrees Kelvin, and K = Celsius + 273). Assuming the temperature is 230 K and the
pressure is 1050 hPa, what is the atmospheric density? (Hint: write down all variables you
are given, together with their units. Figure out how to combine them to get the density. Show
all your unit conversions.) (10 pts.)
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Given information: 1Pa = 1 kg m-1 s–2; T = 230 K; P = 1050 hPa; Rd = 287 m2 s-2 K-1
Combine units for T, P and Rd in order to obtain
kg
.
m3
density =
Problem 2. On Mars the average atmospheric pressure at the surface is 6.36 hPa. If we
assume that the radius of Mars is 3396.2 km and the acceleration of gravity is 5 m/s2, what is
the mass of the Marian atmosphere? (Hint: you will need to use the surface area of Mars, not
just the radius) (10 pts.)
Combine units of P (pressue in Pascals,
to obtain kg.
kg
⋅ m2
2
P ⋅ SA m s
=
= kg ;
m
g
s2
mass = 𝟔. 𝟑𝟔𝒉𝑷𝒂×
𝟏𝟎𝟎 𝒉𝑷𝒂
𝟏 𝒉𝑷𝒂
kg
), g, and the surface area of the Mars (m2)
2
m⋅s
where SA = 4πre2 = 4π(3396.2 *1000 m)2
𝟒𝝅(𝟑𝟑𝟗𝟔. 𝟐𝒌𝒎
𝟏𝟎𝟎𝟎𝒎
𝒌𝒎
)𝟐 /𝟓 = = 1.84x1016 kg
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Problem 3. One Watt is equal to 1 Joule per second (1W = 1 J/s), while 1 Joule =
1 Newton⋅meter (1 J = 1 N⋅m), and 1 N = 1 Kg⋅m/s2.
(i)
What are the units of a Watt? Simplify. [3 points]
⎛ kg ⋅ m ⎞
⎜
⎟
J ⎛ N ⋅ m ⎞⎜ s 2 ⎟
kg ⋅ m 2
Answer: 1W = 1 ⎜
=
1
⎟
s ⎝ J ⎠⎜ N ⎟
s3
⎜
⎟
⎝
⎠
(ii)
Assume variable W has units of Watts, Variable K has units of kg/s, variable D
is distance (m) and Variable T is time (s). You need to calculate velocity V.
Write an expression for V in terms of W, K, D and T [3 points].
⎛ kg ⋅ m 2 ⎞
⎟⎟ ⋅ T (s )
W ⎜⎜
3
s
⎛ m ⎞
⎠
Answer: V ⎜ ⎟ = ⎝
= WT/DK ; another possible solution is
⎛ kg ⎞
⎝ s ⎠
D(m ) ⋅ K ⎜ ⎟
⎝ s ⎠
3
WD
KT
⎛ m ⎞ D(m )
Give half credit for V ⎜ ⎟ =
.
⎝ s ⎠ T (s )
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