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) = _____ _______ D

Question 2. Area (circle) = _____ _______ C

Question 3. Volume (sphere) = _____ 3

34 R⋅π _____G

Question 4. Velocity = ____ td ________I

Question 5. Weight = ____ gm ⋅ ______B

Question 6. Kinetic Energy = ____ ______F

Question 7. Density = ____ ______E

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 ____ 2m ______B

Question 9. Area (sphere) is measured in _____ 2m _____B

24 R⋅π

2R⋅π

2

2vm ⋅

Vm

2

Question 10. Velocity is measured in _____ _____E

Question 11. Volume (sphere) is measured in ____ ______C

Question 12. Weight is measured in ___2smkg ⋅ _______F

Question 13. Density is measured in ____ 3mkg ______G

Question 14. Kinetic Energy is measured in ____2

2

smkg ⋅ ______I

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 µG (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

sm

3m

3

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)

4

A. C/A

B. A/B

C.

D. C/B

E. B/C

F. A/C

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 = 22 BA + 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.)

22 BA +

Figure 1.

5

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 =1vd

= 380/80 = 4.75 hours

t2 =2vd

= 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 =1vd

; t2 =2vd

, then 2vd

-1vd

=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

6

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 0.0534

Question 44. express 87.586 × 100 as a standard decimal number 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.)

7

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 3mkg .

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, 2smkg⋅

), g, and the surface area of the Mars (m2)

to obtain kg.

kg

sm

msmkg

gSAP

=

⋅

=⋅

2

22

; where SA = 4πre2 = 4π(3396.2 *1000 m)2

mass = 𝟔.𝟑𝟔𝒉𝑷𝒂× 𝟏𝟎𝟎  𝒉𝑷𝒂𝟏  𝒉𝑷𝒂

𝟒𝝅(𝟑𝟑𝟗𝟔.𝟐𝒌𝒎 𝟏𝟎𝟎𝟎𝒎𝒌𝒎

)𝟐/𝟓 = = 1.84x1016 kg

8

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]

Answer: 3

22111

smkg

Nsmkg

JmN

sJW ⋅

=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ ⋅

⎟⎠

⎞⎜⎝

⎛ ⋅=

(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].

Answer: ( )

( ) ⎟⎠

⎞⎜⎝

⎛⋅

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅

=⎟⎠

⎞⎜⎝

⎛

skgKmD

sTsmkgW

smV

3

2

= WT/DK ; another possible solution is 3KTWD

Give half credit for ( )( )sTmD

smV =⎟⎠

⎞⎜⎝

⎛ .