Q: A NASA mission failed due to a unit conversion error between metric and English units. If a force was calculated as 100 Newton-seconds (N·s) but entered as 100 pound-seconds (lb·s), what is the correct conversion factor to use between these units?

$$1 \ \text{N} \cdot \text{s} = 0.2248 \ \text{lb} \cdot \text{s}$$

Q: Convert 2.50 kilometers to centimeters using the correct metric conversion factors.

$$2.50 \ \text{km} \times \frac{1000 \ \text{m}}{1 \ \text{km}} \times \frac{100 \ \text{cm}}{1 \ \text{m}} = 2.50 \times 10^5$ \ \text{cm}$$

Q: A piece of platinum has a density of $$21.5 \ \text{g/cm}^3$$ and a volume of $$4.49 \ \text{cm}^3. $$What is its mass?

$$m = d \times V = 21.5 \ \text{g/cm}^3 \times 4.49 \ \text{cm}^3 = 96.5 \ \text{g}$$

Q: A 747 jet is fueled with $$173,231 \ \text{L} of $$jet fuel with a density of $$0.768 \ \text{g/cm}^3. $$What is the mass of the fuel in kilograms?

$$1.33 \times 10^5$ \ \text{kg}$$

Q: A motorcycle is traveling at $$105 \ \text{km/h}. $$What is its speed in meters per second?

$$105 \ \text{km/h} \times \frac{1000 \ \text{m}}{1 \ \text{km}} \times \frac{1 \ \text{h}}{3600 \ \text{s}} = 29.2 \ \text{m/s}$$

Q: A vineyard has 145 acres of Chardonnay grapes. If a soil supplement requires $$5.50 \ \text{g}$$ for every square meter, how many kilograms are needed for the entire vineyard? (1 km$$^2 = 247 $$acres, 1 km$$^2$$ = $$10^6 m$^2)$$

$$145 \ \text{acres} \times \frac{1 \ \text{km}^2}{247 \ \text{acres}} \times \frac{10^6$ \ \text{m}^2}{1 \ \text{km}^2} \times \frac{5.50 \ \text{g}}{1 \ \text{m}^2} \times \frac{1 \ \text{kg}}{1000 \ \text{g}} = 3.23 \times 10^3$ \ \text{kg}$$

Question 1

A NASA mission failed due to a unit conversion error between metric and English units. If a force was calculated as 100 Newton-seconds (N·s) but entered as 100 pound-seconds (lb·s), what is the correct conversion factor to use between these units?

Accepted Answer

$$1 \ 	ext{N} \cdot 	ext{s} = 0.2248 \ 	ext{lb} \cdot 	ext{s}$$

Question 2

Which of the following statements best describes the difference between accuracy and precision in scientific measurements?

Accepted Answer

Accuracy is how close measurements are to the true value, while precision is how close measurements are to each other.

Question 3

A student measures the mass of a sample as 0.00420 g. How many significant figures does this measurement have?

Accepted Answer

3

Question 4

Convert 2.50 kilometers to centimeters using the correct metric conversion factors.

Accepted Answer

$$2.50 \ 	ext{km} 	imes \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} 	imes \frac{100 \ 	ext{cm}}{1 \ 	ext{m}} = 2.50 	imes 10^5$ \ 	ext{cm}$$

Question 5

A piece of platinum has a density of $$21.5 \ 	ext{g/cm}^3$$ and a volume of $$4.49 \ 	ext{cm}^3. $$What is its mass?

Accepted Answer

$$m = d 	imes V = 21.5 \ 	ext{g/cm}^3 	imes 4.49 \ 	ext{cm}^3 = 96.5 \ 	ext{g}$$

Question 6

Which of the following is an example of an intensive property?

Accepted Answer

Density

Question 7

A temperature is measured as $$77 \ 	ext{K}. $$What is this temperature in degrees Celsius?

Accepted Answer

$$t(\degree C) = 77 - 273.15 = -196 \degree C$$

Question 8

A 747 jet is fueled with $$173,231 \ 	ext{L} of $$jet fuel with a density of $$0.768 \ 	ext{g/cm}^3. $$What is the mass of the fuel in kilograms?

Accepted Answer

$$1.33 	imes 10^5$ \ 	ext{kg}$$

Question 9

Which of the following best describes an exothermic process?

Accepted Answer

Heat flows from the system to the surroundings, increasing the temperature of the surroundings.

Question 10

How many significant figures are in the measurement $$0.00801008$$?

Accepted Answer

6

Question 11

A motorcycle is traveling at $$105 \ 	ext{km/h}. $$What is its speed in meters per second?

Accepted Answer

$$105 \ 	ext{km/h} 	imes \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} 	imes \frac{1 \ 	ext{h}}{3600 \ 	ext{s}} = 29.2 \ 	ext{m/s}$$

Question 12

Which of the following is the correct scientific notation for the number 0.0000000000000000000000199?

Accepted Answer

$$1.99 	imes 10$$^{-23}$$

Question 13

Which of the following is an exact number and does NOT limit the number of significant figures in a calculation?

Accepted Answer

The number of students in a classroom

Question 14

A vineyard has 145 acres of Chardonnay grapes. If a soil supplement requires $$5.50 \ 	ext{g}$$ for every square meter, how many kilograms are needed for the entire vineyard? (1 km$$^2 = 247 $$acres, 1 km$$^2$$ = $$10^6 m$^2)$$

Accepted Answer

$$145 \ 	ext{acres} 	imes \frac{1 \ 	ext{km}^2}{247 \ 	ext{acres}} 	imes \frac{10^6$ \ 	ext{m}^2}{1 \ 	ext{km}^2} 	imes \frac{5.50 \ 	ext{g}}{1 \ 	ext{m}^2} 	imes \frac{1 \ 	ext{kg}}{1000 \ 	ext{g}} = 3.23 	imes 10^3$ \ 	ext{kg}$$

Question 15

Which of the following is the correct relationship for converting calories to joules?

Accepted Answer

$$1 \ 	ext{cal} = 4.184 \ 	ext{J}$$

Question 16

A drop of gasoline has a mass of $$22 \ 	ext{mg}$$ and a density of $$0.754 \ 	ext{g/cm}^3. $$What is its volume in cubic centimeters?

Accepted Answer

$$V = \frac{m}{d} = \frac{0.022 \ 	ext{g}}{0.754 \ 	ext{g/cm}^3} = 0.0292 \ 	ext{cm}^3$$

Question 17

Which of the following best describes the First Law of Thermodynamics?

Accepted Answer

Energy cannot be created or destroyed, only converted from one form to another.

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