Exersizes

2.9. Exersizes#

Units and Dimensions#

  1. Which of the following is not a base dimension?

a. Length

b. Mass

c. Weight

d. Time

  1. Take the quantity selected in question 1 and write that quantity in terms of base dimensions.

Dimensional Analysis#

  1. The following mathematical relation is written in terms of base dimensions. What is the required dimension of \(k\) to make the equation dimensionally consistent?

\[ ML^{2}t^{2} = ML^{2}t^{2}e^{kMt} \]

Unit Conversions#

  1. The earth can be approximated as a sphere with a radius of \(6.37 \times 10^6\) meters. Determine:

a. The diameter of the earth in feet

b. The circumference of the earth in miles

  1. A league is equivalent to 6076 yards. Jules Verne wrote a book titled 20,000 Leagues Under the Sea. Does this length reference a depth or horizontal distance traveled? Your solution must use conversions to justify your answer.

  2. The equation for kinetic energy is \(KE = \frac{1}{2}mv^2\) where \(m\) is mass and \(v\) is velocity.

Given the values of \(m\) = 5.90 slugs and \(v\) = 75.8 miles/hour, calculate the following:

a. Convert the value for mass into the appropriate mass units such that the value for kinetic energy could be reported in Joules (J). Report your converted value to the appropriate number of significant figures.

b. Convert the value for velocity into the appropriate unit of velocity such that the value for kinetic energy could be reported in Joules (J). Report your converted value to the appropriate number of significant figures.

c. What is the kinetic energy of the object in kilo-Joules, kJ?

  1. The yield stress for a titanium alloy (6% Al, 4% V) is approximately 830 MPa. Convert this value to units of ksi (kilo-pounds per square inch).

  2. Convert 745 gallons per minute to cubic feet per second (cfs).

  3. Convert \(3.50 \times 10^3 \ kg/m^3\) to \(slug/in^3\)

  4. Power can be written as a function of Time and Energy. Using either units or base dimensions determine the appropriate mathematical relation.

  5. Using the answer found for Problem #10. A steam power plant produces 945 MW of power. How much total energy does the power plant produce in 5 years? Express your answer in units of Joules (J).

Significant Figures#

  1. Determine the number of significant figures in the following values:

15 miles

11,763 m

3.287 km

  1. Determine the number of significant figures in the following values:

10.7636 mi/h

1009607

32.17400 g

2.2040 cm

  1. Determine the number of significant figures in the following values:

0.100 kg/m

01 cm

\(900 \times\) \(10^{-8}\) mm

  1. Round the values below to 2 significant figures

1450 ft/s

\(9.549 \times\) \(10^{4}\) g

5.996 Pa

  1. Round the values below to 3 significant figures

0280800 min

5.996

  1. Round the value below to 4 significant figures

20.8855 lb/ft

Scientific Notation#

  1. Convert the following values to scientific notation

695 \(g\)

0.00974 \(mg/cm^2\)

\(0.9843 \times 10^{-4}\) slug

  1. Convert the following values from scientific notation into standard notation

\(1.00 \times 10^{2}\)

\(9.000 \times 10^{-6}\)

\(2.040 \times 10^{4}\)

Engineering Notation#

  1. Convert the following values to engineering notation

\(133000 \ ^{\circ}C\)

\(8.0 \times 10^5\) km/s

5.1 angstroms (note: 1 angstrom = \(10 \times 10^{-10}\) m)

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