Chapter 8 Notes

Chapter 8.1 Force

• Mass:
  • Dimension of how much.
  • Units: grams
• Force:
  • Newton's Second Law
  • Units: newtons
  • F = m a
  • 1N \equiv (1kg) (\frac{m}{s^2})

Example

• A ship with a mass of 30,000 kg has an engine that provides a constant acceleration of 0.06 m/s². The thrust (force) provided by the engine needs to be calculated in pound-force.

Concept Check

• Rank the following from largest force to smallest force:
  • A. 10 kg object accelerating at a rate of 1,000 mm/s²
  • B. 10 lbm object accelerating at a rate of 100 ft/s²
  • C. 10-slug object accelerating at a rate of 100 cm/s²

Example

• A spacecraft nearing Mars has an engine that provides a thrust of 5,000 N.
• The spacecraft has a mass of 850 kg.
• The acceleration of the spacecraft needs to be calculated in mi/h².

Chapter 8.2 Weight

• Mass:
  • Dimension of how much.
  • Units: g
• Force:
  • Newton's Second Law
  • Units: N
  • F = m a
• Weight:
  • weight = mass * gravity
  • Units: N
  • W = m g
  • 1N \equiv (1kg) (\frac{m}{s^2})

Relationships

• m, g, W are related.

Concept Check

• What is the weight of a 5-kg bowling ball in N?
  • A. 0.5 N
  • B. 5 N
  • C. 50 N

Solution Steps:

*   (1) Determine equation
*   (2) Insert known quantities
*   (3) Calculate, reasonable
*   W = m g
*   W = (5 kg)(9.8 \frac{m}{s^2})
*   W = 49 N

Concept Check

• Rank the following from largest weight to smallest weight if all the objects were moved to the Earth.
  • Gravity on the Moon = 1.6 m/s²
  • Gravity on Mars = 3.7 m/s²
  • A. 10 kg object on Earth
  • B. 25 kg object on the Moon
  • C. 20 kg object on Mars

Chapter 8.3 Density

• Density (\rho):
  • \rho = \frac{m}{V}
• Specific Gravity (SG):
  • SG = \frac{Density \, of \, the \, Object}{Density \, of \, Water}

Relationships

• \rho, V, m and SG, \rho_w, \rho are related

Example

• The density of sugar is 1.61 grams per cubic centimeter.
• What is the density of sugar in units of pound-mass per cubic foot?

Common Values

• Specific Gravity
  • Liquids
    • Water ~ 1
    • Mercury ~ 13.6
  • Solids
    • Gold ~ 19.6
    • Platinum ~ 21.5
    • Osmium & Iridium ~ 22.6
  • Gases
    • Air ~ 0.001
    • H ~ 0.0001
• Density of Water
  • 1000 \frac{kg}{m^3}
  • 1 \frac{kg}{L}
  • 1 \frac{g}{cm^3}
  • 1.94 \frac{slugs}{ft^3}
  • 62.4 \frac{lbm}{ft^3}
  • 8.35 \frac{lbm}{gal}

Example

• A 75-gram [g] cylindrical rod is measured to be 10 centimeters [cm] long and 2.5 centimeters [cm] in diameter.
• What is the specific gravity of the material?

Concept Check

• Which of the following are reasonable values for the specific gravity of a metal object?
  • 0. 6
  • 40
  • 21
  • 0. 0052
  • −21
• Which of the following are reasonable values for the specific gravity of a fragrance mist?
  • 0. 6
  • 40
  • 21
  • 0. 0052
  • -21

Concept Check: SOLUTION

• Which of the following are reasonable values for the specific gravity of a metal object?
  • 0. 6
  • 40
  • 21
  • 0. 0052
  • −21
• Which of the following are reasonable values for the specific gravity of a fragrance mist?
  • 0. 6
  • 40
  • 21
  • 0. 0052
  • -21

Concept Check

• Which of the following quantities has the highest density?
  • A. Fluid A = SG of 0.787
  • B. Fluid B = 1.025 g/cm³
  • C. Fluid C = 1,350 kg/m³
  • D. Fluid D = 75 lbm/ft³

Concept Check

• Which is the mass of water in a volume of 3 ft³?
  • A. 187.2 kg
  • B. 5.82 kg
  • C. 84.9 g
  • D. 84.9 kg

Example

• A cube of DrS45 has a density of 250 lbm/ft³.
• What is the specific gravity of DrS45?

Chapter 8.4 Amount

• Amount of Substance
  • Mass
    • Dimension representing how much
    • Units [=] g
  • Amount
    • Dimension representing how many
    • Units [=] mol
    • 1 mole = 6.022 x 10²³ units
    • Avogadro's number = 6.022 x 10²³ units/mol

Amount of Substance Definitions

• atomic weights of elements
• 58.4 g/mol

Example

• Humans require about 85 mol/d of oxygen for survival.
• How many g/min of oxygen does a human require for survival?
• Many gasses exist as diatomic compounds in nature, meaning two of the atoms of the same element are attached to form a molecule. Hydrogen (H2), oxygen (O2), and nitrogen (N2) all exist in a gaseous diatomic state under standard conditions.
• The atomic weight of oxygen is 16.

Example: SOLUTION

• MW = \frac{m}{n}
• MW of oxygen = 2 * 16 g/mol = 32 g/mol
• n = 85 \frac{mol}{d} * \frac{1 d}{24 h} * \frac{1 h}{60 min} = 0.059 \frac{mol}{min}
• m = (MW) (n) = 32 \frac{g}{mol} * 0.059 \frac{mol}{min}
• m = 1.89 \frac{g}{min}

Example

• Tetrafluoromethane (CF4) is one type of greenhouse gas.
• How many moles [mol] of tetrafluoromethane do we have, if we have a sample of 300 g?
• Atomic weight of Carbon = 12
• Atomic weight of Fluorine = 19

Example: SOLUTION

• MW = \frac{m}{n}
• MW of CF4 = (12 g/mol * 1 molecule of C) + (19 g/mol * 4 molecules of F)
• MW of CF4 = 88 g/mol
• n = \frac{m}{MW} = \frac{300 g}{\frac{1 mol}{88 g}} = 3.41 mol
• n = 3.4 mol

Chapter 8.5 Temperature

• Relative Scales
  • SI
    • Celsius [°C]
  • AES, USCS
    • Fahrenheit [°F]
• Absolute Scales
  • SI
    • Kelvin [K]
  • AES, USCS
    • Rankine [°R]

Temperature Reading

• Compare how each thermometer will read with different scales.
• \frac{T[°F] - 32°F}{212 - 32}°F} = \frac{T[°C] - 0°C}{(100 - 0)°C}
• T[°F] = 1.8 * T[°C] + 32

Temperature Change

• Comparing the step size (change between two values) with different scales.

Converting and Calculating Temperature

• T{°F} = 1.8T{°C} + 32
• \Delta{°F} = 1.8\Delta{°C}
• TK = T{°C} + 273
• \Delta{°C} = \DeltaK
• T{°R} = T{°F} + 460
• \Delta{°R} = \Delta{°F}

Common Values

• Boiling point of water: 100 °C = 212 °F
• Freezing point of water: 0 °C = 32 °F
• Room temperature: 21 °C = 70 °F
• Absolute zero: 0 K = −273 °C, 0 °R = −460 °F

Concept Check

• Which of the following quantities is the highest temperature?
  • (A) −150 °F
  • (B) −150 °C
  • (C) 150 K
  • (D) 150 °R

Concept Check

• Which of the following is the highest value?
  • (A) 5 lbm/°F
  • (B) 5 kg/°C
  • (C) 3 kg/K
  • (D) 3 lbm/°R

Example

• If the temperature of water warming on a hot plate reads 40 °C, what is the temperature in units of °F?
• If the temperature of water warming on a hot plate rises 10 °C, what is the change in temperature in units of °F?
• If the temperature of water warming on a hot plate reads 50 °C, what is the temperature in units of °F?

Example: SOLUTION

• 40 °C = 104 °F
• Δ(10 °C) = Δ(18 °F)
• 50 °C = 122 °F

Chapter 8.6 Pressure

• Pressure
  • P = \frac{F}{A}

Relationships

• P, A, F are related

Common Values

• Standard atmospheric pressure defined as 1 atmosphere [atm] at sea level
• 1 atm ≡ 14.7 lbf/in² [psi] ≡ 101,325 Pascals [Pa]

Atmospheric pressure

• Atmospheric pressure varies by elevation

Hydrostatic Pressure

• Weight of a fluid pushing down on an object
• Pascal's Law
• P_{hydro} = \rho g H

Relationships

• \rho, H, P_{hydro}, g are related

Total Pressure

• Sum of:
  • Hydrostatic pressure
  • Surface pressure
• P{total} = P{surface} + P_{hydro}
• P{total} = P{surface} + \rho g H

Concept Check

• Which of the following is the highest value?
  • A. 5 atm
  • B. 5 bar
  • C. 50,000 Pa
  • D. 50 psi

Example

• The book has a mass of 1.8 kilograms [kg] and has dimensions of 8 inches [in] by 10 inches [in] by 1.5 inches [in].
• How much pressure is the book exerting on the surface of desk, in units of pascals [Pa]?

Example

• The hull of seaQuest Deep Submergence Vehicle (DSV) is rated to withstand a hydrostatic pressure of 90 MPa.
• If sea water has a specific gravity of 1.03, how deep in km can seaQuest DSV descend before reaching this pressure limit?

Example: SOLUTION

• P_{hydro} = 90 MPa * \frac{1 x 10^6 Pa}{1 MPa} = 90 x 10^6 Pa
• \rho{ocean} = SG * \rho{water} = 1.03 * 1,000 \frac{kg}{m^3} = 1,030 \frac{kg}{m^3}
• Hydrostatic Pressure = (Density) (Gravity) (Height)
• H = \frac{P{hydro}}{\rho{ocean} g} = 90 x 10^6 Pa * \frac{m^3}{1,030 kg} * \frac{s^2}{9.8 m} * \frac{m}{s^2} * \frac{kg}{Pa}
• H = 8,916 m * \frac{1 km}{1,000 m} = 8.92 km

Example

• In the year 2027, Titan Submersible Explorer (TSE) lands on a lake of methane (SG = 0.415) and submerges to a depth of 40 m to explore the bottom of the lake.
• The surface pressure on Titan is 21.3 psi and the acceleration due to gravity is 1.35 m/s².
• What is the total pressure on the TSE at that depth in kPa?

Example: SOLUTION

• P_{hydro} = \rho g H
• P_{hydro} = 0.415 * \frac{1000 kg}{m^3} * 1.35 \frac{m}{s^2} * 40m * \frac{Pa}{\frac{m}{s^2} kg} * \frac{1 kPa}{1,000 Pa} = 22.4 kPa
• P_{surface} = 21.3 psi * \frac{101,325 Pa}{14.7 psi} * \frac{1 kPa}{1,000 Pa} = 146.8 kPa
• P{total} = P{hydro} + P_{surface}
• P_{total} = 22.4 kPa + 146.8 kPa = 169.2 kPa