Thinking Like an Engineer: An Active Learning Approach (4th Edition)
4th Edition
ISBN: 9780134639673
Author: Elizabeth A. Stephan, David R. Bowman, William J. Park, Benjamin L. Sill, Matthew W. Ohland
Publisher: PEARSON
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Chapter 8, Problem 15RQ
The density of gasoline is 0.72 grams per cubic centimeter [g/cm3]. What is the mass in units of kilograms [kg] of a 5-gallon [gal] container filled completely with gasoline? Ignore the mass of the container.
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Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.
Problem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).
Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the string
Chapter 8 Solutions
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Ch. 8.1 - The engine on a spacecraft nearing Mars can...Ch. 8.2 - The mass of the human brain is 1360 grams [g]....Ch. 8.2 - The mass of the human brain is 1360 grams [g]....Ch. 8.3 - Convert 50 grams per cubic centimeter [g/cm3] into...Ch. 8.3 - A 75-gram [g] cylindrical rod is measured to be 10...Ch. 8.4 - Determine the mass in units of grams of 0.025...Ch. 8.4 - Determine the amount in units of moles [mol] of 5...Ch. 8.5 - The temperature of dry ice is 109.3 degrees...Ch. 8.5 - The specific heat capacity of copper is 0.09...Ch. 8.6 - If the pressure is 250 feet of water [ft H2O],...
Ch. 8.6 - A car tire is inflated to a gauge pressure of 35...Ch. 8.6 - An object is completely submerged in a liquid with...Ch. 8.7 - A 5-gallon [gal] container holds 35 grams [g] of...Ch. 8.7 - An 8-liter [L] container holds nitrogen (formula:...Ch. 8.8 - You push an automobile with a constant force of 20...Ch. 8.8 - One gram of material A is heated until the...Ch. 8.9 - A motor with a power of 100 watts [W] is connected...Ch. 8.10 - A motor with an input power of 100 watts [W] is...Ch. 8.10 - If a 50-kilogram [kg] load was raised 5 meters [m]...Ch. 8.11 - The current through a 12 kilo-ohms [k] resistor is...Ch. 8.11 - A device contains a 1000-ohm [] resistor with 120...Ch. 8.11 - A constant current transfers 12 1014 electrons...Ch. 8.11 - A 100-millihenry [mH] inductor has a current...Ch. 8.11 - Express 1LC in terms of base SI units, where L is...Ch. 8 - The space shuttle fleet was designed with two...Ch. 8 - Complete the following table assuming the object...Ch. 8 - Rank the following from largest mass to smallest...Ch. 8 - A typical American football weighs 14.5 ounces...Ch. 8 - The weight of the Hubble Space Telescope (HST) on...Ch. 8 - The value of gravitational acceleration on Earth,...Ch. 8 - Complete the following table: Density Compound...Ch. 8 - If the density of sodium is 98 kilograms per cubic...Ch. 8 - The specific gravity of iodine is 4.927. State the...Ch. 8 - Complete the following table. Assume you have a...Ch. 8 - Complete the following table. Assume you have a...Ch. 8 - Fluid A fills a one-gallon [gal] container and...Ch. 8 - A golden bar of metal (5 centimeters [cm] by 18...Ch. 8 - A lab reports the density of a new element is X...Ch. 8 - You have been hired as an intern for a plastics...Ch. 8 - A submersible robot is exploring one of the...Ch. 8 - Several students calculate the density of a gas,...Ch. 8 - You have been working to develop a new fictitious...Ch. 8 - Determine the mass in units of grams [g] of 0.35...Ch. 8 - A eutectic alloy of two metals contains the...Ch. 8 - Which of the following plastic has the highest...Ch. 8 - The outside air temperature of an airplane...Ch. 8 - The inside of an airplane is kept at 75 degrees...Ch. 8 - The Newton [N] temperature scale was devised by...Ch. 8 - In the Spring of 2004, NASA discovered a new...Ch. 8 - Is there a physical condition at which a...Ch. 8 - Complete the table: atmosphere pascal Inches of...Ch. 8 - If the pressure is 250 feet of water [ft H2O],...Ch. 8 - A normal blood pressure has a gauge pressure of...Ch. 8 - Prob. 30ICACh. 8 - If a force of 15 newtons [N] is applied to a...Ch. 8 - You wish to submerge an object in a liquid at sea...Ch. 8 - (a) Determine the maximum volume in gallons [gal]...Ch. 8 - A sensor is submerged in a silo to detect any...Ch. 8 - Complete the table, using the ideal gas law:...Ch. 8 - A 10-liter [L] flask contains 1.3 moles [mol] of...Ch. 8 - An ideal gas in a 1.25-gailon [gal] container is...Ch. 8 - An ideal gas is kept in a 10-liter [L] container...Ch. 8 - Football A is filled with 50 grams [g] of Gas X,...Ch. 8 - Determine the specific gravity of chlorine (Cl2)...Ch. 8 - Complete the table for specific heat conversions:...Ch. 8 - Which of the following requires the expenditure of...Ch. 8 - Which objectA, B, or Chas the most potential...Ch. 8 - Measurements indicate that boat A has twice the...Ch. 8 - A 10-gram [g] rubber ball is released from a...Ch. 8 - If a ball is dropped from a height (H) its...Ch. 8 - Eight hundred kilograms [kg] of paint solvent will...Ch. 8 - We go out to sunbathe on a warm summer day. If we...Ch. 8 - The specific heats of aluminum and iron are 0.214...Ch. 8 - Complete the table for thermal conductivity...Ch. 8 - The thermal conductivity of a plastic is 0.325...Ch. 8 - The heat transfer coefficient of steel is 25 watts...Ch. 8 - Complete the table. This problem involves the...Ch. 8 - When we drive our car at 100 feet per second...Ch. 8 - The power required by an airplane is given by P =...Ch. 8 - Complete the table. This problem involves the...Ch. 8 - A 100-watt [W] motor (60% efficient) is available...Ch. 8 - When boiling water, a hot plate takes an average...Ch. 8 - One problem with solar energy is that any given...Ch. 8 - Prob. 60ICACh. 8 - A resistor is dissipating 125 milliwatts [mW] of...Ch. 8 - An average cloud-to-ground lightning strike...Ch. 8 - Most electric stoves in the United States operate...Ch. 8 - A 3-volt [V] battery delivers a constant current...Ch. 8 - Prob. 65ICACh. 8 - A constant current charges a 20-nanofarad [nF]...Ch. 8 - Prob. 67ICACh. 8 - a. What is the average power, in units of watts...Ch. 8 - The National Football League specifies that all...Ch. 8 - A space probe is built with a mass of 1700...Ch. 8 - A person who has a weight of 165 pound-force [lbf]...Ch. 8 - A person who has a weight of 165 pound-force [lbf]...Ch. 8 - A person who has a weight of 165 pound-force [lbf]...Ch. 8 - The European Space Agency launched a probe called...Ch. 8 - The European Space Agency launched a probe called...Ch. 8 - The European Space Agency launched a probe called...Ch. 8 - The European Space Agency launched a probe called...Ch. 8 - A basketball has a mass of approximately 624 grams...Ch. 8 - A website you discover lists the density of a...Ch. 8 - Consider the following strange, but true, units: 1...Ch. 8 - Consider the following strange, but true, units: 1...Ch. 8 - A cube of material X, 1 inch [in] on all sides,...Ch. 8 - The density of gasoline is 0.72 grams per cubic...Ch. 8 - The Eco-Marathon is an annual competition...Ch. 8 - Prob. 17RQCh. 8 - Soccer is also called association football. A...Ch. 8 - A rod on the surface of Jupiters moon Callisto has...Ch. 8 - Prob. 20RQCh. 8 - Prob. 21RQCh. 8 - When an object is made of the plastic polyester...Ch. 8 - If we increase the temperature in a reactor by 90...Ch. 8 - If we increase the temperature in a reactor by 90...Ch. 8 - We are making a cup of coffee and want the...Ch. 8 - We want to construct a thermometer using mercury....Ch. 8 - A normal blood pressure has a gauge pressure of...Ch. 8 - The force on the inside of a cork in a champagne...Ch. 8 - One of the National Academy of Engineering Grand...Ch. 8 - A new gel is being developed to use inside padding...Ch. 8 - A 2-liter [L] soda bottle, made of PET, will fail...Ch. 8 - A storage tank is being designed for iodine. The...Ch. 8 - The specific gravity of honey is 1.43. A...Ch. 8 - NASA is designing a mission to explore Titan, the...Ch. 8 - Airspeed (v) is related to dynamic pressure using...Ch. 8 - When a flowing fluid is stopped, its pressure...Ch. 8 - A 10-liter [L] flask contains 5 moles [mol] of gas...Ch. 8 - A company that produces footballs uses a...Ch. 8 - A 5-liter [L] container holds nitrogen (formula:...Ch. 8 - A typical hot air balloon has a volume of 100,000...Ch. 8 - An ideal gas, kept in a 5-liter [L] container at...Ch. 8 - A container holding 1.5 moles [mol] of oxygen...Ch. 8 - A spacecraft is equipped with nine sensors,...Ch. 8 - A robotic rover on Mars finds a spherical rock...Ch. 8 - On February 15, 2013, Asteroid 2012 DA14 passed...Ch. 8 - If a 10-kilogram [kg] rotating solid cylinder...Ch. 8 - If a ball is dropped from a height its velocity...Ch. 8 - A bail is thrown vertically into the air with an...Ch. 8 - The maximum radius (R) a falling liquid drop can...Ch. 8 - A heat recovery system (HRS) is used to conserve...Ch. 8 - At noon on a clear day in midsummer, a cylindrical...Ch. 8 - In a factory, various metal cylinders are forged...Ch. 8 - A 3-kilogram [kg] projectile traveling at 100...Ch. 8 - Plutonium isotopes undergo decay, producing heat....Ch. 8 - The power required by an airplane is given by P =...Ch. 8 - When gasoline is burned in the cylinder of an...Ch. 8 - A spacecraft utilized Earths gravity and...Ch. 8 - A spacecraft is fueled using hydrazine (N2H4;...Ch. 8 - A 100-watt [W] motor (60% efficient) is used to...Ch. 8 - You need to purchase a motor to supply 400 joules...Ch. 8 - The Curiosity rover landed oil Mars on August 6,...Ch. 8 - A robotic rover on Mars finds a spherical rock...Ch. 8 - Consider the following strange, but true, unit: 1...Ch. 8 - When boiling water a hot plate takes an average of...Ch. 8 - Prob. 65RQCh. 8 - The power available from a wind turbine is...Ch. 8 - The computer system on the Indian Mars Orbiter...Ch. 8 - Prob. 68RQCh. 8 - Prob. 69RQCh. 8 - A 10,000-microfarad [F] capacitor is charged to 25...Ch. 8 - A 250,000-microfarad [F] capacitor is used to keep...Ch. 8 - A 250-kilo-ohm [k] resistor and a 0.2-microfarad...Ch. 8 - A 0.05-microfarad [F] capacitor discharges through...Ch. 8 - A variable capacitor has a range from 100...Ch. 8 - A constant voltage of 5 volts [V] is applied...Ch. 8 - A 20-millihenry [mH] inductor, a 0.5-mtcrofarad...
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