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engineering
introduction mechanical engineering

Questions and Answers of Introduction Mechanical Engineering

Obtain the surface and contour plots for the function z = x2 = -2xy + 4y2, showing the minimum at x = y = 0.
A robot rotates about its base at 2 rpm while lowering its arm and extending its hand. It lowers its arm at the rate of 120° per minute and extends its hand at the rate of 5 m/min. The arm is 0.5 m
The popular amusement ride known as the corkscrew has a helical shape. The parametric equations for a circular helix arex = a cos ty = a sin tz = btwhere a is the radius of the helical path and b is
An approximation to the function sin x is sin x ≈ x - x3/6. Plot the sin x function and 20 evenly spaced error bars representing the error in the approximation.
The circuit shown in Figure P26 consists of a resistor and a capacitor and is thus called an RC circuit. If we apply a sinusoidal voltage υi, called the input voltage, to the circuit as shown, then
Figure P25 is a representation of an electrical system with a power supply and a load. The power supply produces the fixed voltage υ1 and supplies the current i1 required by the load, whose voltage
The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by where n is the number of times per year the interest is compounded. For
The volume V and surface area A of a sphere of radius r are given by a. Plot V and A versus r in two subplots, for 0.1 ≤ r ≤ 100 m. Choose axes that will result in straight-line graphs for
A sum of $10 000 invested at 4 percent interest compounded annually will grow according to the formulay(k) = 104(1.04)kwhere k is the number of years (k = 0, 1, 2, . . .). Plot the amount of money in
The following table shows the average temperature for each year in a certain city. Plot the data as a stem plot, a bar plot, and a stairs plot. Year 2000 2001 2002 2003 2004 Temperature (°C) 21 18
When a constant voltage was applied to a certain motor initially at rest, its rotational speed s(t) versus time was measured. The data appear in the following table:Determine whether the following
Oscillations in mechanical structures and electric circuits can often be described by the functionwhere t is time and ( is the oscillation frequency in radians per unit time. The oscillations have a
The perfect gas law relates the pressure p, absolute temperature T, mass m, and volume V of a gas. It states thatPV = mRTThe constant R is the gas constant. The value of R for air is 286.7 (N ·
The height h(t) and horizontal distance x(t) traveled by a ball thrown at an angle A with a speed ! are given byAt Earth’s surface the acceleration due to gravity is g % 9.81 m/s2.a. Suppose the
In certain kinds of structural vibrations, a periodic force acting on the structure will cause the vibration amplitude to repeatedly increase and decrease with time. This phenomenon, called beating,
The following functions describe the oscillations in electric circuits and the vibrations of machines and structures. Plot these functions on the same plot. Because they are similar, decide how best
The function y(t) = 1 -! e-bt, where t is time and b > 0, describes many processes, such as the height of liquid in a tank as it is being filled and the temperature of an object being heated.
Use a plot over the range 0 ≤ x ≤ 5 to con rm that sin( ix) = i sinh x.
The complex number identity eix = cos x + i sin x is often used to convert the solutions of equations into a form that is relatively easy to visualize. Con rm this identity by plotting the imaginary
You can use trigonometric identities to simplify the equations that appear in many applications. Con rm the identity tan(2 x) = 2 tan x/(1 - tan2 x) by plotting both the left and the right sides
Many applications use the following “small angle” approximation for the sine to obtain a simpler model that is easy to understand and analyze. This approximation states that sin x ≈ x, where x
Plot columns 2 and 3 of the following matrix A versus column 1. The data in column 1 are time (seconds). The data in columns 2 and 3 are force (newtons). 0 -7 6. 5 -4 3 A A =| 10 -1 9. 15 1 20 -1 2.
A certain shing vessel is initially located in a horizontal plane at x = 0 and y = 10 mi. It moves on a path for 10 hr such that x = t and y = 0.5t2 + 10, where t is in hours. An international shing
It is known that the following Leibniz series converges to the value π/4 as n → ). Plot the difference between π/4 and the sum S(n) versus n for 0 ≤ n ≤ 200. 1 S(n) = E(-1)*- k=0 2k + 1
Using estimates of rainfall, evaporation, and water consumption, the town engineer developed the following model of the water volume in the reservoir as a function of time where V is the water
Cables are used to suspend bridge decks and other structures. If a heavy uniform cable hangs suspended from its two endpoints, it takes the shape of a catenary curve whose equation iswhere a is the
To compute the forces in structures, sometimes we must solve equations similar to the following. Use the fplot function to find all the positive roots of this equation:x tan x = 9
a. Estimate the roots of the equationby plotting the equation.b. Use the estimates found in part a to nd the roots more accurately with the fzero function. TTX 2 - 3x + 5x sin 4 + 3 = 0 4
Consider the following costs for a certain chemical product:Fixed cost: $2.045 million/year.Variable costs:Material cost: 62 cents per gallon of product.Energy cost: 24 cents per gallon of
Breakeven analysis determines the production volume at which the total production cost is equal to the total revenue. At the breakeven point, there is neither pro t nor loss. In general, production
Redo Problem 48 with the restriction that the next week’s production is set to zero if the inventory exceeds 40 carts.Problem 48A certain company manufactures and sells golf carts. At the end of
A certain company manufactures and sells golf carts. At the end of each week, the company transfers the carts produced that week into storage (inventory). All carts that are sold are taken from the
Suppose you project that you will be able to deposit the following monthly amounts into a savings account for a period of 5 years. The account initially has no money in it.At the end of each year in
Using the program developed in Problem 19, write a program that uses the switch structure to compute the number of days in a year up to a given date, given the year, the month, and the day of the
Consider the college enrollment model discussed in Example 4.9–2. Suppose the college wants to limit freshman admissions to 120 percent of the current sophomore class and limit sophomore transfers
Engineers often need to estimate the pressures and volumes of a gas in a container. The van der Waals equation is often used for this purpose. It is where the term b is a correction for the
The height and speed of a projectile (such as a thrown ball) launched with a speed of υ0 at an angle A to the horizontal are given by where g is the acceleration due to gravity. The projectile
Use the switch structure to write a MATLAB program to compute the amount of money that accumulates in a savings account in one year. The program should accept the following input: the initial amount
The following table gives the approximate values of the static coefficient of friction 1 for various materials.Materials ................................ µMetal on metal ....................
Assume that the human player makes the first move against the computer in a game of Tic-Tac-Toe, which has a 3 x 3 grid. Write a MATLAB function that lets the computer respond to that move. The
Consider the following script file. Fill in the lines of the following table with the values that would be displayed immediately after the while statement if you ran the script file. Write in the
Many applications require us to know the temperature distribution in an object. For example, this information is important for controlling the material properties, such as hardness, when cooling an
The equations describing the circuit shown in Figure P37 area. The given values of the resistances and the voltage υ1 are R1 = 5. R2 = 100, R3 = 200, R4 = 150, R5 = 250 kΩ, and υ1 = 100V.(Note
In the structure in Figure P36a, six wires support three beams. Wires 1 and 2 can support no more than 1200 N each, wires 3 and 4 can support no more than 400 N each, and wires 5 and 6 can support no
A weight W is supported by two cables anchored a distance D apart (see Figure P35). The cable length LAB is given, but the length LAC is to be selected. Each cable can support a maximum tension force
Use a loop in MATLAB to determine how long it will take to accumulate $1 000 000 in a bank account if you deposit $10 000 initially and $10 000 at the end of each year; the account pays 6 percent
One bank pays 5.5 percent annual interest, while a second bank pays 4.5 percent annual interest. Determine how much longer it will take to accumulate at least $50 000 in the second bank account if
Use a while loop to determine how many terms in the series 2k, k = 1, 2, 3, . . . , are required for the sum of the terms to exceed 2000. What is the sum for this number of terms?
Plot the function y = 10(1 = e-x/4) over the interval 0 ≤ x ≤ xmax, using a while loop to determine the value of xmax such that y(xmax) = 9.8.Properly label the plot. The variable y represents
A certain company makes televisions, stereo units, and speakers. Its parts inventory includes chassis, picture tubes, speaker cones, power supplies, and electronics. The inventory, required
A company has the choice of producing up to four different products with its machinery, which consists of lathes, grinders, and milling machines. The number of hours on each machine required to
A company wants to locate a distribution center that will serve six of its major customers in a 30 × 30 mi area. The locations of the customers relative to the southwest corner of the area are given
a. An ideal diode blocks the flow of current in the direction opposite that of the diode’s arrow symbol. It can be used to make a half-wave rectifier as shown in Figure P27a. For the ideal diode,
The price, in dollars, of a certain stock over a 10-day period is given in the following array.price = [19, 18, 22, 21, 25, 19, 17, 21, 27, 29]Suppose you owned 1000 shares at the start of the 10-day
Electrical resistors are said to be connected “in series” if the same current passes through each and “in parallel” if the same voltage is applied across each. If in series, they are
We want to analyze the mass-spring system discussed in Problem 20 for the case in which the weight W is dropped onto the platform attached to the center spring. If the weight is dropped from a height
Consider the array A.Write a program that computes the array B by computing the natural logarithm of all the elements of A whose value is no less than 1, and adding 20 to each element that is equal
The (x, y) coordinates of a certain object as a function of time t are given byx(t) = 5t – 10 y(t) = 25t2 = 120t + 144for 0 ≤ t ≤ 4. Write a program to determine the time at which the
Use a for loop to determine the sum of the rst 10 terms in the series 5k3, k % 1, 2, 3, . . . , 10.
Use a for loop to plot the function given in Problem 16 over the interval -2 ≤ x ≤ 6. Properly label the plot. The variable y represents height in kilometers, and the variable x represents time
Figure P20 shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the
Write a program that accepts a year and determines whether the year is a leap year. Use the mod function. The output should be the variable extra_day, which should be 1 if the year is a leap year and
Write a program that accepts a numerical value x from 0 to 100 as input and computes and displays the corresponding letter grade given by the following table.A. x ≥ 90B. 80 ≤ x ≤ 89C. 70 ≤ x
Rewrite the following statements to use only one if statement.if x < yif z < 10w = x*y*zendend
Write a script le using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function isY = ex+1 for x < -1, y = 2 + cos(πx) for -1 ≤
Are these following expressions equivalent? Use MATLAB to check your answer for specific values of a, b, c, and d.a. 1. (a == b) & ((b == c)|(a == c))2. (a == b)|((b == c)&(a == c))b. 1. (a
Let e1 and e2 be logical expressions. DeMorgan’s laws for logical expressions state thatNOT(e1 AND e2) implies that (NOT e1) OR (NOT e2)andNOT(e1 OR e2) implies that (NOT e1) AND (NOT e2)Use these
Suppose that x = [-3, 0, 0, 2, 5, 8] and y = [-5, -2, 0, 3, 4, 10]. Find the results of the following operations by hand and use MATLAB to check your results.a. z = y < ~ xb. z = x & yc. z =
The arrays price_A, price_B, and price_C given below contain the price in dollars of three stocks over 10 days.a. Use MATLAB to determine how many days the price of stock A was above both the price
The arrays price_A and price_B given below contain the price in dollars of two stocks over 10 days. Use MATLAB to determine how many days the price of stock A was above the price of stock B.price_A =
The array price given below contains the price in dollars of a certain stock over 10 days. Use MATLAB to determine how many days the price was above $20.price = [19, 18, 22, 21, 25, 19, 17, 21, 27,
For the arrays x and y given below, use MATLAB to find all the elements in x that are greater than the corresponding elements in y.x = [-3, 0, 0, 2, 6, 8] y = [-5, -2, 0, 3, 4, 10]
Suppose that x = [10, -2, 6, 5, -3] and y = [9, -3, 2, 5, -1]. Find the results of the following operations by hand and use MATLAB to check your results.a. z = (x < 6)b. z = (x <= y)c. z = (x
Find the results of the following operations by hand and use MATLAB to check your results.a. z = 6 > 3 + 8b. z = 6 + 3 > 8c. z = 4 > (2 + 9)d. z = (4 < 7) + 3e. z = 4 < 7 + 3f. z =
Suppose that x = 6. Find the results of the following operations by hand and use MATLAB to check your results.a. z = (x < 10)b. z = (x == 10)c. z = (x >= 4)d. z = (x ~= 7)
It is desired to compute the sum of the first 10 terms of the series14k3 = 20k2 + 5k, k = 1, 2, 3, …a. Develop a pseudocode description of the required program.b. Write and run the program
The roots of the quadratic equation ax2 + bx + c = 0 are given by a. Develop a pseudocode description of a program to compute both roots given the values of a, b, and c. Be sure to identify the
Use a text editor to create a le from the data given in Problem 23, but separate each number with a semicolon. Then use the Import Wizard to load and save the data in the MATLAB variable A.Problem
The volume V and surface area A of a sphere of radius r are given by a. Develop a pseudocode description of a program to compute V and A for 0 ≤ r ≤ 3 m and to plot V versus A.b. Write and
Enter and save the data given in Problem 23 in a spreadsheet. Then import the spreadsheet le into the MA TLAB variable A. Use MATLAB to compute the sum of each column.Problem 23Use a text editor to
Use a text editor to create a le containing the following data. Then use the load function to load the le into MATLAB, and use the mean function to compute the mean value of each column. 55 42 98 49
Create a primary function that uses a function handle with a nested function to compute the minimum of the function 20x2 - 200x + 12 over the range 0 ≤ x ≤ 10.
Use a primary function with a subfunction to compute the zeros of the function 3x3 - 12x2 - 33x + 80 over the range $10 ≤ x ≤ 10.
Create four anonymous functions to represent the function 6e3cosx2, which is composed of the functions h(z) = 6ez, g(y) = 3 cos y, and f(x) = x2. Use the anonymous functions to plot 6e3cosx2 over the
Create an anonymous function for 20x2 - 200x + 3 and use ita. To plot the function to determine the approximate location of its minimumb. With the fminbnd function to precisely determine the location
Create an anonymous function for 10e-2x and use it to plot the function over the range 0 ≤ x ≤ 2.
Suppose it is known that the graph of the function y = ax3 + bx2 + cx + d passes through four given points (xi, yi ), i = 1, 2, 3, 4. Write a userdefined function that accepts these four points as
A torus is shaped like a doughnut. If its inner radius is a and its outer radius is b, its volume and surface area are given by a. Create a user-defined function that computes V and A from the
The volume V and paper surface area A of a conical paper cup are given bywhere r is the radius of the base of the cone and h is the height of the cone.a. By eliminating h, obtain the expression for A
Using estimates of rainfall, evaporation, and water consumption, the town engineer developed the following model of the water volume in the reservoir as a function of time where V is the water
A fenced enclosure consists of a rectangle of length L and width 2R and a semicircle of radius R, as shown in Figure P13. The enclosure is to be built to have an area A of 2000 ft2. The cost of the
A fence around a field is shaped as shown in Figure P12. It consists of a rectangle of length L and width W, and a right triangle that is symmetrical about the central horizontal axis of the
A water tank consists of a cylindrical part of radius r and height h and a hemispherical top. The tank is to be constructed to hold 600 m3 when filled. The surface area of the cylindrical part is
An object thrown vertically with a speed υ0 reaches a height h at time t, where Write and test a function that computes the time t required to reach a specified height h, for a given value of
Write a function that accepts temperature in degrees Fahrenheit (°F) and computes the corresponding value in degrees Celsius (°C). The relation between the two isBe sure to test your function. 5
The output of the MATLAB atan2 function is in radians. Write a function called atan2d that produces an output in degrees.
When a belt is wrapped around a cylinder, the relation between the belt forces on each side of the cylinder isF1 = F2eµβwhere β is the angle of wrap of the belt and & is the friction
The capacitance of two parallel conductors of length L and radius r, separated by a distance d in air, is given by where ∈ is the permittivity of air (∈ = 8.854 × 10-12
For several values of x, use MATLAB to con rm that cosh-1 x = ln(x + √x2 - 1), x ≤ 1
For several values of x, use MATLAB to con rm that sinh x = (ex – e-x)/2.

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