Engineering Fundamentals: Chapter 18
An Introduction to Engineering
1. In general, engineering problems are mathematical models of physical situations.
a. True
b. False
2. Greek alphabetic characters quite commonly are used to express angles, dimensions, and
physical variables in drawings and in mathematical equations and expressions. It is therefore
very important to be familiar with these characters in order to communicate with other engineers.
a. True
b. False
3. What is the name of the following Greek alphabetic character?
a. Epsilon
b. Zeta
c. Gamma
d. Lambda
Analysis:
4. What is the name of the following Greek alphabetic character?
a. Omega
b. Mu
c. Gamma
d. Lambda
Analysis:
5. What is the name of the following Greek alphabetic character?
a. Omega
b. Mu
c. Gamma
d. Lambda
Analysis:
6. The simplest form of equations commonly used to describe a wide range of engineering
situations is
a. linear models.
b. nonlinear models.
c. exponential models.
d. logarithmic models.
7. The quantity or numerical value within a linear model that shows by how much the dependent
variable changes each time a change in the independent variable is introduced is known as
Engineering Fundamentals: Chapter 18
An Introduction to Engineering
Analysis:
8. For many engineering situations, nonlinear models are used to describe the relationships
between dependent and independent variables because they predict the actual relationships more
accurately than linear models do.
a. True
b. False
9. For many engineering situations, exponential and logarithmic models are used to describe the
relationships between dependent and independent variables because they predict the actual
relationships more accurately than linear models do.
a. True
b. False
10. Hooke’s Law describes the relationship between force F and elastic deflection x in a spring
according to the following equation:
kxF
. Which type of mathematical model is used in
Hooke’s Law?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Logarithmic model
Analysis:
11. The velocity of an object under constant acceleration can be modeled using the following
function: v(t) = v0 + at
where v = velocity
v0 = initial velocity
a = acceleration
t = time
Which type of mathematical model is used to describe velocity in this application?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Logarithmic model
Analysis:
12. The path of flight (trajectory) of a football thrown by a quarterback is described by the
following function:
0
2
22
0
tan
cos2 yxx
v
g
xy
where y = vertical position of football relative to the ground
y0 = vertical launch position of football relative to the ground
x = horizontal position of football relative to launch position
g = magnitude of gravitational acceleration
v0 = launch speed
θ = launch angle relative to horizontal
Which type of mathematical model is used here to describe the football’s trajectory?
13. The path of flight (trajectory) of a football thrown by a quarterback is described by the
following function:
77.0002.0 2 xxxy
where y = vertical position of football relative to the ground (ft)
x = horizontal position of football relative to launch position (ft)
How high above the ground is the football as it leaves the quarterback’s hand?
a. 0.002 ft
b. 0.7 ft
c. 7 ft
d. 7.7 ft
Analysis:
14. The path of flight (trajectory) of a football thrown by a quarterback is described by the
following function:
77.0002.0 2 xxxy
where y = vertical position of football relative to the ground (ft)
x = horizontal position of football relative to launch position (ft)
How high above the ground is the football when it is 30 yards downfield from the quarterback?
a. 26.2 ft
b. 29.8 ft
c. 13.8 ft
d. 53.8 ft
Engineering Fundamentals: Chapter 18
An Introduction to Engineering
Analysis:
15. The position of an object subjected to constant acceleration can be described by the following
function:
2
2
1
00 attvxtx
where
x
position (m)
0
x
initial position (m)
0
v
initial velocity (m/s)
a
acceleration (m/s^2)
t
time (sec)
Which type of mathematical model is used here to describe the object’s position?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Trigonometric model
Analysis:
16. The gravitational force between two masses is modeled using the following function:
2
21
r
mm
GrFg
where
g
F
gravitational force (Newtons)
2
2
11
10673.6 kg
mN
G
1
m
mass number 1 (kilograms)
Engineering Fundamentals: Chapter 18
An Introduction to Engineering
2
m
mass number 2 (kilograms)
r
distance between centers of masses (meters)
Which type of mathematical model is used here to describe the gravitational force?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Trigonometric model
Analysis:
17. The loudness
of sound is dependent upon the sound intensity I according to the following
equation:
12
10log10 I
. Which type of mathematical model is used in this relationship?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Logarithmic model
Analysis:
18. The future worth of a present value is modeled using the following function:
n
iPnF 1
where
F
future worth ($)
P
present value ($)
i
interest rate (%)
n
length of investment (years)
Which type of mathematical model is used here to describe the gravitational force?
Engineering Fundamentals: Chapter 18
An Introduction to Engineering
a. Linear model
b. Nonlinear model
c. Exponential model
d. Trigonometric model
Analysis:
19. Calculus is commonly divided into two broad areas:
a. single variable and multivariable calculus.
b. differential and integral calculus.
c. vector and matrix calculus.
d. linear and nonlinear calculus.
Analysis:
20. The rate of change refers to how a dependent variable changes with respect to an independent
variable.
a. True
b. False; that’s the definition of slope.
21. The term rate of change always refers to the physical quantity of time.
a. True
b. False
22. Many engineering problems are modeled using differential equations with a set of
corresponding boundary and/or initial conditions.
a. True
b. False
23. What kind of mathematical model contains derivatives of functions?
a. nonlinear equation
b. differential equation
c. exponential equation
d. logarithmic equation
Analysis:
24. The drag force acting on a car can be modeled using the following function:
AVCF dd 2
2
1
where
d
F
drag force
d
C
drag coefficient
air density
V
speed of car relative to air
A
frontal area of car
The power P required to overcome air resistance can be modeled according to
VFP d
.
When analyzing power as a function of velocity P(V), what order is the resulting function?
a. first order
b. second order
c. third order
d. none of the above
