Category Archives: Engineering Mathematics Blog

Solution Guides to College Physics Chapter 2 Banner

Chapter 2: Kinematics

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Displacement

Problem 1

Problem 2

Problem 3

Problem 4

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Time, Velocity, and Speed

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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Acceleration

Problem 16

Problem 17

Problem 18

Problem 19

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Motion Equations for Constant Acceleration in One Dimension

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

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Problem 40

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Falling Objects

Problem 41

Problem 42

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Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

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Graphical Analysis of One-Dimensional Motion

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

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Solution Guide to College Physics by Openstax Chapter 1 Banner

Chapter 1: Introduction: The Nature of Science and Physics

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Physical Quantities and Units

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

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Accuracy, Precision, and Significant Figures

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

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Approximation

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

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Solution Guides for College Physics by Openstax Banner

College Physics by Openstax

You can browse on the itemized questions with solutions of the College Physics by Openstax below. Also, you can buy the whole Complete Solution Manual here.

College Physics Cover of Chapter 1: Introduction: The Nature of Science and Physics

Chapter 1: Introduction: The Nature of Science and Physics

College Physics Cover of Chapter 2: Kinematics

Chapter 2: Kinematics

College Physics Cover of Chapter 3: Two-Dimensional Kinematics

Chapter 3: Two-Dimensional Kinematics

College Physics Cover of Chapter 4 Dynamics: Force and Newton's Law of Motion

Chapter 4: Dynamics: Force and Newton’s Law of Motion

College Physics Cover of Chapter 5 Further Applications of Newton's Laws: Friction, Drag, and Elasticity

Chapter 5: Further Applications of Newton’s Laws: Friction, Drag, and Elasticity

College Physics Cover of Chapter 6 Uniform Circular Motion and Gravitation

Chapter 6: Uniform Circular Motion and Gravitation

College Physics Cover of Chapter 7 Work, Energy, and Energy Resources

Chapter 7: Work, Energy, and Energy Resources

College Physics Cover of Chapter 8 Linear Momentum and Collisions

Chapter 8: Linear Momentum and Collisions

College Physics Cover of Chapter 9

Chapter 9: Statics and Torque

College Physics Cover of Chapter 10

Chapter 10: Rotational Motion and Angular Momentum

College Physics Cover of Chapter 11

Chapter 11: Fluid Mechanics

College Physics Cover of Chapter 12

Chapter 12: Fluid Dynamics and Its Biological and Medical Applications

College Physics Cover of Chapter 13

Chapter 13: Temperature, Kinetic Theory, and the Gas Laws

College Physics Cover of Chapter 14

Chapter 14: Heat and Heat Transfer Methods

College Physics Cover of Chapter 15

Chapter 15: Thermodynamics

College Physics Cover of Chapter 16

Chapter 16: Oscillatory Motion and Waves

College Physics Cover of Chapter 17

Chapter 17: Physics of Hearing

College Physics Cover of Chapter 18

Chapter 18:
Electric Charge and Electric Field

College Physics Cover of Chapter 19

Chapter 19:
Electric Potential and Electric Field

College Physics Cover of Chapter 20

Chapter 20:
Electric Current, Resistance, and Ohm’s Law

College Physics Cover of Chapter 21

Chapter 21: Circuits and DC Instruments

College Physics Cover of Chapter 22

Chapter 22:
Magnetism

College Physics Cover of Chapter 23

Chapter 23:
Electromagnetic Induction, AC Circuits, and Electrical Technologies

College Physics Cover of Chapter 24

Chapter 24:
Electromagnetic Waves

College Physics Cover of Chapter 25

Chapter 25: Geometric Optics

College Physics Cover of Chapter 26

Chapter 26: Vision and Optical Instrument

College Physics Cover of Chapter 27

Chapter 27: Wave Optics

College Physics Cover of Chapter 28

Chapter 28: Special Relativity

College Physics Cover of Chapter 29

Chapter 29: Introduction to Quantum Physics

College Physics Cover of Chapter 30

Chapter 30: Atomic Physics

College Physics Cover of Chapter 31

Chapter 31: Radioactivity and Nuclear Physics

College Physics Cover of Chapter 32

Chapter 32: Medical Applications of Nuclear Physics

College Physics Cover of Chapter 33

Chapter 33:
Particle Physics

College Physics Cover of Chapter 34

Chapter 34: Frontiers of Physics

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.3, Problem 12

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PROBLEM:

Evaluate \displaystyle \lim\limits_{x\to 0}\left(\frac{1}{x}\left(\frac{1}{3}-\frac{1}{\sqrt{x+9}}\right)\right)

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SOLUTION: 

A straight substitution of x=0 leads to the indeterminate form 0\cdot 0 which is meaningless.

Therefore, to evaluate the limit of the given function, we proceed as follows

\begin{align*}
\lim\limits_{x\to \:0}\left(\frac{1}{x}\left(\frac{1}{3}-\frac{1}{\sqrt{x+9}}\right)\right) & =\lim\limits_{x\to 0}\left(\frac{1\cdot \:\left(\frac{1}{3}-\frac{1}{\sqrt{x+9}}\right)}{x}\right) \\ \\
& =\lim\limits_{x\to 0}\left(\frac{\frac{\sqrt{x+9}-3}{3\sqrt{x+9}}}{x}\right) \\ \\
& =\lim\limits_{x\to 0}\left(\frac{\sqrt{x+9}-3}{3x\sqrt{x+9}}\right) \\ \\
& =\lim\limits_{x\to 0}\left(\frac{\sqrt{x+9}-3}{3x\sqrt{x+9}}\right)\cdot \frac{\sqrt{x+9}+3}{\sqrt{x+9}+3} \\ \\
& =\lim\limits_{x\to 0}\left(\frac{x}{3x\left(\sqrt{x+9}+3\right)\sqrt{x+9}}\right) \\ \\
& =\lim\limits_{x\to 0}\left(\frac{1}{3\left(\sqrt{x+9}+3\right)\sqrt{x+9}}\right) \\ \\
& =\frac{1}{3\left(\sqrt{0+9}+3\right)\sqrt{0+9}} \\ \\
& =\frac{1}{54} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}
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Differential and Integral Calculus by Feliciano and Uy, Exercise 1.3, Problem 11

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Evaluate \displaystyle \lim\limits_{x\to 3}\left(\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right)

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Solution:

A straight substitution of x=3 leads to the indeterminate form \frac{0}{0} which is meaningless.

Therefore, to evaluate the limit of the given function, we proceed as follows.

\begin{align*}
\begin{align*}

\lim\limits_{x\to \:3}\left(\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right) & =\lim\limits_{x\to \:\:3}\left(\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right)\cdot \frac{\sqrt{x-2}+\sqrt{4-x}}{\sqrt{x-2}+\sqrt{4-x}} \\

& =\lim\limits_{x\to 3}\left[\frac{\left(x-3\right)\left(\sqrt{x-2}+\sqrt{4-x}\right)}{\left(\sqrt{x-2}-\sqrt{4-x}\right)\left(\sqrt{x-2}+\sqrt{4-x}\right)}\right] \\

& =\lim\limits_{x\to3}\left[\frac{\left(x-3\right)\left(\sqrt{x-2}+\sqrt{4-x}\right)}{2x-6}\right]\\

& =\lim\limits_{x\to3}\left[\frac{\left(x-3\right)\left(\sqrt{x-2}+\sqrt{-x+4}\right)}{2\left(x-3\right)}\right] \\

& =\lim\limits_{x\to 3}\left[\frac{\sqrt{x-2}+\sqrt{4-x}}{2}\right]\\

& =\frac{\sqrt{3-2}+\sqrt{4-3}}{2}\\

& =1 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)

\end{align*}
\end{align*}
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Differential and Integral Calculus by Feliciano and Uy, Exercise 1.3, Problem 10

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PROBLEM:

Evaluate \displaystyle \lim\limits_{x\to 2}\left(\frac{x^3-8}{x^2-4\:}\right)

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SOLUTION:

A straight substitution of  x=2 leads to the indeterminate form \frac{0}{0} which is meaningless.

Therefore, to evaluate the limit of the given function, we proceed as follows

\begin{align*}
\lim\limits_{x\to 2}\left(\frac{x^3-8}{x^2-4\:}\right) & =\lim\limits_{x\to 2}\left[\frac{\left(x-2\right)\left(x^2+2x+4\right)}{\left(x+2\right)\left(x-2\right)}\right] \\

&=\lim\limits_{x\to 2}\left[\frac{\left(x^2+2x+4\right)}{\left(x+2\right)}\right] \\

& =\frac{2^2+2\cdot 2+4}{2+2} \\

& =3 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

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Differential and Integral Calculus by Feliciano and Uy, Exercise 1.3, Problem 9

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PROBLEM:

Evaluate \displaystyle \lim\limits_{x\to 4}\left(\frac{\frac{1}{x}-\frac{1}{4}}{x-4\:}\right).

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SOLUTION:

A straight substitution of x=4 leads to the indeterminate form \frac{0}{0} which is meaningless.

Therefore, to evaluate the limit of the given function, we proceed as follows:

\begin{align*}
\\
 \lim\limits_{x\to 4}\left(\frac{\frac{1}{x}-\frac{1}{4}}{x-4}\right)& =\lim\limits_{x\to 4}\left(\frac{\frac{4-x}{4x}}{x-4}\right)\\
\\
& =\lim\limits_{x\to 4}\frac{4-x}{4x\left(x-4\right)}\\
\\

&=\lim\limits_{x\to 4}\left(\frac{4-x}{-4x\left(4-x\right)}\right)\\
\\

& =\lim\limits_{x\to 4}-\frac{1}{4x}\\
\\

& =-\frac{1}{4\cdot 4}\\
\\

& =-\frac{1}{16} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)\\
\\
\end{align*}
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Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists 8th Ed | Walpole| Problem 1.2

According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber is taken and the absorbency on each piece was measured. The following are the absorbency values:

18.71 21.41 20.72 21.81 19.29 22.43 20.17
23.71 19.44 20.50 18.92 20.33 23.00 22.85
19.25 21.77 22.11 19.77 18.04 21.12  

a. Calculate the sample mean and median for the above sample values.

b. Compute the 10% trimmed mean.

c. Do a dot plot of the absorbency data. 

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Problem 1-2|Stress | Mechanics of Materials| Ninth Edition| R.C. Hibbeler|

Determine the resultant internal normal and shear force in the member at (a) section a–a and (b) section b–b, each of which passes through point A. The 500-lb load is applied along the centroidal axis of the member.

Problem 1-2

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Problem 6-1: Odometer reading based on the number of wheel revolutions

Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions—it then calculates the distance traveled. If the wheel has a 1.15 m diameter and goes through 200,000 rotations, how many kilometers should the odometer read?

Solution:

The formula for the total distance traveled is

\Delta s=\Delta \theta \times r

Therefore, the total distance traveled is

\begin{align*}
\Delta s & =\left(200000\:\text{rotations}\:\times \frac{2\pi \:\text{radian}}{1\:\text{rotation}}\right)\left(\frac{1.15\:\text{m}}{2}\right) \\
\Delta s & =722566.3103\:\text{m} \\
\Delta s & =722.6\:\text{km} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)

\end{align*}
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