# Mechanics for Scientists and Engineers

ePrep Course for University Preparation

Mechanics for Scientists and Engineers ePrep course is one of the ten ePrep courses specially developed to help NSF, NSmen and others to better prepare themselves for studies in universities in Singapore, or overseas. Poor foundation in mechanics, especially for those without going through A-level physics, has been a big source of difficulties faced by those doing conventional engineering such as mechanical or civil engineering, and physical sciences.

This university preparatory course on mechanics is developed in collaboration with the publishers of the popular physics textbook by Serway and Jewett. The course comes with the textbook at no additional cost, together with excellent learning materials provided by the publishers and a retired NTU professor as the tutor.

In order to further assist the students in preparing for their university studies, additional learning materials on many other subjects are also provided. These include materials on physics, mathematics (algebra, calculus, and statistics, etc.), business finance, engineering economy, economics, corporate finance, biotechnology, biology (or life science), business ethics, Python Programming, discrete mathematics, etc. Samples of these materials can be found below.

While this university preparatory course on physics was designed to help NSFs, it is now opened to everybody and it is highly recommended, especially for those who do not have a strong foundation in physics but are doing engineering, science or technological courses.

##### Audio: Fuller Intro to Mechanics for Scientists and Engineers ePrep Course

**Mechanics for Scientists and Engineers ePrep Course**

**– The Learning Contents**

**I. Compulsory Chapters**

**1 Physics and Measurement.**

1.1 Standards of Length, Mass, and Time

1.2 Modeling and Alternative Representations

1.3 Dimensional Analysis

1.4 Conversion of Units

1.5 Estimates and Order-of-Magnitude Calculations

1.6 Significant Figures

**2 Motion in One Dimension.**

2.1 Position, Velocity, and Speed of a Particle

2.2 Instantaneous Velocity and Speed

2.3 Analysis Model: Particle Under Constant Velocity

2.4 The Analysis Model Approach to Problem Solving

2.5 Acceleration

2.6 Motion Diagrams

2.7 Analysis Model: Particle Under Constant Acceleration

2.8 Freely Falling Objects

2.9 Kinematic Equations Derived from Calculu

**3 Vectors.**

3.1 Coordinate Systems

3.2 Vector and Scalar Quantities

3.3 Basic Vector Arithmetic

3.4 Components of a Vector and Unit Vectors

**4 Motion in Two Dimensions.**

4.1 The Position, Velocity, and Acceleration Vectors

4.2 Two-Dimensional Motion with Constant Acceleration

4.3 Projectile Motion

4.4 Analysis Model: Particle in Uniform Circular Motion

4.5 Tangential and Radial Acceleration 4.6 Relative Velocity and Relative Acceleration

**5 The Laws of Motion.**

5.1 The Concept of Force

5.2 Newton’s First Law and Inertial Frames

5.3 Mass

5.4 Newton’s Second Law

5.5 The Gravitational Force and Weight

5.6 Newton’s Third Law

5.7 Analysis Models Using Newton’s Second Law

5.8 Forces of Friction

**6 Circular Motion and Other Applications of Newton’s Laws.**

6.1 Extending the Particle in Uniform Circular Motion Model

6.2 Nonuniform Circular Motion

6.3 Motion in Accelerated Frames

6.4 Motion in the Presence of Resistive Forces

**7 Energy of a System.**

7.1 Systems and Environments

7.2 Work Done by a Constant Force

7.3 The Scalar Product of Two Vectors

7.4 Work Done by a Varying Force

7.5 Kinetic Energy and the Work-Kinetic Energy Theorem

7.6 Potential Energy of a System

7.7 Conservative and Nonconservative Forces

7.8 Relationship Between Conservative Forces and Potential Energy

7.9 Energy Diagrams and Equilibrium of a System

**8 Conservation of Energy.**

8.1 Analysis Model: Nonisolated System (Energy)

8.2 Analysis Model: Isolated System (Energy)

8.3 Situations Involving Kinetic Friction

8.4 Changes in Mechanical Energy for Nonconservative Forces

8.5 Power

**9 Linear Momentum and Collisions.**

9.1 Linear Momentum

9.2 Analysis Model: Isolated System (Momentum)

9.3 Analysis Model: Nonisolated System (Momentum)

9.4 Collisions in One Dimension

9.5 Collisions in Two Dimensions

9.6 The Center of Mass

9.7 Systems of Many Particles

9.8 Deformable Systems

9.9 Rocket Propulsion

**10 Rotation of a Rigid Object About a Fixed Axis**

10.1 Angular Position, Velocity, and Acceleration

10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration

10.3 Angular and Translational Quantities

10.4 Torque

10.5 Analysis Model: Rigid Object Under a Net Torque

10.6 Calculation of Moments of Inertia

10.7 Rotational Kinetic Energy

10.8 Energy Considerations in Rotational Motion

10.9 Rolling Motion of a Rigid Object

**11 Angular Momentum**

11.1 The Vector Product and Torque

11.2 Analysis Model: Nonisolated System (Angular Momentum)

11.3 Angular Momentum of a Rotating Rigid Object

11.4 Analysis Model: Isolated System (Angular Momentum)

11.5 The Motion of Gyroscopes and Tops.

**12 Static Equilibrium and Elasticity.**

12.1 Analysis Model: Rigid Object in Equilibrium

12.2 More on the Center of Gravity

12.3 Examples of Rigid Objects in Static Equilibrium

12.4 Elastic Properties of Solids

**13 Universal Gravitation.**13.1 Newton’s Law of Universal Gravitation

13.2 Free-Fall Acceleration and the Gravitational Force

13.3 Analysis Model: Particle in a Field (Gravitational)

13.4 Kepler’s Laws and the Motion of Planets

13.5 Gravitational Potential Energy

13.6 Energy Considerations in Planetary and Satellite Motion

**14 Fluid Mechanics.**

14.1 Pressure

14.2 Variation of Pressure with Depth

14.3 Pressure Measurements

14.4 Buoyant Forces and Archimedes’s Principle

14.5 Fluid Dynamics

14.6 Bernoulli’s Equation

14.7 Flow of Viscous Fluids in Pipes

14.8 Other Applications of Fluid Dynamics

**II. Optional Chapters**

- Oscillatory Motion.
- Wave Motion.
- Superposition and Standing Waves.
- Temperature.
- Heat and the First Law of Thermodynamics.
- The Kinetic Theory of Gases.
- Heat Engines, Entropy, and the Second Law of Thermodynamics.
- Electric Fields
- …… see complete topics

**What You Get in Mechanics for Scientists and Engineers ePrep Course**

**I. Free Textbook**

##### “Physics for Scientists and Engineers” is a very popular physics textbook, authored by RA Serway and JW Jewett, Jr, 10th Ed.

**II. Free Consultation**

##### A retired NTU professor is acting as the tutor for this NTU ePrep course. You can consult him via email or WhatsApp.

**III. Materials Online**

##### 1. Notes, video lessons and PowerPoint files.

##### 2. Answers/solutions to all questions/problems in the textbook.

##### 3. Online exercises.

##### 4. Problems and solutions in files.

##### 5. Bonus learning materials in various branches of mathematics, including calculus, algebra, geometry, trigonometry, probability and Statistics, as well as on other subjects such as physics, biotechnology, life science, business finance, corporate finance, engineering economy, economics, Python programming, discrete mathematics, business and engineering ethics, and psychology.

**IV. Digital Certificate**

##### A digital certificate will be issued if you have successfully completed this NTU ePrep course and passing all the tests at the end of each of the ten compulsory chapters.

**Mechanics for SCientists and Engineers ePrep Course **

**Sample Materials**

**1. Video Lesson** (Position and Velocity Vectors)

**2. Problem and Solution** (Motion of Satellite)

**Question: **An artificial satellite circles the Earth in a circular motion at a location where the acceleration is 9.00 m/s^{2}. Determine the orbital period of the satellite.

**Solution:**

**Mechanics for Scientists and Engineers**

**Samples of Bonus Materials**

**1. Video Lesson on Business Finance** (Hedge Funds)

**2. Video Lesson on Corporate Finance** (Managing Working Capital)

**3. Cross-Word Puzzle on Biotechnology** (Genetically Modified Organisms)

**4. Worked Example on Engineering Economy** (Cost Concepts and Design Economics)

**Question**: A lash adjuster keeps the pressure constant on engine valves, thereby increasing fuel efficiency in automobile engines. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D = (2,000 − p)/0.10. What is the demand (Dˆ ) when total revenue is maximized? What important data are needed if maximum profit is desired?

**Answer**:

**5. Python Programming** (Plotting a Sine Curve)

Code:import matplotlib

import matplotlib.pyplot as plt

import numpy as np

# Data for plotting

pi = 22/7

theta = np.arange(0.0, 2*pi, 0.05) #uniformly from 0 to 2 pi in step of 0.05

sine = 1 + np.sin(theta)

plt.plot(theta, sine)

plt.show()Output:Plot for y = 1 + sin (theta)

**6. Economics** (Analyzing Changes in Equilibriums)

Three Steps to Analyzing Changes in equilibrium:

Step 1. Decide whether the event shifts the supply or demand curve (or perhaps both).

Step 2. Decide in which direction the curve shifts.

Step 3. Use the supply-and-demand diagram to see how the shift changes the equilibrium price and quantity.

Three steps explained using the market for milk.

1 Example: A Change in Demand — the effect of hot weather on the market for Change in tastes and increase in demand at any given price.

2 Example: A Change in Supply – drought drives up the price of animal feed for dairy cattle. Higher costs reduce supply at any given price.

3 Example: A Change in Both Supply and Demand – 1. Suppose that the hot weather and the rise in animal feed occur during the same time period.

4 Example: A Change in Both Supply and Demand – 2. Forecasters predict a heat wave for some weeks. Hot weather is likely to increase demand for milk and so the demand curve will shift to the right. However, sellers’ expectations that sales of milk will increase as a result of the forecasts mean that they take steps to expand the production of milk.

**7. Discrete Mathematics** (Converse and Contraposition of Statements)

**Question**:

**Solution**:

**Remarks:**

##### These samples of bonus materials on other subjects illustrate how comprehensive and broad-base the course is for preparing students for their university studies. While not all the materials are of interest to the students who take up this ePrep course on Mechanics, they can choose what are beneficial to them and ignore the rest.

**Who should take this ePrep Course**

##### It is a very important fundamental course for students doing physical science and traditional engineering degrees. Many of these students do not have a strong foundation and face difficulties in their studies.

##### Even for those not going to any university due to various reasons, this is an opportunity to prove that they are capable of completing a university-level course.

##### Everyone is welcome and there is no pre-requisite. We will provide the necessary guidance when needed.