Introduction

Question 1

What is mechanics?

Answer 1

A physical science concerned with the study of the motion or rest of bodies subjected to a force.

Question 2

What is a physical science?

Answer 2

Any field that involves finding meaning behind natural phenomena through mathematics.

Question 3

What are the three branches of mechanics?

Answer 3

1. Rigid-body Mechanics
2. Deformable-body Mechanics
3. Fluid Mechanics

Question 4

Why study Rigid-body Mechanics?

Answer 4

1. It is a prerequisite for Fluid and Deformable-body Mechanics.
2. It is essential in the analysis and design of structures, mechanical components, and electrical devices.

Question 5

How many types of Rigid-body Mechanics are there?

Answer 5

Two (2).

Question 6

Name the two types of Rigid-body Mechanics.

Answer 6

1. Statics.
2. Dynamics.

Question 7

What is Statics?

Answer 7

The study of the equilibrium of bodies either at rest or moving with a constant velocity (zero acceleration).

Question 8

What is Dynamics?

Answer 8

The study of the motion of accelerated bodies.

Question 9

What conclusion can one draw from the definitions of statics and Dynamics, and why is it not useful in engineering?

Answer 9

A. That statics is a special case of dynamics with zero-acceleration (constant velocity).

*B. Tricky problems can be solved through the study of the equilibrium of bodies.

Question 10

Why did statics develop much earlier than Dynamics?

Answer 10

The principles of equilibrium can easily be devised through simple measurements of force and geometry.
Archimedes and his successors used simple machines like the lever, pulley, and inclined plane to devise the principles.

Question 11

Why is Statics independent of time?

Answer 11

The study of equilibrium does not require accurate measurements of time as no bodies experience acceleration.

Question 12

Which two scientists made Dynamics mainstream and how?

Answer 12

1. Galileo Galilei—studied the acceleration of bodies under the effect of gravity.
2. Isaac Newton—devised three Laws of Motion and a Universal Law of Gravitation.

Question 13

Why are Newton’s Laws of Motion important in Mechanics?

Answer 13

Mechanics is concerned with the rest or motion of bodies subjected to a force. Newton’s Laws govern the motion of all bodies as measured from a non-accelerating reference frame.

Question 14

What is a non-accelerating reference frame?

Answer 14

A point in space assumed to be stationary relative to a body in motion.

Question 15

What do Newton’s Laws of Motion state?

Answer 15

1. A body either originally at rest or moving in a straight line with a constant velocity will remain in that state unless subjected to an unbalanced force.
2. A body subjected to an unbalanced force will experience an acceleration in the direction of the force with a magnitude that is directly proportional to that of the applied force.
   If the body has a mass, m, the magnitude of the force is given by:
   F = ma … (1)
   Here, the mass is the constant of proportionality.
3. The mutual forces of action and reaction are equal, opposite, and colinear (act along a straight line).

Question 16

What does Newton’s Universal Law of Gravitation state?

Answer 16

Any two bodies experience a mutual force of attraction (gravity) between them as a consequence of their masses.
*The magnitude of the force is inversely proportional to the distance between said bodies.

Mathematically, the law is expressed as:
F = G × (m1.m2)/r² … (2)

• | G is the Gravitational Constant = 66.73 (10-¹²) Kg.m³/s².
  |m1 is the mass of the first body.
  |m2 is the mass of the second body.
  |r is the distance between said bodies (on Earth, the distance between a body’s height above the surface and Earth’s core).

Question 17

If there exists a mutual force of attraction between any two bodies, why are all other gravitational forces on the surface of the earth negligible?

Answer 17

The mutual attraction (gravity) is a consequence of the masses of any two bodies. Planetary bodies such as the Earth have exponentially greater masses than any other bodies that may be on their surfaces. “Cancelling out” any smaller attractions that may result.

Question 18

What are the four basic quantities used in Mechanics?

Answer 18

1. Length
2. Time
3. Mass
4. Force

Question 19

What is mass?

Answer 19

Mass is a measure of a quantity of matter that is used to compare the action of one body with that of another.
This property manifests itself as a mutual force of attraction (gravity) between any two bodies.
Mass is also a measure of a body’s resistance to changes in velocity.

Question 20

What is time?

Answer 20

Time is the succession of events. While statics is independent of time, it is a useful property for solving dynamics problems.

Question 21

What is length?

Answer 21

Length is used to locate the position of a point in space. With length, one can determine the size of a system.
When a unit of length is selected, it is possible to determine distances between points and define geometrical properties of objects by expressing measurements as multiples of the unit.

Question 22

What is a force?

Answer 22

A force is any “push” or “pull” that one body exerts on another.
Forces can be contact (pushing against a wall), or non-contact (electricity, magnetism, gravity).

Question 23

What are all forces characterized by?

Answer 23

1. Magnitude
2. Direction
3. Point of Application

Question 24

What is an idealization?

Answer 24

An abstraction that is made in the analysis of a problem to generalize its solution.

Question 25

What are some idealizations that are made in the analysis of mechanics problems.

Answer 25

1. Assuming a body is a particle.
2. Assuming a body is rigid.
3. Representing a load as a concentrated force.

Question 26

What is a particle?

Answer 26

Anything with mass but negligible size.
Idealizations involving particles do not consider the geometry of the body and allow for easy analysis and generalization.

Question 27

What is a Rigid-body?

Answer 27

A collection of particles that remains at a fixed distance from each other before and after a load is applied.
Idealizations involving rigid bodies are of problems that must consider the geometry of a body–by assuming it remains unchanged at all times, several generalizations can be made that make the solution simpler.
**In reality, materials always deform when a load is applied. These deformations are usually so minute that they are neglected in the analysis.

Question 28

What is a concentrated force?

Answer 28

A representation of the effect of a load assumed to act at a point on a body.
A load can be represented as a concentrated force if the area of its point of Application is less than the overall area of the body subjected to the load.