Engineering Mechanics: Lecture Notes

Unit 1 - Basics and Equilibrium of Particle

Introduction to Mechanics:

1. Draw the tree diagram showing classification of mechanics?

2. What is particle and rigid body? Distinguish particle and rigid body?

3. The size of the earth can be neglected when calculation being performed involving the orbit, hence the

earth can be treated as …………… (a) rigid body (b) deformable body (c) fluid (d) particle

4. For a person standing on the surface of the earth the satellite revolving in the orbit of the earth is

considered to be …………….. (a) rigid body (b) deformable body (c) fluid (d) particle

5. Static deals with bodies at rest only and do not deals with bodies at uniform motion True / False

Units of Measurement:

The system of unit what we are following is International System of units abbreviated as SI units

Unit of force is 1 Newton (Unit : 1N= 1 Kg.m/s2)

1 Newton is equal to force required to give one kilogram of mass acceleration of 1m/s2

Prefixes in SI units: 109=giga= G , 106=mega= M , 103=kilo= k , 10-3=milli= m

10-6=micro= μ , 10-9=nano= n

Have a glance at Rules for Use of SI Units @ Pg No 7-8 in R.C.Hibbeler

Newton’s Law of Motion:

Law of Inertia

No net force acting on a particle

Net force / Resultant force

No external force required for object moving with constant speed

Objects keep on doing what they are doing

1. State the law that is holding good for the given example:

The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle

against a hard surface.

2. An external forces is required to keep an object moving. State the reason : True /False

3. An object that is not accelerating or decelerating has no net forces acting on it. True/False

4. A stationary object has no forces acting on it. True/False

5. Objects in orbit around the Earth (like a satellite) still have net forces acting on them. Explain

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Note:

Inertia is the tendency of an object to resist change in velocity. It is not a force that causes an

object to accelerate or decelerate.

The tendency of an object to resist changes in its state of motion varies with mass. Mass is that

quantity that is solely dependent upon the inertia of an object. 

A common physics demonstration relies on this principle that the more massive the object, the

more that object resist changes in its state of motion. 

6. Objects tend to stay moving because of a force called inertia. True/False

7. An object's inertia causes it to come to a rest position. True/False

8. Which law predicts the behavior of an object for which all the external forces are balanced

Note:

According to Newton, an object will only accelerate if there is a net or unbalanced force acting

upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its

direction, or both its speed and direction.

Objects at equilibrium (the condition in which all forces balance) will not accelerate.

Law of conservation of momentum : there is no external force acts on the system total linear

momentum is conserved”

When an object is accelerated at x m/s in upward direction then its weight W= m (g+a)

When an object is decelerated at x m/s in downward direction then its weight W= m (g-a)

9. Which law of motion pertains to the behavior of objects for which all existing forces

are not balanced…………………….. ?

10. The product of mass and velocity is called

a) Force b) Momentum c) Torque d) Work

11. When a bus suddenly takes a turn, the passengers are thrown outwards because of

a)Inertia of motion b)Speed of motion c)Acceleration of motion d)Both (b) and (c)

12. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object and then to a

6-kg object.

13. A person sitting in an open car moving at constant velocity throws a ball vertically up into air. The

ball falls .

a)Outside the car b)In the car to the side of the person

c)In the car ahead of the person d)Exactly in the hand which threw it up

14. State Newton’s law of motion? Diagrammatically represent the three laws . (Refer Hibbeler - Pg 5)

15. State Newton’s law of gravity?

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16. The unit of universal constant of gravitation is ……………..

17. One Newton is equal to ……………

18. Statement of Newton’s second law

a) F = m(dv/dt) b)F = ma c) F = dp/dt d) All of the above

19. When there is no external force acts on the system total linear momentum is conserved”- What is

this statement

a) Law of conservation of momentum b) Law of conservation of force

c) Law of conservation of mass d) Law of conservation of energy

20. In uniformly accelerated motion, the shape of the displacement- time graph is

a)Hyperbola b) Parabola c) Straight line d) No fixed shape

Forces and system of forces:

Force: It is represented by its magnitude , direction , line of action , sense/ nature of force (push

or pull) , point of application

The principle of transmissibility:

States that the conditions of equilibrium (uniform motion) of a rigid body will remain unchanged

if a force acting at a given point of the rigid body is transmitted along its line of action to another

point with the same magnitude and same direction.

Resultant Force:

It is a single equivalent force which can replace the given force system for an equivalence of

effect

Equilibrium :

A body is said to be in equilibrium if the body is at rest or moving with constant velocity

Conditions for equilibrium / Equations of equilibrium: ΣH = 0 , ΣV = 0, ΣM = 0

Equilibrant Force:

The force which brings equilibrium state is called equilibrant. It is considered to be the equal and

opposite of the resultant force. Equilibrant force is the force, which keeps any object motion less

and acts on virtually every object in the world that is not moving.

Two force equilibrium:

If a body is in equilibrium acted upon by two forces they must be collinear forces of equal

magnitude and opposite in sense

Three force equilibrium:

If a body is in equilibrium acted upon by three forces the resultant of any two forces must be

collinear forces of equal magnitude and opposite in sense to the third force

Four force equilibrium:

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If a body is in equilibrium acted upon by four forces the resultant of any two forces must be

collinear forces of equal magnitude and opposite in sense with the resultant of other two forces

Free Body Diagram:

It is the sketch of the particle which represents it as being isolated from its surrounding. It

represents all forces acting on it.

Parallelogram law of force : (Refer Hibbeler - Pg 65) (Two Coplanar / Concurrent Forces- only )

It states that if two forces acting simultaneously on a particle be represented in magnitude and

direction by two adjacent sides of a parallelogram, their resultant may be represented in

magnitude and direction by the diagonal of the parallelogram which passes through their point of

intersection.

Triangle law of force: (Refer Hibbeler - Pg 65) (Two Coplanar / Concurrent Forces- only )

It states that if two forces acting simultaneously on a particle be represented in magnitude and

direction by two adjacent sides of a triangle taken in an order, then their resultant may be

represented in magnitude and direction by closing side of the triangle taken in an opposite order.

Polygon law of force:

It states that if number of forces acting simultaneously on a particle be represented in magnitude

and direction by sides of a polygon taken in an order, then the resultant of all these forces may be

represented in magnitude and direction by closing side of the polygon taken in an opposite order.

Lami’s theorem: (Three Coplanar / Concurrent Forces under equilibrium- only )

It states that if three coplanar concurrent forces acting at a point be in equilibrium, then each force

is proportional to the sine of angle between the other two forces.

Stable equilibrium :

A body is said to be in stable equilibrium, if it return back to its original position after it is

slightly displaced from its position of rest.

Unstable equilibrium:

A body is said to be in unstable equilibrium, if it does not return back to its original position and

heels farther away after displaced from its original position.

Neutral equilibrium:

A body is said to be in unstable equilibrium, if it occupies a new position (also remains at rest)

after slightly displaced from its position of rest.

Free Body Diagram:

It is the sketch of the particle or a rigid body which represents it as being isolated from its

surroundings. It represents all the forces acting on it. (Refer Hibbeler - Pg 69)

1. Forces are called concurrent when their line of action meets in

(a) one point (b) two points (c) plane (d) perpendicular planes

2.A cow pulls a cart of mass 120kg and produces an acceleration of 2m/sec2 . The force exerted by the

cow is ……………….

3. Define force.

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4. Rate of change of displacement irrespective of its directions is called ……………..

(a) velocity (b) speed (c) acceleration (d) none

5. Force passing through same point is called ………………

6. What are coplanar like and unlike parallel forces?

7. Draw the tree diagram for system of forces?

8. If a point is in equilibrium under the action of applied forces then the value of tensions T AB and TAC are

respectively……………………

(a) 520N and 300N (b) 300N and 520N (c) 450N and 150N (d) 150N and 450N

9. Lamis theorem is valid only for ………………….. System

10. Determine the speed of the car 88.5 km/hr in meters per second ………………….

11. If A = 8i-7j+6k . Determine unit vector of A ……………………

12. The unit vector of force of magnitude 100N is 0.314i + 0.523j – 0.707k . Determine the direction of

the force ……………………..

13. Cos2α + Cos2β + Cos2γ is ……………..

14. A force has the components FX=50 N, FY= 75 N and Fz= 100 N. find out the angles θx , θy and θz that

forms with the x, y and z axes………………….

15. State the conditions for equilibrium of a particle in 2D and 3D. (Refer Hibbeler - Pg 69)

16. Determine the angle θ for connecting member A to the plate so that the resultant force of FA and FB is

directed horizontally to the right. Also, what is the magnitude of the resultant force? Refer Fig.1

Fig.1 Fig.2

17. Determine the x and y components of F1 and F2. Refer Fig.2

18. If the resultant of the force acting on a particle is zero then the particle will

(a) remains at rest (b) move with constant velocity (c) both a and b

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Scalar and Vector:

1. The magnitude of unit vector of i+j+k is ………….. (a) 1 (b) zero (c) 31/2 (d) none

2. Cross product is a ……………. Quantity (a) Scalar (b) Vector

3. Define Scalar and Vector with examples?

4. The quantity which has magnitude only is called …………….

5. The vector whose magnitude one is called……………

6. Equilibrium of the force implies that the resultant of the force is …………………

7. What is the difference between fixed vector and free vector?

A force which is applied at a particular location on a body is fixed vector. Ex: moment

A force which can be moved anywhere in its own plane or in a parallel plane without change in its

effect on the body is called free vector. Ex: couple

8. State two applications of DOT PRODUCT. (Refer Hibbeler - Pg 59)

Free Vector:

A free vector is one whose action is not confined to or associated with a unique line in space.

For example if a body moves without rotation then the movement or displacement of any point in a body

may be taken as a vector. The force is represented by magnitude and direction but at any point in a body.

Sliding Vector:

Has unique line of action in space but not a unique point of application.

Fixed Vector:

A fixed vector is one for which unique point of application is specified. The action of force on a rigid

body or deformable body must be represented by a fixed vector.

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