SYED AMMAL ENGINEERING COLLEGE (Approved by the AICTE, New Delhi, Govt. of Tamilnadu and Affiliated to Anna University, Chennai)

Established in 1998 - An ISO 9001:2000 Certified Institution

Dr. E.M.Abdullah Campus, Ramanathapuram – 623 502.

Phone: 304001, 304002 (04567 ) Fax: 304123(04567)

Web: www.syedengg.ac.in E.mail:saec@syedengg.ac.in

Course Name: ENGINEERING MECHANICS Course Code: GE6263

Semester: III

Important two Mark Questions

Unit I & II

1. Define Kinematics and Kinetics?

Kinematics deals with the study of relationship between displacement, velocity,

acceleration and time of a given motion without considering the forces that causes

motion. Kinetics deals with the relationship between forces acting on the body,

mass of the body and motion of the body.

2. State Parallelogram law?

If two vectors acting at a point be represented in magnitude and direction by the

adjacent sides of a parallelogram, then their resultant is represented in magnitude and

direction by the diagonal of the parallelogram passing through that point.

3. State Triangle law?

If two vectors acting at a point are represented by the two sides of a triangle

taken in order, then their resultant is represented by the third side taken in opposite

order

4. Define Lami’s Theorem?

If three coplanar concurrent forces acting at a point are in equilibrium, each force

will be proportional to the sine of the angle between the other two forces.

5. Define Principle of Transmissibility of forces?

It states that “The state of rest or of motion of a rigid body is unaltered if a force

acting on the body is replaced by another force of same magnitude and direction

but acting anywhere on the body provided the line of action remains same.

Fig – 1 Fig – 2

6. State Varignon’s Theorem?

“The algebraic sum of moment of any number of forces about any point acting

on a system is equal to the moment of the resultant force about that point.

Proof:

7. Define moment of a force about a point?

It is defined as the product of a force and perpendicular distance of the line of

action of the force from a point.

8. Define a Couple?

Two equal parallel forces acting in opposite direction forms a couple

9. Define Resultant force?

It is a single force which replaces all other forces acting on the system is known as

resultant force.

10. What is a force couple system?

The simple representation of a force and a couple in a system is known as force

couple system. Procedure for finding out: 1. find resultant force (Including its

direction) and Net moment about the given point. 2. Plot the resultant force at the

given point along its direction and plot moment at the given point.

11. What is a free body diagram?

It is the diagram of the body in which the body under consideration is free

from all contact surfaces and all the forces acting on it are clearly indicated.

12. State Equilibrium and its Conditions?

When resultant force acting on the system is Zero, then the system is said to be in

equilibrium.

Conditions of Equilibrium are:

1. R=0 Fz=0 Mz=0

2. Fx=0 Mx=0

3. Fy=0 My=0

13. Forces:

Coplanar Force: - line of action of all forces acting on a system lie on same plane

Non Coplanar Force: - do not lie on same plane.

Coplanar collinear force: - line of action lie in same plane and same line

Coplanar concurrent force: - lie in same plane and act at one point

Coplanar non-concurrent force: - lie in same plane and act at different point.

14. Types of Equilibrium:

Stable Equilibrium: - If a body returns back to its original position after being slightly

disturbed from its rest position.

Unstable Equilibrium: - If a body does not return back to its original position after

being slightly disturbed from its rest position.

Neutral Equilibrium: If a body occupies a position and remains at rest in this -

position after being slightly displaced from its rest position.

Unit III –

Properties of surfaces and solids

1. Define Centroid or First moment of area?

It is defined as the point at which the total area of the plane figure namely

rectangle, square etc., is assumed to be concentrated.

2. Define Center of Gravity?

The center of gravity of a body may be defined as the point through which the

entire weight of the body is assumed to be concentrated.

3. What is the difference between the center of gravity and centroid?

Center of gravity is applicable to solid bodies whereas centroid is applicable for

only plane areas.

4. What is ‘Surface of Revolution “and “Body of Revolution”?

Surface of Revolution: It may be defined as the surface which is generated by

rotating a plane curve namely Straight line, arc, etc., about a fixed axis in the plane of

curve.

Body of Revolution: It may be defined as a body which is generated by

rotating a plane area namely triangular area, circular area etc., about a fixed axis.

5. Define Pappus-Guldinus Theorems?

Theorem 1: It states that the area of a surface of revolution is the product of the

length of the generating curve and the distance traveled by the centroid of

the curve, while the surface is being generated.

A = 2πyL (or) 2πxL

Theorem 2: It states that the volume of a body of revolution is obtained from

the product of the generating area and the distance traveled by the centroid of the area,

while the body is being generated.

V = 2πyA (or) 2πxA

6. Define Moment of Inertia or Second moment of area?

Moment of Inertia of a body about any axis is the property by which the body

resists rotation about that axis.

In the case of plane figures Moment of Inertia is the second moment of the area of

the plane figure about the given axis.

Ixx=∫ y2 dA & Iyy = ∫ x2 dA

7. Define Radius of Gyration?

It is defined as the distance at which the entire area ‘A’ of the figure is assumed to

be concentrated such that the moment of Inertia about that axis is same.

I = area x (radius of gyration) 2

8. State Parallel axis Theorem?

This theorem states that the moment of Inertia of a plane area about any axis is the

sum of moment of Inertia of the area about the axis passing through the centroidal

axis and the product of the area of the plane and square of the perpendicular

distance of its centroid from the axis

Iaa = I + a h2

9. State Perpendicular Axis Theorem?

If Ixx and Iyy be the moment of Inertia about two mutually perpendicular axes x

and y in the plane and Izz be the moment of Inertia about the axis normal to the

plane and passing through the point of intersection of x and y axis then

Izz = Ixx + Iyy

10. State Polar Moment of Inertia?

The area moment of Inertia for an area relative to an axis perpendicular to the

plane of the area is called polar moment of Inertia.

IP = Ixx + Iyy

11. Under what circumstances do the following coincide?

a) Center of gravity and center of mass. b) Center of gravity and centroid of area.

Center of gravity and center of mass coincides with the center of mass if

gravitational forces are taken to be uniform and parallel.

Centroid of area coincides with center of gravity of two dimensional bodies

which are having uniform thickness.

12. What is Principal axis and Principal Moment of Inertia?

If the Two Perpendicular Axes (x & y) is rotated then Ixy Values are changes

accordingly. The Perpendicular axes about which product moment of Inertia is

zero are called Principal axes and the moment of Inertia about these axes are called

Principal moment of Inertia.

13. Define Mass moment of Inertia?

The property which measures the resistance of a body to angular acceleration is

known as mass moment of Inertia.

Unit IV

Dynamics of Particles

1. Define Kinematics?

Kinematics is the study of relationships between displacement, Velocity,

acceleration and time of a given motion , without considering the forces that cause

the motion.

2. Define Kinetics?

Kinetics is the study of relationships between the forces acting on a body, the

mass of the body and the motion of the body.

3. What are the types of motion? Explain

Rectilinear motion: When the particle moves along the Straight line Path then the

motion is said to be Rectilinear

Curvilinear motion: When the particle moves along the curved path then that type of

motion is said to be curvilinear motion.

4. Define Average and Instantaneous Velocity?

Average Velocity: The average velocity of the particle over the time interval ∆t may

be defined as the quotient of the displacement ∆s and the time interval ∆t.

Instantaneous Velocity: Instantaneous velocity V of the particle at the instant t is

obtained from the average velocity by choosing shorter and shorter time intervals ∆t

and displacement ∆s.

5. Define Average and Instantaneous acceleration?

Average acceleration: The average acceleration of the particle over the time interval ∆t

may be defined as the quotient of the velocity ∆t and the time interval ∆t.

Instantaneous acceleration: Instantaneous acceleration ‘a’ of the particle at the instant t

is obtained from the average acceleration by choosing shorter and shorter time

intervals ∆t and velocity ∆v.

6. Define Motion Curve?

The curve obtained by plotting the Position, Velocity and acceleration against the

time t is called motion curve.

7. What you mean by uniform rectilinear motion and uniformly accelerated rectilinear

motion?

Uniform Rectilinear Motion: The motion o f a particle in which the acceleration ‘a’

of the particle for every value of‘t’ is called uniform rectilinear motion.

Uniform accelerated Rectilinear Motion: The motion of the particle in which the

acceleration ‘a’ of the particle is constant is said to be uniformly accelerated rectilinear

motion.

8. Write down the equations of motion of a straight line?

V = u + at S = ut + ½ at2

V2 = u2 + 2as

9. Define Relative motion and Dependent rectilinear relative motion?

Relative motion: when a motion of the body is evaluated with respect to another

moving body, then the motion is said to be relative motion.

Dependent rectilinear relative motion: When motion of one particle will depend

upon the motion of several other particles then that type of motion is said to be

dependent rectilinear relative motion.

10. What is projectile?

A particle/body projected upwards into space at an angle to the earth’s

surface is called a projectile. The shape of the path of the projectile is parabolic.

11. What is Trajectory?

The path along which a projectile moves from the point of projection to the point where

it meets the ground is called the trajectory of the particle.

12. What is angle of Projection?

The angle at which a projectile is projected into space is called the angle of

projection.

13. What is time of Flight?

Time during which the projectile is projected into space is called as Time of Flight.

14. What is the range of Projectile?

The velocity with which a projectile is projected into space is termed as the

velocity of projection

15. State Newton’s Law?

First Law: If the resultant force acting on a particle is zero then the particle

remains at rest (if originally at rest) or continue to move in straight line (if

originally in motion)

Second Law: If the resultant force acting on a particle is not zero, then the

acceleration of the particle will be proportional to the resultant force acting in the same

direction. Ie. F = ma

Third Law: To every action there is an equal and opposite reaction.

16. Define Linear Momentum and Angular Momentum?

Linear Momentum (L): The Vector mv (Product of Mass & Velocity) is

called Linear momentum of particle.

Angular Momentum (Ho) : Angular momentum Ho of a particle about a point

‘o’ is the moment about ‘o’ of the Linear momentum (mv) of the particle at that instant. It

is expressed in kg-m2/s

17. Define Impulse?

Ho = r x mv(Cross Product)

If a constant force acts on a body for the given period of time , the product of

force and time during which it acts is termed as Impulse. The force which acts for this

short interval is called impulsive force.

18. Define Impact?

The phenomenon of collision of two bodies which occurs in a very small interval of

time and during which the two bodies exert very large force on each other is called an

impact.

19. State Newton’s law of Collision of elastic bodies?

It States that “when two moving bodies collide with each other, their velocity of separation

bears a constant ratio to their velocity of approach”

Ie. Velocity of separation = (velocity of Approach) constant

v2 – v1 = e ( u1 – u2) where e – co-efficient of restitution

Co-efficient of Restitution: It is defined as the ratio of the relative velocity of their

separation after collision to the relative velocity of their approach before collision.

20. What is meant by plastic and elastic impact?

Elastic Impact: In this type of Impact there is no loss in energy. Theref ore the

relativevelocities before and after impact are equal. (e = 1)

v2 – v1 = u1– u2

Plastic Impact: In this case after collision, both the particles couple or stay together and

move with a common velocity (v) and the coefficient of restitution e = 0.

mA uA+ mB uB = (mA+ mB) v & vA = vB = v

21. Define Line of Impact?

The common normal area to the surfaces in contact during the impact is called the line of

impact.

22. State law of conservation of Momentum?

The total momentum of two bodies remains constant before and after impact.

Initial momentum = Final

momentum mA uA+ mB

uB = mAvA + mBvB

Unit V

Friction and Elements of Rigid bodies

1. What is meant by Friction?

When a body moves over another body, it experiences a opposing force at the

contact surfaces. This opposing force is called friction.

2. State and explain the different types of friction?

Dry Friction: - Dry friction develops between the unlubricated surfaces of bodies in

contact.

Fluid Friction: - Fluid friction developed between two surfaces in the presence of

fluid when adjacent layers of fluid are moving at different velocities.

Internal Friction: - Internal friction occurs in all solid materials which are subjected to

cyclic loading.

3. State Coulomb’s law of dry friction

Laws of Static Friction:

* The force of friction always acts in a direction, opposite to that in which the body tends to

move

* The magnitude of the force of friction is always equal to the applied force.

Laws of Dynamic Friction:

The force of friction always acts in a direction, opposite to that in which the body is moving

For moderate speeds, the force of friction remains constant. But it decreases at a slow rate

with the increase in speed. The magnitude of dynamic friction is slightly less than that of

static friction.

4. Define the following:

Static Friction:- If two surfaces, when are in contact, are at rest then the force experienced

by one surface is called as static friction

Dynamic Friction: If one surface starts moving and the other is at rest, then the force

experienced by the moving surface on the rest is called as dynamic friction.

Sliding Friction: - The friction experienced by a body when it slides over another body.

Rolling Friction: - The friction experienced by a body when it rolls over the other.

5. What is Limiting Friction?

The maximum resistance offered by the body against the external Forces to move is

known as Limiting Friction (Fm).

6. What is impending motion?

The state of motion of a body which is just about to move or slide is called as impending

motion. The force required to cause this motion is called impending force.

7. Define angle of friction?

It is defined as the maximum angle (φ) between normal reaction and the resultant of the

limiting friction

8. Define Angle of Repose?

The angle between an inclined plane and horizontal plane when a body placed on it, is just

Start moving down is called angle of repose.

9. What is wedge?

A wedge is a piece of metal or wood in the shape of a prism to whose cross section is

usually a triangular or trapezoid. It is used for lifting heavy loads and tightening fits.

10. Define Rolling Resistance?

It is defined as one of the friction occurs because of the deformation of the surface under a

rolling load.

11. What is a belt drive?

A belt drive is a power transmission device with belt and pulley arrangement in which

the belt friction is used in application of brakes to stop motion.

12. Define Co-efficient of friction?

It is defined as the ratio of the limiting friction to the normal reaction between the two

bodies and is generally denoted by µ

Dynamics of Rigid body:

1. Define a rigid body?

It is defined as a body which does not deform the action of forces.

2. Define Translation, Rotation and General Plane Motion?

Translation: A rigid body is said to be in translation, if the linear displacement of every

point in the rigid body is the same.

Rotation: A rigid body is said to be in rotation, if all the particles of the body move

along circles centered on a fixed axis called axis of rotation.

General Plane Motion: A rigid body is said to be in General Plane Motion, if it

undergoes a combination of both translation and rotation.

3. Define Torque?

Torque is the turning moment of a force on the body in which it acts. Ie. T = Force x

Radius

4. Define Instantaneous Centre of Rotation of the plane motion?

In general plane motion of a rigid body at any given instant the velocities of various

particles of the slab are same as if the slab bear rotating about certain axis perpendicular to

the plane of the slab called the instantaneous centre of rotation of the slab. The

instantaneous center point is identified with the body where the velocity is zero.

5. Define Inertia Force?

Inertia Force of a body can be defined as the resistance to the change in the condition of

rest or of uniform motion of body

The magnitude of the inertia force is the product of mass and acceleration of the

particle and its direction is opposite to the direction of acceleration of the particle.

6. State Alembert’s principle?

ΣF – ma =0 where –ma is called inertia force

The force system consisting of external forces and inertia force can be considered

to keep the particle in equilibrium since the resultant force externally acting on the

particle is not zero. The particle is said to be in dynamic equilibrium.