MOCK EXAM PAPER FOR PRACTICE; EME-101; ENGINEERING MECHANICS

Printed Pages:4                                    Paper Code: EME-101                                                     

 

B.  Tech –1^st Year (SEM.I)

Pre University Examination, May2012 – 13

Engg.Mechanics

Time:   3hrs                                                                 Total Marks:  100                                        

Note:   (1)        Attempt all questions.

(2)        Be precise in your answer.

Section-A

Tick the appropriate answer:

1. Three forces P, 2P and 3P are exerted along the directions of three sides of equilateral triangle. Their Resultant is 

  a) √3P               b) 3√3P               c) 3P                d) none of the above

2. If two forces P and Q act at an angle Ө, the resultant of these two forces would make an angle α with P such that  

 a) tan α = Q Sin Ө  /  P-Q Sin Ө         b) tan α = P Sin Ө  / P+ Q Sin Ө       

 c) tan α = Q Sin Ө / P+ Q Cos Ө        d) tan α= P Sin Ө / Q - P Cos Ө  

3. The center of gravity of a semicircle  of radius r made of metal is 

 a) on the base                           b) on the perimeter             

 c) 3r/8 above the base              d) 4r/3π above the base.

4. The parallel axis theorem for moment of inertia is

 a) I_zz = I_xx + I_yy                           b) I_Gx= I_xx + AY²             

 c) I_Gx= I_xx - AY²                         d)   I_Gx= I_xx + AX²                 

Fill in the blanks:

5. A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane to the horizontal is 30° degree the angle of friction will be----------------------.

6. The velocity of a particle falling from a height h just  before touching ground is ---------------

7. A beam is having more than two supports is called---------------------- beam and such beams are statically   -----------------.

8. A car moving with uniform acceleration covers 450m in a 5 seconds and covers 700m in the next 5 seconds interval. The acceleration of the car is……………. .m /s^2.

9. Varignon’s theorem is related to……………

10. A truss is said to be rigid in nature when there is no --------------- on application of any external --------------------.             (2x 10=20)

Section-B

Attempt any two parts from each question.           (3x10 = 30)

 Q.1. (a) Define parallelogram law of forces and lami’s theorem.

(b) Find the resultant of the force system given in figure-2, Also find its position:

 (c) A uniform ladder weighting 200 N and length 6m is placed against a vertical wall in a position where its inclination to the vertical is 30 degree. A man weighting 600N climbs the ladder. At what position will he induce slipping? Take coefficient of friction μ = 0.2 at both the contact surfaces of ladder.

Q.2(a) How are the trusses classified? What are the assumptions taken while analyzing a plane truss?

 (b) Draw the reactions for the beam AB loaded through the attached strut.

 (c) Find the reaction in the cantilever beam shown in figure:

Q.3. (a) Define Parallel axis theorem and Perpendicular axis theorem.

(b) Find the Moment of Inertia of the I section shown in figure-5 about x-x and y-y axes.

(c) Derive an expression for mass moment of inertia of a right circular cone of base  radius R, height H and mass M about its axis.   

Section-C

 (5x10=50)   

Q.1. (a) Define impulse. State and explain the D'Alemberts principle.

(b) The equation of motion of a particle moving in a straight line is given by  the equation s =16t +4t²-3t³ where s is the total distance covered from the starting  point in meter at the end of t seconds. Find

(i) Displacement, velocity and acceleration 2 seconds after the start

(ii) the displacement and acceleration when velocity is zero

(iii) the maximum velocity of the particle.

(c) Define the following terms:    i) inertial force (ii) angle of repose (iii) coplanar non concurrent force system (iv) angular momentum 

 

Q.2(a) A car moving with an constant acceleration from rest in the first 50 sec, then in the next 40 second it moves with a constant velocity, in the next 20 second it comes to rest. Find the maximum and average velocity and the acceleration of the car:

(b) 

ASSUMPTIONS CONSIDERED IN ANALYZING AIR STANDARD CYCLE:

AIR STANDARD CYCLE:

• In true sense, internal combustion engines in which combustion of fuels occurs inside the engine cylinder can not be defined as cyclic heat engines. The temperature generated during combustion is very high so that engines must be water cooled to prevent the damage of the engine due to thermal shock. The working fluid here is a mixture of air and fuel that undergoes permanent chemical changes due to combustion and the products of combustions must be exhausted and driven out of the cylinder so that fresh charges can be admitted. Therefore, it does not complete a full thermodynamic cycle.
• The engine cycle analysis is an important tool in the design and study of
• Internal Combustion Engines. 
•  A thermodynamic cycle is defined as a series of processes through which the working fluid progresses and ultimately return to the original state. 
•  Although the thermodynamic cycles are closed cycles and actual engine 
• A real thermodynamic analysis of such an engine quite complex. Hence, we simplified the operation of an I.C. Engine by introducing somewhat idealized version of a real thermodynamic processes occur inside an IC Engine, and this idealized thermodynamic cycles are called "Air standard cycle." In an air standard cycle, a certain mass of a perfect gas like air operates in a complete thermodynamic cycle, where heat is added and rejected reversibly with external heat reservoirs, and all the processes in the cycle are reversible. Air is assumed to behave like a perfect gas, and like a perfect gas, its specific heats are assumed to be constant (although they are certain functions of temperature). These air standard cycles are conceived in such a manner that they may correspond to the operations of internal combustion engines.
•  Although, there are numerous such air standard cycles, the important of them are

a) Otto Cycle (used for petrol engine)

b) Diesel Cycle (used for diesel engine)

c) Mixed, limited pressure or Dual Cycle (used for hot spot engine)

d) Stirling Cycle

e) Ericsson Cycle

To make the analysis simpler, certain assumptions are made during the analysis of air standard cycle. They are as following,

• i) The working substance is a perfect gas obeying the gas equation pV = mRT.
• ii) The working fluid is a fixed mass of air either contained in a closed system or flowing at a constant rate round a closed cycle.
• iii) The physical constants of the working fluid will be those of air.
• iv) The working medium has constant specific heats.
• v) The working media doesn't undergo any chemical change throughout the cycle.

OTTO CYCLE:

The Otto cycle is a thermodynamic cycle used in gasoline (petrol) engines to convert the chemical energy stored in fuel into useful work. It is a four-stroke cycle, consisting of four processes: intake, compression, combustion, and exhaust.

During the intake stroke, the fuel-air mixture is drawn into the engine cylinder as the piston moves downward. During the compression stroke, the mixture is compressed by the upward motion of the piston, which raises the temperature and pressure of the mixture. Near the end of the compression stroke, the spark plug ignites the mixture, causing a rapid combustion that generates a high-pressure wave that drives the piston downward, producing power. This is the power stroke. Finally, during the exhaust stroke, the spent gases are expelled from the cylinder as the piston moves upward.

The Otto cycle is an idealized model of the engine, assuming that the combustion occurs instantaneously and that there are no losses due to friction, heat transfer, or other factors. In practice, real engines operate less efficiently than the idealized model, due to these losses.

The Otto cycle is named after its inventor, Nikolaus Otto, a German engineer who patented the four-stroke engine in 1876. The cycle is widely used in modern gasoline engines, which have been refined and optimized over more than a century of development to achieve high levels of performance, efficiency, and reliability.

DIESEL CYCLE:

The Diesel cycle is a thermodynamic cycle used in diesel engines to convert the chemical energy stored in fuel into useful work. It is a four-stroke cycle, consisting of four processes: intake, compression, combustion, and exhaust.

During the intake stroke, air is drawn into the engine cylinder as the piston moves downward. During the compression stroke, the air is compressed by the upward motion of the piston, which raises the temperature and pressure of the air. Near the end of the compression stroke, fuel is injected into the cylinder, which ignites due to the high temperature and pressure of the air. The fuel-air mixture combusts, generating a high-pressure wave that drives the piston downward, producing power. This is the power stroke. Finally, during the exhaust stroke, the spent gases are expelled from the cylinder as the piston moves upward.

The Diesel cycle is similar to the Otto cycle but differs in that it does not rely on a spark plug to ignite the fuel. Instead, the fuel is injected directly into the cylinder and ignites due to the heat of the compressed air. This allows diesel engines to operate at a higher compression ratio than gasoline engines, which leads to higher efficiency and better fuel economy.

The Diesel cycle is named after Rudolf Diesel, a German inventor who patented the diesel engine in 1892. Diesel engines are widely used in a variety of applications, including cars, trucks, buses, ships, and generators. They are known for their efficiency, durability, and reliability.

Mixed, limited pressure or Dual Cycle (used for hot spot engine):

The Mixed or Dual Cycle is a thermodynamic cycle used in hot-spot engines, which are a type of internal combustion engine that combines elements of diesel and gasoline engines. The cycle is also sometimes referred to as the Limited Pressure cycle.

The Dual Cycle is a combination of the Otto and Diesel cycles. It uses the diesel combustion process, where fuel is injected directly into the cylinder and ignited by the heat of compressed air, but also includes a spark plug like in the Otto cycle. During the intake stroke, air is drawn into the cylinder, and during the compression stroke, the air is compressed to a higher pressure and temperature than in the Otto cycle. Fuel is injected into the cylinder, and the spark plug ignites the fuel-air mixture, creating a flame that spreads through the cylinder. The combustion of the fuel-air mixture produces high pressure and temperature, which drives the piston downward, producing power. Finally, during the exhaust stroke, the spent gases are expelled from the cylinder as the piston moves upward.

The Dual Cycle is designed to provide the advantages of both the diesel and gasoline engines, namely high efficiency and low emissions. It allows for a higher compression ratio than the Otto cycle, which leads to better fuel economy, while also reducing the emission of pollutants like nitrogen oxides (NOx) and particulate matter. The Dual Cycle is used in some specialized applications, such as large marine engines and certain military vehicles. However, it is not as widely used as the Otto and Diesel cycles in most everyday applications.

STERLING CYCLE:

The Stirling cycle is a thermodynamic cycle used in Stirling engines, which are a type of heat engine that converts heat energy into mechanical work. Unlike traditional internal combustion engines, Stirling engines operate on an external heat source, which can be supplied by any fuel source that can produce heat, such as wood, coal, or natural gas.

The Stirling cycle consists of four processes: heating, expansion, cooling, and compression. During the heating process, the working fluid (typically a gas such as helium or hydrogen) is heated by an external heat source, causing it to expand and drive a piston outward. During the expansion process, the expanding gas continues to drive the piston outward, producing mechanical work. During the cooling process, the working fluid is cooled by a heat sink (usually air or water), causing it to contract and pull the piston inward. Finally, during the compression process, the compressed gas is pushed back to the starting point, ready to begin the cycle again.

The Stirling cycle is designed to maximize efficiency by minimizing the losses associated with traditional internal combustion engines, such as friction and heat transfer. However, Stirling engines have a relatively low power-to-weight ratio and are less suitable for high-speed applications. They are typically used in specialized applications, such as in submarines, where quiet operation and long running times are important.

The Stirling engine was invented in the early 19th century by Robert Stirling, a Scottish clergyman, and engineer. Despite its potential benefits, the Stirling engine has not been widely adopted in mainstream applications due to its complexity and high cost compared to other types of engines. However, research and development continue to explore ways to improve the efficiency and practicality of Stirling engines.