apj abdul kalam technological university ......7. define the terms amplitude, period of oscillation...

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Reg. No.______________ Name:_______________________

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2017

(Regular & Supplementary)

Course Code: BE100

Course Name: ENGINEERING MECHANICS

Max. Marks: 100 Duration: 3 Hours

PART A

Answer all questions. Each question carries 5 marks

1. The greatest and least resultants of two forces F1 and F2 are 17N and 3N

respectively. Determine the angle between them when their resultant is 149 N.

2. A simply supported beam AB of span 4m is carrying point loads 5kN, 2kN, and 3kN

at 1m, 2m, and 3m respectively from the support A. Calculate the support reactions at

A and B.

3. State and explain parallel axis theorem.

4. Distinguish static friction and dynamic friction.

5. In an office, a lift is moving upwards with an acceleration of 1.5m/s2. Find the force

exerted by a body of mass 30kg on the floor of the lift?

6. Explain the concept of instantaneous centre? How can you locate it?

7. Distinguish between free vibration and forced vibration.

8. What are the general conditions of simple harmonic motion?

PART B

Answer TWO questions from each SET

SET 1

Each question carries 10 marks

9. ABCD is a square , each side being 20cm and E is the middle point of AB. Forces of

magnitude 7,8,12,5,9 and 6 kN act on lines of directions AB, EC, BC, BD, CA and

DE respectively. Find the magnitude and direction of resultant force.

10. Three cylinders weighing 100N each and 80mm diameter are placed in a channel of

width 180mm as in Figure 1. Determine the force exerted by (a) the cylinder A on B

Department of Mechanical Engineering, SCMS School of Engineering and Technology.


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at the point of contact (b) the cylinder B on the base and (c) the cylinder B on the

wall.

Fig.1

11. Determine the support reactions at A &B for the beam shown in Fig.2

Fig.2

SET 2


12. Locate the centroid of the shaded area given in figure 3.

Fig.3

4cm 5cm 3cm 3cm

800N 500N

30°

3

4

A B

600N

A

B C



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13. A uniform ladder of 4m length rests against a vertical wall with which it makes an

angle of 450. The coefficient of friction between the ladder and the wall is 0.4 and

that between ladder and floor is 0.5. If a man, whose weight is one-half of the weight

of ladder, ascends it, how high will he be when the ladder slips?

14. An effort of 200N is required just to move a certain body up an inclined plane of

angle 150, the force acting parallel to the plane. If the angle of inclination of the plane

is made 200 the effort required, again parallel to the plane is found to be 230N. Find

the weight of the body and the coefficient of friction.

SET 3


15. For a reciprocating pump, crank OA rotates at a uniform speed of 300 rpm. The

length of crank and connecting rod are 12 cm and 50cm respectively. Find (1) the

angular velocity of the connecting rod AB and (ii) the velocity of piston when the

crank makes an angle 300 with the horizontal.

16. Two blocks A and B of weight 150N and 100N are released from rest on a 300

inclined plane, when they are 15m apart. The coefficient of friction between the

upper block A and the plane is 0.2 and that between the lower block B and the plane

is 0.4. In what time block A reach block B? After they touch and move as a single

unit, what will be acceleration with which it will move down?

17. A spring stretches by 0.015m when a 1.75 kg object is suspended from its end. How

much mass should be attached to the spring so that its frequency of vibration is 3.0

Hz?


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Reg. No.____________ Name:_______________________

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

SECOND SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017

Course Code: BE 100

Course Name: ENGINEERING MECHANICS

Max. Marks: 100 Duration: 3 Hours

PART A

Answer all questions. 5 marks each.

1. State and explain the principle of Transmissibility of force with sketches.

2. The x,y,z components of a force are 36kN, -24kN and 24kN respectively. Find the

components of this force along the line joining A(1,2,-3) and B(-1,-2,2).

3. Using first theorem of Pappus and Guldinus, find the surface area of a i) Sphere and

ii) right circular cone.

4. Distinguish between (i) Static and kinetic frictions,(ii) Sliding friction and rolling

friction and (iii) angle of friction and angle of repose.

5. What do you mean by instantaneous centre of rotation? How can it be located for a

body moving with combined motion of rotation and translation?

6. What is a seconds’s pendulum? Derive expressions for the loss or gain of time due to

changes in length of string and gravitational acceleration in the case of a simple

pendulum.

7. Define the terms amplitude, period of oscillation and frequency in a simple harmonic

motion.

8. State D’Alemberts principle giving equations expressing the above Principle on the

motion of a lift moving upwards with an acceleration ‘a’ m/sec2 carrying a weight of

‘W’ N.

PART B

Answer any 2 questions from each SET.

SET 1

Each question carries 10 marks.

9. ABCD is a rectangle in which AB=30mm, BC= 20mm. ‘E’ is the middle point of

‘AB’. Forces of magnitude 16,14,18,8,10 and 20N act along ‘AB’, ‘BC’, ‘CD’, ‘DA’,

‘EC’ and ‘DE’ respectively. Find the magnitude, direction and position with respect to

‘ABCD’ of single force to keep the body in equilibrium. ‘B’ is to right of ‘A’ and

taken in anticlockwise direction.

10. a. A cylindrical road roller of weight 1000N and radius 30 cm is pulled by a force ‘F’

through the centre of the wheel. While moving it comes across an obstacle of height

15 cm. Calculate the least force ‘F’ required to cross the obstacle . (5)

b. A force acts at the origin of a co-ordinate system in a direction defined by the

angles αx=69.30 and αz=57.90 .Knowing that the ‘Y’ component of the force is -174N,

determine the (i) angle αy and (ii) the other components and the magnitude of the

force. (5)


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11.

Determine the reactions at supports for the beam. (10)

SET II


12. a. Calculate the moment of inertia and radius of gyration about X axis for the

sectioned area.

(7)

b. An area ‘A’ has the following properties, Ix= 6.4x106 mm4, Iy= 16x106 mm4 and

Ixy = 6.4x106 mm4. Calculate maximum and minimum principal moment of inertia. (3)

13. a. A ladder 5 m long and weighing 260 N is placed against a vertical wall at an

inclination of 300 with wall. A man weighing 780 N climbs the ladder. When he is at

a distance of 1.64 m along the ladder from lower end, the ladder slips, What is the

coefficient of friction assuming it to be same for all contact surfaces? (5)

b. A simply supported beam of span 5 m is loaded with a concentrated load of 4kN at

a distance of 1 m from right end. The beam is also loaded with a uniformly distributed

load of 2kN/m length over a distance of 2m from the left end of the beam. Find the

reactions at the supports of the beam using principle of virtual work. (5)

14. a. Explain with sketches how the forces involved in the lifting of a load by a wedge

are analysed. (5)

b. Determine the product of inertia of the sectioned area about the X-Y axis. (5)


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SET III


15. a. A lift is ascending with an acceleration of 0.6m/sec2.A man holds a spring balance

from which a parcel weighing 13.6 N is hung. What will be the reading in the spring

balance? (3)

b. The crank ‘OA’ of a reciprocating engine mechanism is of length 15 cm and

rotating at 600 rpm. The connecting rod ‘AB’ is 70cm long. Find the (i) angular

velocity of the connecting rod, (ii) velocity of the piston ‘B’ and (iii) the velocity at a

point ‘C’ on the connecting rod at a distance 50cm from the piston end when the

crank makes an angle 450. (7)

16. a. In a system the amplitude of the motion is 1.6m and time period is 4 sec. find the

time required for the particle in passing between points which are at a distance of

1.2m and 0.6m from the centre of force and are on the same side of it. (7)

b. A roller of radius 12 cm rides between two horizontal bars moving in opposite

directions with velocities 2.88 m/sec and 1.92 m/sec. Calculate the distance defining

the position of the path of the instantaneous centre of rotation of the roller. Assume no

slip at points of contacts. (3)

17. a. A tray of mass ‘m’ is mounted on three identical springs as shown. The period of

vibration of empty tray is 0.5 sec. After placing a mass of 1.5 kg on the tray, the

period was observed to be 0.6 sec. Find the mass of the tray and stiffness of each

spring. (5)

b. A body performing simple harmonic motion completes 8 oscilations in one minute.

The velocity of the body is half the maximum velocity at a distance of 12 cm from the

centre. Determine the amplitude and maximum acceleration. (5)


apj abdul kalam technological university ......7. define the terms amplitude, period of oscillation...

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