total pages: 3€¦ · 10 a beam ab 10m long is hinged at a and supported on rollers over a smooth...

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Total Pages: 3 Reg No.:_______________ Name:__________________________

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY FIRST SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2017

Course Code: BE100

Course Name: ENGINEERING MECHANICS

Max. Marks: 100 Duration: 3 Hours PART A

Answer all questions, each carries 5 marks. Marks

1 State and explain Lami’s theorem. (5) 2 A force of 1000N acts on a bracket as shown in Fig 1. Determine the moment of

the force about Q.

Fig. 1

(5)

3 State and prove parallel axis theorem. (5) 4 Using the principle of virtual work, determine the reactions of a beam AB of span

8m. The beam carries a point load of 4kN at a distance of 3m from A. (5)

5 A wheel is rotating about its axis with a constant angular acceleration of 3 rad/s2. If the initial and final angular velocities are 5.25 rad/s and 10.5rad/s, determine the total angle turned through, during this interval.

(5)

6 a) b)

A vertical lift of total mass 500kg acquires an upward velocity of 2m/s over a distance of 3m of motion with constant acceleration, starting from rest. Apply D’Alembert principle to calculate the tension in the cable supporting the lift. If the lift, while stopping, moves with a constant deceleration and comes to rest in 2s, calculate the force transmitted by a man of mass 75kg on the floor of the lift during that interval.

(3)

(2)

7 Explain longitudinal, transverse and torsional vibrations with sketches. (5) 8 A helical spring of negligible mass is found to extend 0.15mm under a mass of

0.5kg. Then a mass of 40kg is attached at its lower end. The spring mass system is displaced vertically through 100mm and released. Find the stiffness of the spring, period of oscillation and its natural frequency for the SHM produced.

(5)

PART B Answer any 2 questions from each SET

SET 1 Each question carries 10 marks.

9 a) Two forces F and 2F act on a particle. If the first force is increased by 12kN and the second force is doubled, the direction of their resultant remains unchanged. Find the value of F.

(5)

b) Five forces 4, √3, 5, √3 and 3kN respectively act at one of the angular points of a regular hexagon towards other five angular points. Find the magnitude and

(5)

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direction of the resultant forces. 10 A beam AB 10m long is hinged at A and supported on rollers over a smooth

surface inclined at 30° to the horizontal at B. The beam is loaded as shown in Fig 2. Determine the reactions at A and B.

Fig. 2

(10)

11 a) Three cylinders with given diameters are arranged as shown in fig 3. The cylinders A and B weigh 1000N each and the weight of cylinder C is 2000N. Determine the forces exerted at the contact points.

Fig. 3

(5)

b) A rigid bar is subjected to a system of parallel forces as shown in Fig 4. Reduce this system to a single force and moment system at A.

Fig. 4

(5)

SET II

Each question carries 10 marks 12 Locate the centroid of the shaded area shown in Fig. 5

Fig. 5

(10)

13 A rectangular hole is made in a triangular section as shown in Fig 6. Determine the M.I. of the section about x-x axis passing through the CG of the section and

(10)

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parallel to BC. Also find the M.I, with respect to BC.

Fig.6

14 A uniform ladder of weight 850N and of length 6m rests on a horizontal ground and leans against a smooth vertical wall. The angle made by the ladder with the horizontal is 65°. When a man of weight 750N stands on the ladder at a distance 4m from the top of the ladder, the ladder is at the point of sliding. Determine the co-efficient of friction between the ladder and the floor.

(10)

SET III

Each question carries 10 marks 15 a) A cylindrical roller, 50cm in diameter, is in contact with two horizontal conveyor

belts running at uniform speeds of 5m/s and 3m/s as shown in Fig. 7. Assuming that there is no slip at the points of contact, determine,

i) the position of the instantaneous centre of the roller, ii) the linear velocity of the centre C, and iii) the angular velocity of the roller.

Fig. 7

(5)

b) Determine the three parameters asked in the previous question, if the velocities of the belts are in opposite direction.

(5)

16 A mass of 60kg is supported by two springs of stiffnesses 6kN/m and 8kN/m. The springs are arranged in series. The mass is given an initial displacement of 40mm and the released. Determine the period of vibration, the maximum velocity and maximum acceleration.

(10)

17 a) A reciprocating pump plunger is driven by a crank of radius 30cm which is rotating at 120rpm. Assuming SHM for the plunger, find out the velocity and acceleration of the plunger when it is at 15cm from either end of the stroke.

(5)

b) Find out the maximum force required to push the plunger in the previous question, if the mass of the plunger is 10kg.

(5)

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Total Pages: 3 Reg No.:_______________ Name:__________________________

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST/SECOND SEMESTER B.TECH DEGREE EXAMINATION, JULY 2017

Course Code: BE100


Max. Marks: 100 (All figures in page 3) Duration: 3 Hours

PART A

Answer all questions, each carries 5 marks.

1 Explain the concept of free body diagram with examples? (5)

2 Represent a force 100 N passing through the points (2,3,4) and (7,6,9) in vector

form.

(5)

3 Define product of inertia and principle moment of inertia. (5)

4 State and explain the principle of virtual work. (5)

5 What is meant by dynamic equilibrium? Which principle governs a body under

dynamic equilibrium?

(5)

6 A man weighing 60 kg entered a lift which moves up with an acceleration of 3

m/sec2, find the force exerted by the man on the floor.

(5)

7 Distinguish between free and forced vibrations with examples. (5)

8 In a place in space, a simple pendulum of length 2m has a period of oscillation of

3 sec. Determine the magnitude of gravitational acceleration.

(5)

PART B

Answer any 2 questions from each SET

SET 1

Each question carries 10 marks.

9 a) Show that the resultant of forces is zero for the system of forces shown in Figure1. (4)

b) Block P =0.5 kg and block Q of mass m kg are suspended through a chord, which

is in equilibrium as shown in Figure 2. Determine the mass of block Q.

(6)

10 a) State the conditions of equilibrium for a set of coplanar forces. (3)

b) Determine the support reactions at A and B for the beam loaded as shown in

Figure 3.

(7)

11 a) What is meant by a system of forces in space? Explain how the equations of

equilibrium are expressed while dealing with forces in space.

(3)

b) Determine the resultant of system of concurrent forces having the following

magnitudes and passing through origin and the indicated points.

F1=280 N (12, 6, -4), F2 = 520 N (-3, -4, 12) and F3 = 270 N (6, -3, -6)

(7)

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SET II


12 a) For the shaded area shown in Figure 4, find the position of centroid. (7)

b) State the Theorems of Pappus and Guldinus. (3)

13 The cross-section of a plain concrete culvert is shown in Figure 5. Determine the

moment of inertia about the centroidal axes. (All dimensions are in mm.)

(10)

14 a) State the laws of dry friction. (3)

b) Two blocks A and B weighing 3 kN and 1 kN are connected by a wire passing

over a smooth frictionless pulley as shown in Figure 6. Determine the magnitude

of force P required to prevent movement of block A down the plane. Take

coefficient of friction between the planes and blocks as 0.2.

(7)

SET III


15 a) What is meant by instantaneous centre? Explain any one method of locating the

instantaneous centre.

(5)

b) In a simple reciprocating engine, the crank is 300 mm. radius and the connecting

rod 1500 mm. long. If the crank rotates uniformly at 300 rpm, find the velocity of

piston when the crank is inclined at 300 with the inner dead centre.

(5)

16 Two rough planes inclined at 450 and 600 to horizontal are placed as shown in

Figure 7. Two blocks of weights 60 N and 100 N respectively are placed on the

faces and are connected by a string and passing over a frictionless pulley. If the

coefficient of friction between planes and blocks is 0.35, find the resulting

acceleration and tension in the string.

(10)

17 a) A particle has simple harmonic motion. Its maximum velocity was 6 m/s and the

maximum acceleration was found to be 12 m/s2. Determine the angular velocity

and amplitude. Also determine its velocity and acceleration when displacement is

half of the amplitude.

(5)

b) The strength of a spring is such that a load of 50 N is required to elongate it by 10

mm. When a certain load W is suspended from one end and caused to perform

SHM, the complete oscillations per minute is 100. Calculate the stiffness of the

spring and the value of load W.

(5)

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FIGURES: - BE100 ENGINEERING MECHANICS

All dimensions are in mm

500 1000 500

650

1500

Figure 5

30

15 20 40 30

15

Figure 4

P

Q

300

700

B

A

C

D

4

3

Figure 2

A

B P

250

550

Figure 6

Figure 1

4

65 kN

45.2 kN

KN 56.4 kN

80 kN

300

450

3

600

25 kN 20 kN

20 kN.m 5 kN/m

A B

3 m 1 m 2 m 2 m

Figure 3

100 N 60 N

600 450

Figure 7

300

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Page 1 of 3

Reg. No.______________ Name:_______________________

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2017

(Regular & Supplementary)

Course Code: BE100


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


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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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