Code: 9A01101

B.Tech I Year (R09) Supplementary Examinations January/February 2014 ENGINEERING MECHANICS

(Common to AE, BT, CE, ME and MCTE) Time: 3 hours Max Marks: 70

Answer any FIVE questions All questions carry equal marks

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1 In the four bar mechanism ABCD, as shown in fig. below, determine the force P for equilibrium.

2 Determine the forces in all the members of the frame shown in below figure. Indicate the nature of

forces also (Tension as +ve and Compression as -ve)

3 (a) Explain the principles of operation of a screw-jack with a neat sketch. (b) Outside diameter of a square threaded spindle of a screw jack is 40 mm. The screw pitch is 10 mm. If

the coefficient of friction between the screw and the nut is 0.15, neglecting friction between the nut and collar, determine: (i) Force required to be applied at the screw to raise a load of 2000 N. (ii) The efficiency of screw jack. (iii) Force required to be applied at pitch radius to lower the same load of 2000N and (iv) Efficiency while lowering the load. (v) What should be the pitch for the maximum efficiency of the screw and what should be the value of the maximum efficiency?

4 Determine the centroid of the built up section in the below figure. Express the coordinates of centroid

with respect to x and y axes shown. All the dimensions are shown in mm.

R09

Code: 9A01101

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5 (a) State and prove parallel axis theorem. (b) Derive the expression to determine moment of inertia of a semicircular area about its diametral axis. 6 (a) A stone is dropped from the top of a tower. During the last second of its flight it is found to fall 1/4th of

the whole height of tower. Find the height of the tower. What is the velocity with which the stone hits the bottom of the tower?

(b) A small steel ball is shot vertically upwards from the top of building 50 m above the street with an initial velocity of 25 m/sec. (i) In what time, it will reach the maximum height? (ii) How high above the building will the ball rise? (iii) Compute the velocity with which it will strike the street and the total time for which the ball is in motion.

7 Block ‘A’ initially rests on a spring which is tide with a 75 cm long inextensible cord, as shown in

figure. The cord becomes tight home, when the system is released from rest. Determine the stretching of the spring to bring the system at rest. The cylinder weighs 85 kg and rotates on smooth bearings. Consider R = 0.45 m and r = 0.20 m, mA = 75 kg and mB = 40 kg. Take spring constant K = 1.5 N/mm.

8 (a) Two springs of stiffness K1 and K2 are connected in series. Upper end of the compound spring is

connected to a ceiling and lower end series a load ‘w’. Find the equivalent spring stiffness of the system. If the above two springs are connected in parallel then find the equivalent spring stiffness of the system also.

(b) A helical spring under a weight of 20 N extends 0.3 mm. A weight of 700 N is supported on the same spring. Determine the frequency of vibration of the weight when it is displaced vertically by a distance of 0.9 cm and released. Find the velocity of the weight when the weight is 4 mm below its equilibrium position. Neglect the weight of the spring.

R

r

A B

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