Mechanics

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Published on February 20, 2014

Author: varunpanda125

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Mechanics

BTCM TUTOR MARKED ASSIGNMENT ET 202 (Part A) ENGINEERING MECHANICS Maximum Marks : 100 Weightage : 30% Course Code : ET-202A Last Date of Submission : July 31, 2012 Note : All questions are compulsory and carry equal marks. This assignment is based on all Blocks of Engineering Mechanics. Q.1 (a) Two forces of 10 kg and 15 kg act simultaneously at a point. Find the resultant force, if the angle between the two forces be (i) 30 o, (ii) 45o, (iii) 60o, (iv) 90o, and (v) 180o. Draw the force diagram for each situation. (b) Find the angle between two equal force P, when their resultant is equal to (i) P, (ii) P/2, (iii) 2 P, (iv) 3 P, and (v) √2 P. Draw the force diagram for each case. Q.2 (a) A particle is acted upon by three forces equal to 5 kg, 10 kg and 13 kg, along the sides of an equilateral triangle taken in order. Find graphically the magnitude and direction of the resultant force. Find the magnitude and direction of the resultant force if forces are acting along the sides of right angle triangle when one of the angle is 45 o. (b) Four forces of 2, 2.5, 1, and 3 kg are acting simultaneously along straight lines OA, OB, OC and OD, such that ∠ OAB = 40o, ∠ BOC = 100o and ∠ COD = 125o. Find graphically the magnitude and direction of the resultant force. Q.3 A body weighing 10 kg, is suspended by two strings AC and BC at the point C. The lengths of the strings AC and BC are 3 metres and 4 metres respectively and the horizontal distance BC is also 4 metres. Find the tensions in the strings AC and BC. Q.4 (a) (b) A fly wheel of weight 200 N and diameter 20 cm is made to rotate at 10 rotation per second. Determine the K.E. of the wheel. If the frictional couple at its bearing is 10 Nm, determine the number of revolution it will make before coming to rest. If the frictional couple at bearing is double, determine the numbers of revolutions it will make before coming to rest. A mass of 4 kg moving with a velocity of 10 m/sec along x direction follows another mass of 10 kg moving with 5 m/sec in the same direction. Determine the final velocities of the two masses (i) if e = 0.6, (ii) if the impact is fully plastic, determine also the loss in KE, and (iii) the impact is perfectly elastic, determine the final velocities of the two bodies. Q.5 A metal rod A of 25 cm length expands by 0.05 cm when its temperature is raised from 0oC to 100oC. Another rod B of a different metal of length 40 cm expands by 0.04 cm for the same rise in temperature. A third rod C of 50 cm length, made up of pieces of rod A and B placed end to end, expands by 0.03 cm on heating from 0 oC to 50oC. Find the lengths of each portion of the composite rod C. Q.6 A shell of weight 7 kN is fired horizontally from a gun weighing 400 kN, with a velocity 450 m/sec. With what velocity will the gun recoil? What will be the average force of resistance to bring it to rest in a distance of 2 meters. 18

Q.7 (a) Consider a simply supported beam subjected to a uniformly distributed load on the left half of the span as shown in Figure 1. A B 4m 4m Figure 1 Determine SF and BM diagrams for the beam and find the location of the magnitude of maximum BM. (b) Find the forces in all the members of the truss shown in Figure 2. 6m 6m A 3m C E D 150 kN 3m B Figure 2 Q.8 A boy throws a ball so that it may just clean a wall 3.6 m high. The boy is at a distance of 4.8 m from the wall. The ball was found to hit the ground at a distance of 3.6 m on the other side of the wall as shown in Figure 3. Find the least velocity with which the ball can be thrown. B 3.6 m V α O X A 4.8 m 3.6 m Figure 3 Q.9 Locate the centroid for plane section shown in Figure 4 and determine the moment of inertia about AB. C φ 2 cm 12 cm 4 cm B Hole A 4 cm 4 cm Figure 4 19

Q.10 Calculate the force required, P, to cause a block of weight W1 to slide under the another block of weight W2. What will be the tension in the string AB. W1 = 2000 N, W2 = 1000 N, µ = 0.3. A W2 P W1 Figure 5 20 30o

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