Engineering Mechanics Problem Sheet – 3 Module – 3 ...

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FrictionDetermine minimum value of co-efficient of friction so as to maintain the position show figure. Length of Rod AB is 3.5 m and it weighs 250 N.[Dec. 07] [Ans: ? = 0.414]A car of 1000 Kg mass is to be parked on the same 100 incline year round. The static coefficient of friction between the tires and the road varies between the extremes of 0.05 and 0.9. is it always possible to park the car at this place?[May 08][Ans: No]Two 60 wedge are used to push a block horizontal as shown. Calculate the minimum force required to push the block of weight 10 KN. Take ?= 0.25 for all contact surfaces. [May 08][Ans: 1.629 KN N]A block of weight 200 N rests on a horizontal surface. The coefficient of friction between the block and the horizontal surface is 0.4. Find the Frictional force acting on the block if a Horizontal force of 40 N is applied to the block[Dec.09][Ans: F = 40N]Two Blocks A and B of weight 500 N 750 N respectively are connected by a cord that passes over a frictional pulley as shown in fig. the coefficient of friction between the block A and the inclined plane 0.4 and that between the block B and the inclined plane is 0.3. Determine the force P to be applied to block B to produce the impending motion of block B down the plane.Dec. 09[Ans: P = 331.4]Determine the force P to cause motion to impend. Take masses of Blocks A & B as 8 Kg and 4 Kg respectively and the coefficient of sliding friction as 0.3. The force P and rope are parallel to the inclined plane. Assume frictionless pulley.Dec. 10[Ans: P = 10.96 N]Determine the force P required to move the block A of weight 5000 N up the inclined plane. Coefficient of friction between all contact surfaces is 0.25. Neglect the weight of the wedge and the wedge angle is 150.May 11[Ans: P= 3467.1 N]What should be the value of ? so that the motion of block A impend down the plane? The Coefficient of friction ? for all the surface is 1/3.Take Mass of block A = 40 Kg; Mass of block B = 13.5 KgDec. 11[Ans: ? = 29.180]Two blocks A and B are resting against a wall and the floor as shown in fig. Find horizontal force P applied to the lower block that will hold the system in equilibrium. Take ? = 0.25 at floor, ? = 0.3 at wall and ? = 0.2 between the blocks. WA = 500 N, WB = 1000 N.May 12[Ans: P = 81.07 N(←) ]For the block shown in figure, find the minimum value of P which will just disturb the equilibrium of the system.Dec. 12[Ans: P = 27 N ]Assuming the values for ? = 0.25 at the floor and 0.3 at the wall and 0.2 between the blocks, find the minimum value of horizontal force P applied to the lower block that will hold the system in equilibrium.[Ans: P = 80.86 N]Dec. 12A block of weight 1000 N is kept on a rough inclined surface. Find out range of P for which the block will be in equilibrium.[ANs: 370.1 ≤ P ≤ 629.9 N]May 13Find out Min. Value of P to Start the motion.[Ans: P = 27.29 N]May 13 Forces in SpaceDerrick pole having a ball and socket support at its base is provided with wires shown in fig. Loads P1 and P2 act at points A and E. The load P1 is parallel to X-Z plane and inclined at an angle 300 with Y-Z plane. The load P2 is parallel to X-Axis. Points B, C, D and O are in X-Z plane. The tension in the wire AD is known to be 8 KN.CalculateX, Y, Z component of support reaction at OThe reactions in wires AB and AC.[Ans: i) R0 = 6i + 18.03 j KN ii) AB = 12.1 KN AC = 1.41 KN]May 98A beam AB of length 9 M and of weight 2450 N is supported at A in the horizontal floor by a Socket joint and the end B is resting against the corner formed by two smooth walls as shown in Fig. Find the reaction at A and B[Ans: RA = -700 i + 2450 j – 700 k, RB = 700 i + 700 k]Dec. 98The rectangular platform OCDE is hinged to a vertical wall at A and B and supported by a cable which passes over a smooth hook at F. if the tension in the cable is 355 N, find the moment about each of the coordinate axes of the force exerted by the cable at D.Dec. 98[Ans:About X = - 337.5i Nmabout Y = 202.5 j Nmabout Z = 480 k Nm]A rectangular table 1m × 2m is mounted on three equal support at 1, 2 and 3. The table weighs 2 kN which acts at the c.g. of the table. If two vertical loads 2 KN and 6 KN are applied on the surfaces at D and E as shown in Fig. Find the reactions of the support.May 99[Ans: R1 = 5.67k, R2 = 3.67 k, R3 = 0.667k]A vertical mast AB is supported at A by ball and socket joint and by cables BC and DE as shown in figure. A force F = 500i + 400j – 300k N is applied at B. Find the reaction at A.May 99[Ans: RA = 840 j + 5095.33k, TBC = 2272.73 N, TDE = 3612.9 N]A rectangular parallelogram carries 4 forces as shown in fig. Reduce the force system to a resultant force applied at the origin and a moment around origin OA = 5m, OB = 2m, OC = 4m.Dec. 12[Ans: R= (1.27i + 2.364j + 13.16k) KN, ΣMFO = (8.432i – 10.54k) KNm]Force F = 80i + 50 j – 60k passes through a point A (6,2,6). Compute its moment about a point B (8,1,4)Dec. 12[Ans: MFB = -160i + 40j – 180k]Explain conditions for equilibrium for forces in space.May 13Determine component of 6 KN and 4.5 KN forces s shown in fig. Also find angles ?X, ?Y and ?Z with coordinate axis.Determine the safe value “W” that can be supported by the tripod shown if fig without exceeding compressive force of 3 KN in any member.A force F = 80i + 50j -60k passes through a point A (6, 2, 6). Compute its moment about point B (8, 1, 4)A concrete mat in the shape of regular hexagon of side 10m, supports four loads as shown in fig. determine loads P and Q if resultant of six loads is to pass through Centre of the mat. ................
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