Mechcrack - Engineering eclass: Mumbai University - CBCGS mechanics may 2019 paper.

Semester- 1^stMumbai University Exam Time: 16/05/19

3 hours Total Marks: 80 CBCGS Scheme

N.B.: (1) Question No. 1 is compulsory.

(2) Attempt any THREE questions from the remaining FIVE questions.

(3) Assume suitable data if necessary and mention the same clearly.

(4) Draw suitable sketches whenever necessary.

Q.1 Answer any four questions

a) Find the Resultant of forces as shown in fig. [5M]

b) If the cords suspend the two buckets in equilibrium position shown in fig. Determine weight of bucket B if Bucket A has a weight of 60N. [5M]

c) Two blocks A=100N and B=150N are resting on the ground as shown in fig. Find the minimum weight P in the pan so that body a starts. Assume pulley to be mass less and frictionless. [5M]

d) The motion of jet plane while travelling along a Runway is defined by the v-t graph as shown in figure. Construct the s-t graph for the motion. The plane starts from rest. [5M]

e) A 50 kg block is kept on the top of a 15° sloping surface is pushed down the plane with an initial velocity of 20 m/s. if =0.4, determine the acceleration of the block [5M]

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Q.2 a) Four forces acting on a rectangle in the same plane as shown in fig. below. Find magnitude and direction of the resultant force. Also find intersections of line of action of resultant with X and Y axes, assuming D as origin. [6M]

b) Two spheres A and B weight 1000N and 750N respectively are kept as shown in fig. Determine the reactions at all contact points 1, 2, 3 and 4. Radius of A= 400 mm and B=300 mm [8M]

c) Two smooth balls A (mass 3 kg) and B (mass 4 kg) are moving with velocities 25 m/s and 40 m/s respectively. Before impact, the directions of velocity of two balls are 30° and 60° with the line joining the center as shown in fig. If e=0.8, find the magnitude and direction of velocities of the balls after impact. [6M]

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Q.3 a) Find the centroid of shaded area as shown in fig.. [8M]

b) Three forces and Act at the origin O. =70 N acting along OA, where A (2, 1, 3). = 80 N acting along OB, Where B (-1, 2, 0). = 100 N acting along OC, where C (4,-1, 5). Find the resultant of these concurrent forces. [6M]

c) A 4 kg collar is attached to a spring, slides on a smooth Bent rod ABCD. The spring has constant K=500 N/m and is underformed when the collar is at 'C'. If the collar is released from rest at A. Determine the velocity of collar, when it passes through 'B' and 'C'. Also find the distance moved by a collar beyond 'C' before it comes to rest again. Refer fig. [6M]

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Q.4 a) Find the support reactions of bam loaded as shown in fig. [8M]

b) Determine the moment to be applied at C for equilibrium of pin jointed mechanism. Use virtual work method. Refer Fig. [6M]

c) A slider crank mechanism is shown in Fig. The crank OA rotates anticlockwise at 100 rad/s. Find the angular velocity of rod AB and the velocity of the slider at B. [6M]

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Q.5 a) Find the forces in the member BC, BE and AE by method of sections and remaining member by method of joints. [8M]

b) A particle moves in x-y plane and its position is given by r= (3t)i + (4t-3 )j, where r is the position vector of particle in meters at time t sec. Find the radius of curvature of the path and normal and tangential components of acceleration when it crosses X-axis again. [6M]

c) C is a uniform cylinder to which a rod AB is pinned at A and the other end of the rod B is moving along a vertical wall as shown in the fig. If the ends B of the rod are moving upward along the wall with a speed of 3.3 m/s. find the angular velocity of wheel and rod assuming that cylinder is rolling without slipping. [6M]

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Q.6 a) A 100N uniform rod AB is held in position as shown. If =0.15 at A and B calculate range of value of P for which equilibrium is maintained. [8M]

b) A box of size 3m × 4m × 2m is subjected to three forces as shown in fig. Find in vector form the sum of moments of the three forces about diagonal OB. [6M]

c) Two blocks A and B are separately by 10 m as shown in the Figure on a 20° incline plane. If the block starts moving, find the time t when the blocks collide and distance travelled by the each block. Assuming 0.3 for block A and plane and 0.10 for block B and plane. [6M]