Engineering FE Engineering Common Sem 1 Engineering Mechanics May 2023 Question Paper - Mumbai University | munotes

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Q1 Solve any Four
- a) Replace the given force system in two parallel components at B & D. 05
- b) The 30 kg collar may slide on frictionless vertical rod and is connected to a 34 kg 05 counterweight. Find the value of h for which the system is in equilibrium
- c) A block rests on a rough inclined plane making an angle of with the 05 horizontal. The coefficient of static friction between the block and the plane is
- 0.8. If the frictional force on the block is 10 N, Find the mass of the block (in
- d) A force acts at the origin in the direction defined by the angles 0, = & 05 0, = Knowing that the x-component of the force is 750 N. Determine (i) the other components. (ii) Magnitude of the force & (ili) the value of @x
- e) Explain the following with example- 05 li) Instantaneous centre of rotation
- f) Ifx=1-tand where x and y are in meters and t is in second, determine the 05 acceleration of the particle at sec
Q2 Two spheres A and B of weight 7 marks
- A) 1000 N and 750 N respectively are kept as shown in figure Determine the reactions at all contact points 1,2, 3 and 4. Radius of A is 400 mm and radius of B is
- B) the centroid of the shaded 07 areas shown in the fig
- C) A particle starts from rest from origin and its acceleration is given by 06 Knowing that v = 4 m/s when x = 8 m. Find value of k, Also calculate the velocity when displacement is 10 m Find the support reactions of beam loaded as shown in fig. 07
- B) A uniform ladder rests with one end against a smooth vertical wall and other end 07 on the ground, whose coefficient of friction is 0.5. If the inclination of ladder to the ground is find the position of a man (whose weight is same as ladder) from the bottom of the ladder when the ladder is at the verge of slipping. The length of ladder is 8 m
- C) particle moves in x-y plane with acceleration components a, = and 06 ay = -16t m/s’. If its initial velocity is Vo = 50 m/s directed at to the x-axis, compute the radius of curvature of the path at t = 2 sec. Also calculate the velocity at t=5 Sec
Q4 A dam is subjected to three 7 marks
- A) forces, 50 KN on the upstream face AB, 30 kN force on the downstream inclined face and its own weight of 120 KN as shown in figure. Determine the single force and locate its point of intersection with the base AD assuming all the forces to lie in a
- B) A boy throws a ball so that it may 07 clear a wall 3.6 m high. The boy Vo B 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 mon the other side of the wall, Find the least velocity with which the ball can be thrown, and_ the corresponding angle of
- C) For the mechanism shown in B 06 figure, the angular velocity of bar AB is 3 rad/s clockwise. Using instantaneous center of rotation, 2 calculate the angular velocity of bar BC and the velocity of slider = 3 C for this position 607
Q5 A tower is held in position by (x, y) for the cable DA so that the 600N resultant force exerted is directed i 10 marks
- B) Fig shows a-t curve for a particle 10 moving along x axis what is A speed & distance covered by the particle after 50 sec? Find also the maximum speed & the time at which the speed is attain by the
Q6 A block of weight 800 N is acted 5 marks
- A) upon by a horizontal force P as shown in figure, if = 0.35 & uk = 0.25, determine the value of P for impending motion
- B) A wheel of radius 0.75 m rolls 05 surface. Determine the velocities of point P and Q shown in figure, when the velocity of centre of the wheel is 10 m/s towards right
- C) wheel of weight W = 1000 N 05 rest on a smooth incline plane. It W = 1000 N is kept from rolling down the A plane by a string AC. Find the tension in the string and reaction at the point of contact D. D A train starting from rest accelerates uniformly for 3 minutes, runs at constant 05 speed for next 5 minutes and then come to rest in next 2 min. If it covers a total distance of 9 km, draw V- t diagram and find the acceleration and retardation in

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