BE Automobile Engineering Semester 1 (FE First Year) - University of Mumbai Question Bank Solutions

In the truss shown in figure,compute the forces in each member.

The resultant of the three concurrent space forces at A is 𝑹̅ = (-788𝒋̅) N. Find the magnitude of F1,F2 and F3 forces.

Given : A=(0,12,0)
            B=(-9,0,0)
           C=(0,0,5)
          D=(3,0,-4)
 Resultant of forces = (-788𝑗̅) N
To find : Magnitude of forces F1,F2,F3

Refer to figure.If the co-efficient of friction is 0.60 for all contact surfaces and θ = 30o,what force P applied to the block B acting down and parallel to the incline will start motion and what will be the tension in the cord parallel to inclined plane attached to A.
Take WA=120 N and WB=200 N.

Determine the required stiffness k so that the uniform 7 kg bar AC is in equilibrium when θ=30o.
Due to the collar guide at B the spring remains vertical and is unstretched when θ = 0o.Use principle of virtual work.

The system in figure is initially at rest.
Neglecting friction determine the force P required if the velocity of the collar is 5 m/s after 2 sec and corresponding tension in the cable.

A truss is loaded and supported as shown.Determine the following:
(1)Identify the zero force members,if any
(2)Find the forces in members EF,ED and FC by method of joints.
(3)Find the forces in members GF,GC and BC by method of sections

b)A cylinder has a mass of 20kg and is released from rest when h=0 as shown in the figure.Determine its speed when h=3m.The springs have an unstretched length of 2 m.Take k=40 N/m.

Given : m=20 kg
             h=0
            k=40 N/m
To find : Speed when h=3m

Two blocks A and B are resting against the wall and floor as shown in the figure.Find the minimum value of P that will hold the system in equilibrium. Take μ=0.25 at the floor,μ=0.3 at the wall and μ=0.2 between the blocks.

Given : μ=0.25 at floor
             μ=0.2 between blocks
To find : Minimum value of force P

For the truss shown in figure 4, find: (i) zero force members, if any (Justify your answer with FBD), (ii) support reactions at C and D. 

For the composite lamina shown in the figure, determine the coordinates of its centroid.

Using Principle of Virtual Work, determine the force P which will keep the weightless bar AB in equilibrium. Take length AB as 2m and length AC as 8m. The bar makes an angle of 30° with horizontal. All the surfaces in contact are smooth. Refer Figure 9.

Three forces F1, F2 and F3 act at the origin of Cartesian coordinate axes system. The force F1 (= 70N) acts along OA whereas F2 (= 80N) acts along OB and F3 (= 100N) acts along OC. The coordinates of the points A, B and C are (2,1,3), (-1,2,0) and (4,-1,5) respectively. Find the resultant of this force system.

For the truss shown in Figure 16, find the forces in members DE, BD and CB.

Find the co-ordinate of the centroid of the area as shown in the given figure.

A force of 500 N is acting on a block of 50 kg mass resting on a horizontal surface as shown in the figure. Determine the velocity after the block has travelled a distance of 10m. Co efficient of kinetic friction is 0.5.

The position vector of a particle which moves in the X-Y plane is given by 𝒓̅ = (3t³-4t²)𝒊̅ + (0.5t⁴)𝒋̅

Find the resultant of the force acting on the bell crank lever shown. Also locate its position with respect to hinge B.

Given : Forces on the bell crank lever
To find : Resultant and it’s position w.r.t hinge B

Two balls having 20kg and 30 kg masses are moving towards each other with velocities of 10 m/s and 5 m/s respectively as shown in the figure. 
If after the impact ,the ball having 30 kg mass is moving with 6 m/s velocity to the right then determine the coefficient of restitution between the two balls.

Find the support reactions at A and B for the beam loaded as shown in the given figure.