BE Chemical Engineering Semester 1 (FE First Year) - University of Mumbai Important Questions for Engineering Mechanics

state and prove varigon’s theorem.

Find the resultant of the force system as shown in the given figure.

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

In the rocket arm shown in the figure the moment of ‘F’ about ‘O’ balances that P=250 N.Find F. 

Find the force F⁴ , so as to give the resultant of the force as shown in the figure given below. 

Given : Forces and their resultant
To find : Force F⁴

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

A force of 140 kN passes through point C (-6,2,2) and goes to point B (6,6,8). Calculate moment of force about origin.

A machine part is subjected to forces as shown.Find the resultant of forces in magnitude and in direction.
Also locate the point where resultant cuts the centre line of bar AB.

Solution:
Given : A machine subjected to various forces
To find : Resultant of forces
             Point where the resultant force cuts the bar AB

Find the resultant of the parallel force system shown in Figure 1 and locate the same with respect to point C. 

A force of magnitude of 20kN, acts at point A(3,4,5)m and has its line of action passing through B(5,-3,4)m. Calculate the moment of this force about a line passing through points S(2,-5,3) m and T(-3,4,6)m.

Determine the position of the centroid of the plane lamina. Shaded portion is removed.

Find the centroid of the shaded portion of the plate shown in the figure.

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

Determine the reaction at points of constant 1,2 and 3. Assume smooth surfaces.

Given: The spheres are in equilibrium
To find: Reactions at points 1,2 and 3

Explain the conditions for equilibrium of forces in space.

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

Determine the force P required to move the block A of 5000 N weight 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 15 degrees.

Given : Weight of block A = 5000 N
μ_s=0.25
Wedge angle = 15^º

To find : Force P required to move block A up the inclined plane

State Lami’s theorem.
State the necessary condition for application of Lami’s theorem.

Two spheres A and B of weight 1000N and 750N respectively are kept as shown in the figure..Determine reaction at all contact points 1,2,3 and 4. Radius of A is 400 mm and radius of B is 300 mm

Given  : Two spheres are in equilibrium
W₁=1000 N
W₂=750 N
r_A=400 mm
r_B=300 mm 
To find : Reaction forces at contact points 1,2,3 and 4

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.