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state and prove varigon’s theorem.

Concept: Varignon’s Theorem

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

Concept: Resultant of concurrent forces

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

Concept: Resultant of parallel forces

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

Concept: Resultant of concurrent forces

Find the force F^{4} , so as to give the resultant of the force as shown in the figure given below.

Given : Forces and their resultant

To find : Force F^{4}

Concept: Resultant of concurrent forces

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

Concept: Resultant of concurrent forces

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.

Concept: Moment of force about a point

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

Concept: Varignon’s Theorem

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

Concept: Resultant of parallel forces

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.

Concept: Moment of force about a point

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

Concept: Centroid for Plane Laminas

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

Concept: Centroid for Plane Laminas

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

Concept: Centroid for Plane Laminas

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

Concept: Condition of Equilibrium for non-concurrent nonparallel general forces

Explain the conditions for equilibrium of forces in space.

Concept: Condition of equilibrium for concurrent forces

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

Concept: Condition of equilibrium for parallel forces

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

Concept: Condition of equilibrium for concurrent forces

State Lami’s theorem.

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

Concept: Condition of equilibrium for parallel forces

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

W_{1}=1000 N

W_{2}=750 N

r_{A}=400 mm

r_{B}=300 mm **To find : Reaction forces at contact points 1,2,3 and 4**

Concept: Condition of Equilibrium for non-concurrent nonparallel general forces

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.

Concept: Condition of equilibrium for concurrent forces