Important Questions and Answers: Equilibrium of Rigid Bodies

1.State varignon’s theorem?

The algebraic sum of moments due to all forces acting on the object about any point is equal to the moment of their resultant about the same point.

2.Define couple?

Twonon collinear parallel forces having same magnitude but opposite direction from a couple.

3.Why the couple moment is said to be a free vector?

Couple moment is said to be a free vector as it can be transferred to any point in the plane without causing any change in its effect on the body.

4.Distinguish between couple and moment?

Moment represents the turning effect of a force where as couple consists of two equal and opposite forces separate by some distance.moment of force various from point to point but moment of a couple is same about any point in the plane.

5.What is meant by force-couple system?

A system of coplanar non concurrent force system acting in a rigid body can be replaced by a single resultant force and couple moment at a point known as force couple system.

6.Can a coplanar non concurrent system with zero resultant force necessarily be in equilibrium?

A coplanar non concurrent system with zero resultant force is not necessarily In equilibrium as it can have a non zero resultant moment.

7.When is moment of force zero about a point?

The moment of force about a point is zero its line of action passes through that point.

8.When is moment of force maximum about a point ?

Moment of force is maximum about a point when,

i)Its applied at maximum result from the point and,

ii)It is applied perpendicular to the line joining the point to the point of application of force.

9.When is moment of force zero about a line?

Moment of force about a line is zero when, i)Force is parallel to that line or,

ii)Line of action of force intersects that line.

10.Explain free body diagram with one example?

Free body diagram is the isolated diagram of an object\system of objects\any point in the system in which all forces at couple moment acting on it are shown including support reactions example:consider a ladder of weight W having rollers at it’s end’s as shown in figure.

11.Statethe necessary and sufficient conditions for equilibrium of rigid bodies in two dimensions?

The necessary and sufficient conditions for equilibrium of rigid bodies in two dimensions are:

1)algebraic sum of horizontal components of all forces acting on the body is must be zero,

2)Algebraic sum of vertical components all forces acting on the body is must be zero,

3)Algebraic sum of moments due to all forces and couple moments acting the body is in must be zero.

12.Write the equation of equilibrium of a rigid body?

The three equations of a rigid body are:

∑Fx=0,;

∑Fy=0,;

∑M=0.

13.Write the conditions equilibrium of a system of parallel force acting in a plane ?

The two conditions of equilibrium of a system of parallel forces acting in a plane are :

1)Algebraic sum of all forces must be zero,

2)Algebraic sum of moments due to all forces about any point must be zero.

14.What are the reactions at a fixed support of a plane beam that are possible?

The reaction at fixed support of a plane beam consist of ,

1)A reaction force in the plane which can be represented by it’s two components(Generally taken to be horizontal and vertical)&,

2)Areaction moment.

15.How many scalar equations can be obtained for equilibrium of rigid body in three dimensions?

Six scalar equations can be obtained for equilibrium of a rigid body in three dimensions.

1. State Varignon’s theorem

2. What is a couple? what is a moment of a couple?

3. A force vector F has the components Fx = 150N, Fy= -200N and Fx = 300N. Determine the magnitude F and the angle made by the force with coordinate axes.

4. Sketch the different types of supports.

5. Write down the conditions of equilibrium of a particle in space

6. A force vector of magnitude 100N is represented by a line of coordinates A (1, 2, 3) and B (5, 8, 12). Determine components of the force along X, Y and Z axes.

7. Explain will you reduce a force into an equivalent force-couple system with an example.

9. Draw Compute the moment of the 100 N force about point A and B

PART-B

1. Four forces act on a 700mm X 375mm plate as shown in fig. a) Find the resultant of these forces b) Locate the two points where the line of action of the resultant intersects the edge of the plate.

2. Four coplanar non concurrent non parallel forces act on a square plate of side 2m as shown in fig. Locate the resultant force.

3. In figure below, two forces act on a circular disc as shown. If the resultant moment of all these forces about point D on the disc is zero, determine: a) Magnitude of force P (b) Magnitude of the resultant of two forces (c) The point on the Y-axis through which the line of action of the resultant passes through.

4. Four forces act on a square of side 1 m as shown in fig. Reduce the force system into an equivalent force – couple system at A.

5. Reduce the system of forces shown in fig.5 to a force – couple system at A.

6. Blocks A and B of weight 200N and 100N respectively, rest on a 30 inclined plane and are attached to the post which is held perpendicular to the plane by force P, parallel to the plane, as shown in fig. Assume that all surfaces are smooth and that the cords are parallel to the plane. Determine the value of P. Also find the Normal reaction of Blocks A and B.

8. A Uniform meter rod AB, assumed rigid of mass 0.5 kg is suspended from its ends in an inclined position and a mass of 1 kg is suspended from a point D, as shown in fig. etermine the tension in each string. Where should the suspended mass be placed in order to get equal tension in the strings.

9. A rod AB of weight 200 N is supported by a cable BD and the corner of wall and floor surface as shown in fig. Find the reaction at A and tension in the cord.

10. Find reactions at points A & B