Equilibrium of system of coplanar forces

Equilibrium of system of coplanar forces

Definition of equilibrium:

If a body continues in its state of rest or of uniform motion in a straight line under the action of coplanar forces is said to be in equilibrium.

In following figure, the coplanar forces F1, F2, F3 etc., are acting on a body. Under the action of these forces the body is in rest condition or moving with the same speed, such condition of a body is called as equilibrium condition of a body.

Equilibrium condition for coplanar concurrent forces:

∑Fx = 0;       (Algebraic sum of all the horizontal forces must be zero)

∑Fy = 0;       (Algebraic sum of all the vertical forces must be zero)

R = 0;           (Resultant must be zero)

Equilibrium condition for coplanar non-concurrent forces:

∑Fx = 0;       (Algebraic sum of all the horizontal forces must be zero)

∑Fy = 0;       (Algebraic sum of all the vertical forces must be zero)

∑M = 0;           (Algebraic sum of moments of all the forces about a point must be zero)

Equilibrium condition for coplanar parallel forces:

∑F = 0;            (Algebraic sum of all the parallel forces must be zero)

∑M = 0;           (Algebraic sum of moments of all the forces about a point must be zero)

 

Condition of equilibrium for couple:

∑M = 0;           (Algebraic sum of moments of all the forces about a point must be zero)

Equilibrium of rigid bodies:

If the net force as well as the net moment about any arbitrary point is zero then the body is said to be in equilibrium.

∑F = 0;            (Algebraic sum of all the forces must be zero)

∑M = 0;           (Algebraic sum of moments of all the forces about a point must be zero)

Free body diagram:

When we isolate the body from its surrounding and shows all the forces acting on it is known as free body diagram.

Where,

Rb = Reaction at point B

N = Normal reaction at point A

R = Resistive force at point A

W = Wait of ladder

G = Centre of gravity of ladder

 

If P and Q are known the magnitude of the resultant 'R' can be found out.

Let, R make an angle α with the direction of P.

In right angle triangle ΔODC,

tan α = CD / OD = CD / (OA + OD) = Q sinϴ / (P + Q cosϴ)

α = tan^-1 [Q sinϴ / (P + Q cosϴ)]   ----------- (direction of resultant)

If P, Q and ϴ are known then the direction of resultant force can be found out.