FORCE

 

FORCE

Definition: - It may be defined as an agent which produces or tends to produces, destroy or tends to destroy the motion of a body.

A force while acting on a body may –

• Change the motion of a body
• Retard the motion of a body
• Balance the forces already acting on a body
• Give rise to the internal stress in a body

Parameters to describe a force: -

• Magnitude of the force,
• Direction of the force,
• Point of application.

Units – In CGS System – dyne = 10⁵ N

        In SI System – N

        In MKS System – Kgf = 9.81 N

Principle of Transmissibility: -

If a force is acting on a body at any point, it can be transferred to another point on its line of action, Provided this point is rigidly connected with the body.

Fig. 1 | Principle of Transmissibility

System of forces: -

Types-

Coplanar forces: - The forces, which lines of action lying in the same plane, are called Coplanar forces.

Collinear forces: - The forces, which lines of action lying in the same line, are called collinear forces.

Concurrent forces: - If a set of forces are meeting at a point, then the set of forces are called, concurrent forces.

Parallel forces: - If the lines of actions of a number of forces are parallel to each other, then the forces are called Parallel forces.

a.   LikeParallel forces: - The parallel forces which lines of action are in the same direction.

b.   UnlikeParallel forces: - The parallel forces which lines of action are in the opposite direction. 

Coplanar, concurrent forces: - The forces, which lines of action lying in the same plane and also meet at a point, are called coplanar concurrent forces.

Coplanar, non-concurrent forces: - The forces, which lines of action do not lying in the same plane but do not meet at a point, are called coplanar non-concurrent forces.

Non-coplanar, concurrent forces: - The forces, which lines of action do not lying in the same plane but meet at a point, are called non-coplanar concurrent forces.

Non-Coplanar, Non-concurrent forces: - The forces, which lines of action do not lying in the same plane and do not meet at a point, are called Non-coplanar Non-concurrent forces.

 

Resultant Force – It is a single force which produces the same effect as produced by all the given forces acting on a body.

Resultant force can be determined by –

• Parallelogram law of forces
• Triangle law of forces
• Polygon law of forces 

Parallelogram Laws of Forces: -

It states that if two forces acting simultaneously on a particle, be represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant may be represented in magnitude and direction by the diagonal of the parallelogram which passes through the point of intersection.

Fig.2 | Parallelogram law for force

If R is the resultant force, then

R = √ (P² + Q² + 2PQcosθ)

If the resultant force is act at an angle ‘α’ then,

tan α = Qsinθ/ (P+Qcosθ)

• If θ = 0⁰, i.e. cosθ = 1; Forces are acting in the same line and at the same direction then, Resultant (R) = P +Q
• If θ = 90⁰, i.e. cosθ = 0; Forces are acting at perpendicular direction, then Resultant R = √ (P² + Q²)
• If θ = 180⁰, i.e. cosθ = (-1); Forces are acting in the same line and at the opposite direction then, Resultant (R) = P – Q (If P > Q)
• If P = Q, forces are equal then resultant force R = 2P cos(θ/2)

Triangular Laws of Forces: -It states that if two forces are acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle taken in order, then their resultant may be represented in magnitude and direction by the third sides of the triangle taken in opposite order.

Fig.3  | Triangle Law of force

Polygon Laws of Forces: -It states that if a number of  forces are acting simultaneously on a particle, be represented in magnitude and direction by the sides of a polygon taken in order, then their resultant is represented in magnitude and direction by the closing sides of the polygon taken in opposite order.

Fig. 4 | Polygon Law of Force

Resolution of force: - It is the process of splitting up a given force into no. of components without changing its effect on the body, is called resolution of force.

Fig. 5 | Resolution of force

A force is generally resolved along two mutually perpendicular directions.

Equilibrium: -If the resultant of a number of forces acting on a rigid body are exactly balanced i.e. zero, then the particle is said to be in equilibrium.

Condition of Equilibrium:

For coplanar concurrent forces: -

• Σ H = 0
• Σ V = 0

For coplanar non concurrent forces: -

• Σ H = 0
• Σ V = 0
• Σ M = 0

Lami’s Theorem: -If three coplanar forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between other two forces.

 

Fig.6 | Lami's Theorem

P/ Sinα = Q / sinβ = R/ sinγ