Forces and Equilibrium-Types
Constant force if the direction and magnitude of a force is constant, it is said to be a constant force. For example, weight W = mg; force on a changed particle in uniform electric field F = qE
Time dependent force in case of impulse or motion of a changed particle in a alternating electric field, the force depends upon time.
Position dependent force if force acting on a body depends upon the position of a body. It is said to be position dependent force, for example, gravitational and electrostatic forces are position dependent forces
Velocity dependent force if force acting on a body depends upon its velocity it is said to be velocity dependent force. Viscous force F = 6πηrv and the force experienced by a charged particle in a magnetic field F = qv x B are example of velocity dependent forces
Types of equilibrium
Translator equilibrium when several forces act on a body such that the resultant force is zero that is, ∑F = 0, the body is said to be in translator equilibrium. It may be mentioned if ∑F = 0.
Then ∑Fx = ∑Fy = ∑Fz = 0
F = 0 implies a = 0 or dv / dt = 0, that is, either v = 0 or v is constant.
It means the body is in the state of rest (static equilibrium) or in uniform motion (dynamic equilibrium). If the force is conservative F = 0 = du / dr, the PE (potential energy) is maximum, minimum of constant.
Stable equilibrium if on slight displacement form equilibrium position, body has the tendency to reign its original position, it is said to be in stable equilibrium. In case of stable equilibrium, PE is minimum (d2u / dr2 = + ve).
So the centre of gravity is lowest.
Unstable equilibrium if on slight displacement from equilibrium position the body moves in the direction of displacement, the equilibrium is known to be unstable. PE in this case is maximum (d2u / dr2 = - ve), So centre of gravity is highest.
Neutral equilibrium if the body on slight displacement has no tendency to come back or to move in the direction of displacement the equilibrium is knows to be neutral and centre of gravity remains at constant height.
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