Hooke's Law:

Within the limit of proportionality, the extension produced in a material is directly proportional to the force/load applied

F = kx
Force constant k = force per unit extension (F/x)

Elastic potential energy/strain energy = Area under the F-x graph {May need to “count the squares”}

For a material that obeys Hooke‟s law,

Elastic Potential Energy, E = ½ F x = ½ k x2

Forces on Masses in Gravitational Fields:
A region of space in which a mass experiences an (attractive) force due to the presence of another mass.

Forces on Charge in Electric Fields:
A region of space where a charge experiences an (attractive or repulsive) force due to the presence of another charge.

Hydrostatic Pressure p = ρgh

{or, pressure difference between 2 points separated by a vertical distance of h }

Upthrust: An upward force exerted by a fluid on a submerged or floating object; arises because of the difference in pressure between the upper and lower surfaces of the object.

Archimedes' Principle: Upthrust = weight of the fluid displaced by submerged object.

ie Upthrust = Volsubmerged x ρfluid x g

Frictional Forces:

Viscous Forces:

Centre of Gravity of an object is defined as that pt through which the entire weight of the object may be considered to act.

A couple is a pair of forces which tends to produce rotation only.

Moment of a Force: The product of the force and the perpendicular distance of its line of action to the pivot

Torque of a Couple: The produce of one of the forces of the couple and the perpendicular distance between the lines of action of the forces. (WARNING: NOT an action-reaction pair as they act on the same body.)

Conditions for Equilibrium (of an extended object):

  1. The resultant force acting on it in any direction equals zero
  2. The resultant moment about any point is zero

If a mass is acted upon by 3 forces only and remains in equilibrium, then

  1. The lines of action of the 3 forces must pass through a common point
  2. When a vector diagram of the three forces is drawn, the forces will form a closed triangle (vector triangle), with the 3 vectors pointing in the same orientation around the triangle.

Principle of Moments: For a body to be in equilibrium, the sum of all the anticlockwise moments about any point must be equal to the sum of all the clockwise moments about that same point.