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 x^{2}

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 = Vol_{submerged} x ρ_{fluid} x g

Frictional Forces:

- The contact force between two surfaces = (friction
^{2} + normal reaction^{2})^{½} - The component along the surface of the contact force is called
**friction** - Friction between 2 surfaces always opposes relative motion {or attempted motion}, and
- Its value varies up to a maximum value {called the static friction}

Viscous Forces:

- A force that opposes the motion of an object in a fluid
- Only exists when there is (relative) motion
- Magnitude of viscous force increases with the speed of the object

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):

- The resultant force acting on it in any direction equals zero
- The resultant moment about any point is zero

If a mass is acted upon by

3 forces *only* and remains in

equilibrium, then

- The lines of action of the 3 forces must pass through a common point
- 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.