# Forces

#### 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.