5. Forces, Density, Pressure

Finding resultant (nose to tail)
- By accurate scale drawing
- Using trigonometry

Field
Gravitational fields: a region of space in which a mass experiences an (attractive) force due to the presence of another mass.
Electric fields: a region of space where a charge experiences an (attractive or repulsive) force due to the presence of another charge.

Upthrust
an upward force exerted by a fluid on a submerged or floating object
Origin of Upthrust:
Pressure on Bottom Surface > Pressure on Top Surface
\therefore∴ Force on Bottom Surface > Force on Top Surface
\Rightarrow⇒ Resultant force upwards

Frictional force
force that arises when two surfaces rub
- Always opposes relative or attempted motion
- Always acts along a surface
- Value varies up to a maximum value

Viscous forces
- A force that opposes the motion of an object in a fluid;
- Only exists when there is motion.
- Its magnitude increases with the speed of the object

Moment of a Force
product of the force and the perpendicular distance of its line of action to the pivot
Moment = Force \times \ \bot Distance\ from\ PivotMoment=Force × perpendicular distance from pivot
Couple
a pair of forces which produce rotation only
To form a couple:
- Equal in magnitude
- Parallel but in opposite directions
- Separated by a distance dd
Torque of a Couple
the product of one of the forces of the couple and the perpendicular distance between the lines of action of the forces.
Torque = Force \times \ \bot Distance\ between\ ForcesTorque=Force× perpendicular distance between force

Conditions for Equilibrium
- Resultant force acting on it in any direction equals zero
- Resultant torque about any point is zero.
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.

Pressure in Fluids

Fluids refer to both liquids and gases
Particles are free to move and have E_{K}\thereforeE_k ∴ they collide with each other and the container. This exerts a small force over a small area causing pressure to form.
Derivation of Pressure in Fluids