4-Forces Notes

Forces

Hooke’s law – the force applied to any solid is proportional to the extension it produces within the proportionality limit for that solid.

Centre of gravity – the center of gravity of a body is a single point where the body’s weight appears to act.

Common type of forces in a Free Body Diagram –

1. Normal contact force (always ⊥ to surface of contact)
2. Resistive forces (always oppose motion)
• Friction
• Viscous drag (air resistance, drag in liquid)
3. Contact force (Normal contact force + friction)
4. Tension (always away from body along the spring/string/rope/cable)
5. Weight (always vertically downwards)
6. Upthrust (always vertically upwards)
7. Electric force
8. Magnetic force
9. Gravitational force

Weight – a force acting on a body due to gravity.
Resistive Force – frictional force (static and kinetic) and viscous force (force on body when it moves through fluids)

Mass – it is a measure of a body’s resistance to change in velocity. (Note: Do not confuse mass with amount of substance. The latter quantity is measured in moles).

Density – mass per unit volume

Pressure – the force exerted normally per unit area.

Upthrust - the upward force exerted on an object due to the displacement of fluid in which the object is submerged.

Archimedes’ Principle – states that when an object is totally or partially immersed in a fluid, it experiences an upward force (upthrust) equal to the weight of fluid displaced.
U = V fluid displaced ρ fluid g

Principle of Flotation – a floating object in a fluid displaces a weight of fluid equal to its own weight.

System in equilibrium – when there is no resultant force and no resultant torque (moment) on the system.

Conditions for equilibrium -
1) Vector sum of all forces acting on a body must be zero. ΣF = 0
(no translational/linear motion)
 Closed vector triangle / polygon, all arrows pointing in the same direction
2) Vector sum of all external torques acting on body must be zero. ∑τ=0 Equilibrium
 (no rotational motion)

 For 3 forces ONLY, lines of action must intersect at a common point  concurrent

Moment of a force – the product of the force and the perpendicular distance from the pivot to the line of action of the force.

Torque of a couple – the product of one of the forces and the perpendicular distance separating the forces. It tends to produce rotation only.

Principal of moments – The total clockwise moments about any pivot point is equal to the total anti-clockwise moments about the same pivot .