# Physics: Forces and Equilibrium

Mind Map by Meldy Miyashita, updated more than 1 year ago
 Created by Meldy Miyashita almost 4 years ago
122
4

### Description

This mind map includes a lot of concepts such as moments, CG, Center of mass, stability, Hooke's Law, objects in equilibrium and pressure (Atmospheric & Hydrostatic Pressure).

## Resource summary

Physics: Forces and Equilibrium
1 1. Moments
1.1 Defined as the product of the force and the perpendicular distance from the pivot to the line of action of the force.
1.1.1 Moment of a force about the pivot = F x d , where F= force and d=perpendicular distance from the pivot
1.1.1.1 Moments have a unit of Nm
1.1.1.2 The equation of moments can also be t = r x F , where t = torque (another term for moments), r = radius (picture the distance from the pivot as a radius) and F = force.
1.1.2 is a vector quantity, since force is also a vector quantity.
2 2. Centre of Mass and Centre of Gravity
2.1 Centre of Mass
2.1.1 The Centre of Mass of a body is a single point at which the entire mass of the body is considered to act.
2.2 Centre of Gravity
2.2.1 The Centre of Gravity of a body is a single point at which the entire weight of the body is considered to act.
2.3 At places with uniform gravitational fields, (where gravitational force is constant), the Centre of Mass coincides with the Centre of Gravity.
2.3.1 Objects close to the ground are under uniform gravitational fields, so their Centre of Mass and Gravity coincides.
2.3.2 Gravitational force decreases with increasing distance from the ground.
2.3.2.1 A tall building has a Centre of Gravity that is lower than its Centre of Mass.
3 3. Stability
3.1 An object is said to be in stable equilibrium if it returns to its original position after being displaced slightly.
3.1.1 Toppling occurs when the centre of gravity of an object falls outside of its base.
3.1.1.1 Increasing Stability
3.1.1.1.1 Increasing the base area of an object.
3.1.1.1.1.1 Because a larger base area means that an object would have to be displaced greatly in order for the centre of gravity to fall outside of its base.
3.1.1.1.2 Lowering the Centre of Gravity of an object.
3.1.1.1.2.1 A lower Centre of Gravity does not fall outside of the object's base easily
4 4. Equilibrium
4.1 For an object acted upon by two or more coplanar forces (forces acting in the same plane) to be in static equilibrium (at rest or uniform motion)...
4.1.1 The resultant force on the system is zero.
4.1.1.1 This is translational equilibrium = no linear acceleration, i.e. no acceleration in a straight line in one direction.
4.1.1.1.1 When doing vector additions, the vector sum of the forces would be 0.
4.1.1.1.2 Graphical methods (drawing the vectors in a triangular/polygonal shape) will yield a closed triangle/polygon.
4.1.2 The resultant moment of the system about every axis is zero.
4.1.2.1 This is rotational equilibrium
4.1.2.1.1 Principle of moments: sum of anticlockwise moments = sum of clockwise moments
5 5. Hooke's Law
5.1 When the top of a spring is attached to a fixed point and a force (weight) is applied at the bottom of the spring, the spring will extend.
5.1.1 Hooke's Law states that within the limit of proportionality, the extension produced in a material is directly proportional to the load attached to the spring.
5.1.1.1 F = kx , where F=force/load (i.e. weight), x = the extension of the spring, k= spring constant
5.1.1.2 The weight attached to the bottom of the spring is the load.
6 6. Pressure
6.1 Pressure is defined as the force per unit area acting in the direction perpendicular to the surface of the object.
6.1.1 P = F/A
6.1.1.1 With the SI unit Nm^-2 or Pa (Pascal)
6.1.1.2 where P=pressure, F=force, A=area
6.2 Atmospheric Pressure
6.2.1 Is the force per unit area exerted against a surface by the weight of air above the surface at any given point in Earth's Atmosphere.
6.2.1.1 Earth's atmospheric pressure is 101kPa (101kN/m^2)
6.2.1.1.1 but this value varies at different altitudes
6.2.1.1.1.1 it decreases at higher altitudes
6.2.1.1.1.2 it increases at lower altitudes
6.3 Hydrostatic Pressure
6.3.1 Is the pressure at any given point in a non-moving, static liquid. (Such as water)
6.3.1.1 It is calculated by the formula: P = hpg, where P=pressure, h=height of the liquid above the point. p (rho)=density, g=gravitational acceleration
6.3.1.1.1 However, the actual pressure at a given point in the liquid is: hpg+atmospheric pressure on the surface of the liquid.
6.3.2 The hydrostatic pressure of a static liquid is equal at the same level/height.
6.3.2.1 If a liquid had different hydrostatic pressures at the same height, it would mean that the liquid is moving.

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