Notes, summaries, assignments, exams, and exercises for Physics for Secondary education

Fundamental Concepts of Fluid Statics

Definition of Pressure

The Pressure (P) is defined as the ratio of the exerted Force (F) to the surface Area (S) over which it acts:

$$P = \frac{F}{S}$$

Hydrostatic Pressure

Hydrostatic Pressure is the pressure exerted by a liquid at all points within it.

Fundamental Equation of Fluid Statics

The pressure at a depth $h$ in a fluid of density $\rho$ under gravity $g$ is given by:

$$P = \rho g h$$

Communicating Vessels Principle

When several containers of different shapes containing the same liquid are connected at the bottom, the height of the liquid surface is identical in all vessels.

Application of Communicating Vessels

This principle is fundamental to water distribution systems for communities.

Determining Relative

Core Concepts of Motion & Force

Understanding Motion

Motion

Change in position relative to a reference point.

Frame of Reference

A system for specifying the precise location of objects in space and time.

Displacement

The change in position of an object. Always includes direction.

Speed

The distance traveled divided by the time interval during which the motion occurs.

Velocity

The speed of an object in a particular direction.

Acceleration

The rate at which velocity changes.

Forces and Their Effects

Force

Any action that can change the state of motion of an object.

Friction

An unbalanced force that acts against an object's direction of motion.

Static Friction

The force that resists the initiation of sliding motion between two surfaces that are in contact at

Electricity

The smallest part in which matter can be divided is the atom. Its construction is like this:

Nucleus: protons - mass and positive charge / neutrons - mass and negative charge

Orbits of electrons: they do not have mass but they have negative electric charge

Electric charge is a property of subatomic particles which influences the action of forces between items.

Charges of the same sign repel each other / Charges of different signs attract each other

1 coulomb = 6.25x10^18 electrons / The atoms of an object can lose electrons and become charged / The atoms of an object can gain electrons and become charged / Electric current is the flow of electrons through a conductor material

An Electric Device

1) An electric device has a resistance of

Physics Formulas

Speed

V: Average velocity

• V = s / t
• s: Distance traveled
• s = v · t
• t: Time spent
• t = s / v
• Minutes to hours = min / 60

SI units:

• Speed is the distance traveled by a mobile unit per unit of time.
• m / s
• km / h
• cm / s

Acceleration

a: Acceleration

• a = V_f - V₀ / t
• V_f: Final velocity
• V_f = V₀ + a · t
• V₀: Initial velocity
• V₀ = V_f - a · t
• t: Time

SI units:

• Acceleration is the change in speed per unit of time.
• m / s²

Forces

F: Force in newtons

• F = m · a
• m: Mass in kg
• a: Acceleration in m / s²

SI units:

• Force is a physical quantity associated with movement.
• Newton (N)
• Kilogram-force (kgf)
• Pound (lb)
• Dyne (dyn)

Forces in the same direction:

• F_R = F₁ + F₂

Forces in opposite directions:

• F_R = F₁ - F₂

Mass

m: Mass in kg

• m = F / a
• F: Force in newtons
• a: Acceleration in m / s²

SI units:

It is the view that our mind and our brain are different things. One way to understand this concept is to consider our self as a container including our physical body and physical brain along with a separate non-physical mind, spirit, or soul. The mind, spirit, or soul is considered the conscious part that manifests itself through the brain in a similar way that picture waves and sound waves manifest themselves through a television set. The picture and sound waves are also non-material just like the mind, spirit, or soul.

Shear Stress in Beams

• 16.1 Rectangular beam: b = 100 mm, d = 250 mm, L = 3 m, w = 40 kN/m → Find τmax + distribution
• 16.2 Triangular section: b = 100 mm, h = 150 mm, F = 13.5 kN → Find τmax + distribution
• 16.3 Circular section: d = 100 mm, F = 30 kN → Find τmax + distribution
• 16.4 I-section: Flange = 150×20 mm, Web = 300×10 mm, F = 50 kN → Find τmax
• 16.5 I-section: D = 350 mm, B = 200 mm, web = 12.5 mm, flange = 25 mm, F = 200 kN → Shear stress distribution
• 16.6 T-section: F = 100 kN, I = 113.4 × 10⁶ mm⁴ → Shear at points + distribution
• 16.7 Unequal I-section: σc = 17.5 MPa, F = 100 kN → Bending moment + shear distribution
• 16.8 Irregular section: F = 20 kN → Shear at points + distribution
• 16.9 Square (diagonal): Diagonal

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Simple Machines and Mechanical Advantage

Simple machines are devices that make work easier. They do this by changing the magnitude or direction of a force. Many simple machines are combined to create complex machines.

Wheel and Axle

A wheel is attached to a central axle so that when one turns, the other must turn. A longer motion at the wheel's edge is converted to a shorter, more powerful motion at the axle. Conversely, a short, powerful force at the axle moves the wheel's edge a greater distance.

Pulley System

A single pulley simply reverses the direction of a force. When two or more pulleys are connected together, they permit a heavy load to be lifted with less force. The trade-off is that the rope's end must move a greater distance than the...

- Scalars and Vectors

• Scalars require magnitude and unit (distance, time, speed, mass)

• Vectors require magnitude, unit, AND direction (displacement, velocity, acceleration, force)

• Force vectors are drawn with their tails attached to the point of application on the object.

• 1D vectors use right/left, up/down, +/-

• 2D vectors described using angles, measured clockwise and anticlockwise from the vertical and horizontal

- Adding Vectors

• 1D vector: make one direction (up, right) a positive value and the opposite direction (down, left) a negative value, then add them all up.

• 2D vector: draw the first vector in the appropriate direction, then the second vector from the head of the first. Then use a² + b² = c² to find the hypotenuse...