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Physics for Engineers - Lecture Notes 1-10

Units and Dimensions:
- Measurable quantities in physics are assigned units.
- Quantities are categorized into basic (fundamental) and derived quantities.
- Basic quantities include length (meter, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd).
- Derived quantities are described in terms of fundamental quantities. Examples include volume, pressure, and density.
- The standard metre is marked on a platinum-iridium alloy bar kept at 0°C.
- The standard second is based on the oscillation period of a cesium atom.
- The standard kilogram is the mass of a platinum-iridium cylinder.
Dimension and Dimension Analysis:
- Dimension refers to physical properties (time, length, mass).
- Dimension analysis checks the dimensional consistency of equations and solutions.
- Consistent dimensional units are needed for addition, subtraction, division and multiplication.
- Fundamental units needed for any equations to be valid.
- Constants and angles have dimensional units of 1 (π, cosθ, sinθ, tanθ, etc.).
Vectors:
- Scalar quantities have only magnitude. Examples include mass and time.
- Vector quantities have both magnitude and direction. Examples include velocity and force.
- Vectors are represented by directed line segments (arrows).
- Vector addition can be done using the triangle or parallelogram methods.
- Vector subtraction is the addition of the negative vector.
- Dot product of vectors results in a scalar.
  - A⋅B = |A||B| cosθ, where θ is the angle between A and B
- Vector product results in a vector.
  - AxB = |A||B| sinθ,
Force:
- A force is a push or pull on a body.
- Measured in Newtons (N).
Newton's Laws of Motion:
- First Law: A body continues in a state of rest or uniform motion unless acted upon by a resultant force.
- Second Law: The rate of change of momentum of a body is directly proportional to the resultant force acting on it and in the same direction.
- Third Law: For every action, there is an equal but opposite reaction.
Impulse-momentum Theorem: The change in momentum of a body is equal to the impulse.
Conservation of Linear Momentum:
- The total linear momentum of an isolated system is conserved.
- Example: Collision problems.
Elastic/Inelastic Collisions:
- Elastic collisions involve the conservation of both kinetic energy and momentum.
- Inelastic collisions involve the conservation of momentum but not kinetic energy.
Motion in Two Dimensions:
- The motion of bodies in two dimensions can be analyzed by considering the x and y components of velocities and acceleration.
Circular Motion:
- Centripetal force is required to keep a body moving in a circle.
- centripetal force results from a net force acting on a body along the radius, always towards the centre.
Vertical Motion Under Gravity:
- The acceleration due to gravity (g) is constant in a vertical direction.
- Equations of motion can be used to analyze vertical projectile motion.
Projectile Motion:
- A body thrown at an angle to the horizontal.
- Consider the vertical and horizontal components separately.
Motion on an Inclined Plane:
- Resolved the forces acting on a body on an inclined plane into components parallel and perpendicular to the plane.
Motion of Connected Bodies:
- Analysis of systems with connected bodies.
Thermal Physics and Thermodynamics:
- The study of heat and temperature.
- Types of thermometers.
- Gas thermometry.
Properties of Matter:
- Elasticity.
- Tensile stress and strain.
- Young's modulus.
- Energy stored in a wire.
- Surface tension
Fluid Dynamics:
- Steady flow (streamline flow).
- Equation of continuity.
- Bernoulli's Theorem
Heat Transfer:
- Three types: Conduction, convection, radiation.
Stefan’s Law:
- Energy radiated by an object.
  - The rate of radiation of energy is proportional to the surface area of the object and the fourth power of its absolute temperature.
- Wien’s Law:
  - Maximum wavelength of electromagnetic radiation is inverse to the temperature of the object.
Wave Motion:
- Classifications: Mechanical waves vs. electromagnetic waves, Transverse waves vs. longitudinal waves.
- Definition of terms: Amplitude, wavelength, frequency, period
- Principle of superposition**: The total displacement of any point is the sum of displacements due to individual waves
Standing Waves:
- Standing waves are formed when waves interfere with each other in opposite directions.
- Characteristics: Nodes, antinodes, mode of vibration
Beats:
- A periodic variation in loudness.
- Occurs when two waves of slightly different frequencies interfere.
- Frequency of beats is the difference between the frequencies of the two waves.
Ultrasonic/Sound:
- Sounds above the audible range
- Applications of Ultrasound

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Questions and Answers

According to Newton's second law, how can you represent the relationship between force, mass, and acceleration?

What does the impulse-momentum theorem state about the change in momentum of a body?

In an isolated system, what happens to the total momentum during a collision?

Using kinetic energy, how can you show the relationship between kinetic energy and momentum?

What is the average force applied by the brakes if a car of mass 1200kg is brought to rest from 45m/s in 9 seconds?

What are the key differences between static friction and kinetic friction?

Using the scenario where a 5kg mass is on a 30-degree incline with a coefficient of friction of 0.5, calculate the total force required to pull the mass up at a uniform velocity.

State Newton's First Law of Motion and its implication regarding inertia.

Explain how the gravitational force affects the motion of an object on an inclined plane.

What role does tension play in a system involving pulleys and inclined planes?

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Physics for Engineers - Lecture Notes 1-10

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