Chapter 1: Statics
* Concepts: Force, moment, equilibrium, free body diagrams
* Example: A beam supported by two columns experiences a vertical force of 1000 N at its midpoint. Draw the free body diagram and determine the vertical reaction forces at the columns.
Chapter 2: Dynamics
* Concepts: Newton's laws of motion, kinematics, work, energy
* Example: A ball is thrown vertically upward with an initial velocity of 10 m/s. What is its maximum height? How long does it take to reach maximum height?
Chapter 3: Strength of Materials
* Concepts: Stress, strain, elasticity, plasticity, failure criteria
* Example: A steel rod is subjected to a tensile force of 5000 N. If the rod has a cross-sectional area of 50 mm², determine the stress and strain in the rod.
Chapter 4: Mechanics of Materials
* Concepts: Beams, bending, shear, torsion
* Example: A simply supported beam carries a uniformly distributed load of 100 N/m over its 2-meter span. Determine the maximum bending stress and deflection in the beam.
Chapter 5: Fluid Mechanics
* Concepts: Viscosity, fluid flow, pressure, buoyancy
* Example: A water pipe with a diameter of 10 cm carries water at a velocity of 2 m/s. Determine the flow rate and pressure drop over a 10-meter length of pipe.
Chapter 6: Thermodynamics
* Concepts: Energy, entropy, heat transfer, Carnot cycle
* Example: A heat engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. Determine the maximum thermal efficiency of the engine.
Chapter 7: Vibrations
* Concepts: Simple harmonic motion, resonance, damping
* Example: A mass-spring system has a natural frequency of 10 Hz. Determine the amplitude of the system when it is subjected to a harmonic force with a frequency of 5 Hz.
Chapter 8: Control Systems
* Concepts: Feedback, transfer functions, frequency response
* Example: A feedback control system is used to regulate the temperature of a room. Determine the transfer function of the system and analyze its stability and performance.
