Mechanical engineering for EEs

Define a free-body diagram for a rigid body to identify all external forces and moments.

Resolve forces into components and calculate resultant forces and moments using vector methods.

Apply equilibrium equations to solve for unknown forces and support reactions in 2D systems.

Analyze forces in simple truss structures using the method of joints and the method of sections.

Analyze forces in frames and machines with multiple connected members.

Apply equilibrium concepts to solve for reactions in simple 3D rigid bodies.

Apply Coulomb's friction law to determine if objects will slip or tip under applied forces.

Calculate normal stress and strain in axially loaded members.

Interpret material properties from stress-strain curves and apply Hooke's Law.

Calculate shear stress and strain in materials under direct shear and bearing stress in connections.

Analyze deformation and elongation in bars under axial loads, including statically indeterminate cases.

Determine stresses in thin-walled pressure vessels using hoop and longitudinal stress formulas.

Apply factors of safety to determine allowable stresses and assess simple designs.

Calculate centroids and area moments of inertia for common and composite cross-sections.

Calculate shear stress and angle of twist in circular shafts under torsion and apply to power transmission.

Construct shear force and bending moment diagrams for beams under various loads.

Apply the flexure formula to calculate normal stress in beams due to bending.

Determine maximum bending stress and select appropriate beam sections for strength.

Calculate beam deflections and slopes using standard formulas and the principle of superposition.

Apply stress transformation equations to determine stresses on inclined planes.

Calculate principal stresses and maximum in-plane shear stress using transformation equations or Mohr's circle.

Analyze states of combined loading involving axial, torsional, and bending stresses.

Apply failure theories (e.g., Maximum Shear Stress, von Mises) to predict material failure under combined stress.

Apply kinematic equations to solve problems of rectilinear and curvilinear motion for a particle.

Analyze projectile motion and motion in normal-tangential coordinates.

Apply Newton's second law (F=ma) to solve for forces and accelerations in particle dynamics problems.

Apply the work-energy principle to analyze changes in particle speed due to applied forces.

Apply the impulse-momentum principle to analyze collisions and impacts between particles.

Relate angular and linear motion quantities for a rigid body in fixed-axis rotation.

Analyze velocity in planar rigid body motion using the relative velocity equation.

Determine the instantaneous center of zero velocity to simplify velocity analysis.

Analyze acceleration in planar rigid body motion using the relative acceleration equation.

Solve kinematics problems for bodies rolling without slipping.

Calculate the mass moment of inertia for composite shapes using the parallel axis theorem.

Apply the three equations of motion for a rigid body in general planar motion.

Solve rigid body kinetics problems involving fixed-axis rotation.

Apply the work-energy method for rigid bodies to relate forces, moments, and changes in speed.

Apply the principles of linear and angular impulse-momentum to rigid bodies.

Derive the equation of motion for a single degree-of-freedom spring-mass system.

Calculate the natural frequency and period for undamped free vibrations.

Analyze the characteristics of underdamped, critically damped, and overdamped systems.

Determine the steady-state response of a damped system under harmonic forcing.

Explain the concept of resonance and its significance in mechanical design.

Define and calculate key fluid properties such as density, viscosity, and specific gravity.

Apply the hydrostatic pressure equation to determine pressure in static fluids.

Calculate hydrostatic forces and the center of pressure on submerged plane surfaces.

Apply Archimedes' principle to solve problems of buoyancy and stability for submerged bodies.

Distinguish between laminar and turbulent flow using the Reynolds number.

Apply the continuity equation (conservation of mass) to incompressible flows.

Apply Bernoulli's equation to analyze pressure and velocity in frictionless fluid flow.

Calculate major head loss in pipes due to friction using the Darcy-Weisbach equation and Moody chart.

Account for minor losses in pipe systems from fittings, bends, and valves using loss coefficients.

Apply the linear momentum equation to determine forces exerted by flowing fluids on objects.

Analyze flow around immersed bodies using drag and lift coefficients.

Apply the steady flow energy equation to analyze pumps and turbines in a fluid system.

Define thermodynamic systems, states, processes, and properties (e.g., enthalpy).

Apply the Ideal Gas Law to relate pressure, volume, and temperature for ideal gases.

Distinguish between heat, work, and internal energy, and apply sign conventions.

Apply the First Law of Thermodynamics to analyze closed systems (non-flow processes).

Analyze common thermodynamic processes for ideal gases: isobaric, isochoric, isothermal, and adiabatic.

Apply the steady-flow energy equation (First Law for open systems) to components like nozzles, diffusers, and heat exchangers.

State the Second Law of Thermodynamics and define entropy as a property.

Apply the principle of increasing entropy to determine the possibility and direction of a process.

Calculate entropy changes for ideal gases undergoing various thermodynamic processes.

Analyze the Carnot cycle and define its role as a benchmark for thermal efficiency.

Analyze the ideal Brayton cycle for gas turbine engines, including its T-s and P-v diagrams.

Calculate the thermal efficiency and back work ratio for an ideal Brayton cycle.

Apply isentropic efficiencies to analyze the performance of real turbines and compressors in a cycle.