Mechanical Engineering: Fundamentals

What is the primary purpose of a Free Body Diagram (FBD) in statics?

A Free Body Diagram is used to isolate a single body or subsystem from its surroundings and represent all external forces and moments acting upon it to solve for unknowns.

State the three scalar equations of equilibrium for a 2D rigid body.

The sum of forces in the x-direction equals zero (ΣFx = 0), the sum of forces in the y-direction equals zero (ΣFy = 0), and the sum of moments about any point equals zero (ΣM = 0).

Define engineering stress and provide its standard SI unit.

Engineering stress (σ) is the applied load (F) divided by the original cross-sectional area (A₀), expressed as σ = F/A₀. Its SI unit is the Pascal (Pa) or N/m².

How is Young's Modulus (E) determined from a stress-strain curve?

Young's Modulus is the slope of the linear-elastic region of the stress-strain curve, representing the material's stiffness (E = σ/ε).

What is the physical significance of the yield strength on a stress-strain diagram?

Yield strength is the stress level at which a material transitions from elastic deformation (reversible) to plastic deformation (permanent).

Define ductility and name one common way it is measured.

Ductility is the ability of a material to undergo significant plastic deformation before fracture; it is commonly measured by percent elongation or percent reduction in area.

Why is the Carnot cycle considered a theoretical limit for heat engine efficiency?

The Carnot cycle consists entirely of reversible processes (two isothermal and two adiabatic), and the Second Law of Thermodynamics states no engine can be more efficient than a reversible one between the same two reservoirs.

Identify the four main components of an ideal Rankine cycle.

The four components are the pump (isentropic compression), the boiler (constant pressure heat addition), the turbine (isentropic expansion), and the condenser (constant pressure heat rejection).

In the context of an internal combustion engine, what are the four strokes of the ideal Otto cycle?

The strokes are Intake, Isentropic Compression, Power/Expansion (Isentropic), and Exhaust.

State Newton's Law of Cooling and define the variable 'h'.

The law is Q = hA(Ts - T∞), where 'h' is the convective heat transfer coefficient, representing the rate of heat transfer between a surface and a moving fluid.