SCE Engineering Sciences 4 — Questions and Answers
Question 1: What is the principle of virtual work?
- A system in equilibrium does zero virtual work for any virtual displacement (Correct answer)
- Work done equals kinetic energy change
- Potential energy is always minimized
- Virtual forces cause real displacements
Correct answer: A system in equilibrium does zero virtual work for any virtual displacement
The principle states that for a system in static equilibrium, the total virtual work done by all forces during any compatible virtual displacement is zero. It is powerful for solving indeterminate structures.
Question 2: Fourier's law of heat conduction states that heat flux is proportional to:
- The negative temperature gradient (Correct answer)
- The temperature
- The square of temperature
- The positive temperature gradient
Correct answer: The negative temperature gradient
Fourier's law: q = -k(dT/dx), where the negative sign indicates heat flows from high to low temperature. The thermal conductivity k depends on the material.
Question 3: The natural frequency of a single degree of freedom system is:
- ωn = √(k/m) (Correct answer)
- ωn = k/m
- ωn = m/k
- ωn = √(m/k)
Correct answer: ωn = √(k/m)
The natural frequency ωn = √(k/m) where k is stiffness and m is mass. This determines the frequency at which the system oscillates freely and is critical for avoiding resonance.
Question 4: In materials science, what is creep?
- Time-dependent deformation under constant stress at elevated temperature (Correct answer)
- Sudden fracture without warning
- Elastic recovery after unloading
- Cyclic loading fatigue
Correct answer: Time-dependent deformation under constant stress at elevated temperature
Creep is the slow, progressive plastic deformation of a material under constant stress over time, especially at temperatures above ~0.4 of the melting point. This is particularly relevant in Saudi Arabia's hot climate.
Question 5: The drag coefficient of a sphere in laminar flow is given by Stokes' law as:
- CD = 24/Re (Correct answer)
- CD = 0.44
- CD = 12/Re
- CD = 48/Re
Correct answer: CD = 24/Re
For very low Reynolds numbers (Re < 1), Stokes' law gives CD = 24/Re for a sphere. This applies to slow-moving particles, sediment settling, and dust particle analysis.
Question 6: What is the Stefan-Boltzmann law?
- The total radiant heat energy emitted is proportional to the fourth power of absolute temperature (Correct answer)
- Heat conduction is proportional to temperature gradient
- Convection heat transfer depends on fluid velocity
- Radiation only occurs in vacuum
Correct answer: The total radiant heat energy emitted is proportional to the fourth power of absolute temperature
The Stefan-Boltzmann law states q = εσT⁴, where σ = 5.67×10⁻⁸ W/m²K⁴. This is critical for solar radiation calculations in Saudi Arabia's intense desert environment.
SCE Engineering Sciences 4
What is the principle of virtual work?