Twenty frequently asked questions about equilibrium and elasticity.
Q1: Why does a beam deflect more when we load it at the center than at the end?
A: Deflection is proportional to F L³. At the center, the effective distance is maximum, so deflection is greatest. At the end, the effective length is smaller.
Q2: Does Young's modulus change for a material?
A: Young's modulus is a material property and typically constant for a given material. However, it does change with temperature (e.g., cold steel is stiffer).
Q3: What's the difference between Young's modulus and shear modulus?
A: Young's modulus applies to tension or compression (length change). Shear modulus applies to shear (shape change). Shear modulus is typically smaller than Young's.
Q4: Is a stationary object always in equilibrium?
A: Yes! If an object is at rest and stays at rest, it satisfies equilibrium (ΣF = 0, Στ = 0). But if external conditions change, equilibrium can break.
Q5: What if two equal and opposite forces act along the same line of action?
A: They cancel completely. ΣF = 0 and Στ = 0. No net effect.
Q6: Can an object be in rotational equilibrium but not translational equilibrium?
A: No. For a rigid body: if Στ = 0 (rotational equilibrium), then by definition ΣF = 0 (translational equilibrium) for the object to remain at rest or move at constant velocity.
Q7: Why does a pliers make pulling a nail easier than pulling by hand?
A: A pliers is a lever. The effort arm (handle) is longer than the load arm (nail). Mechanical advantage is greater.
Q8: If a rope under tension breaks, does stress instantly become zero?
A: Yes! When the rope snaps, it's severed and can't bear load. Stress instantly becomes zero (or undefined). But kinetic energy remains and can cause injury.
Q9: Can the bulk modulus ever be negative?
A: No. Bulk modulus is always positive. Under pressure, volume decreases, not increases.
Q10: What's the difference between ductile and brittle fracture in terms of energy?
A: Ductile materials absorb more energy in the plastic region before fracture. Brittle materials absorb little energy and fail suddenly.
Q11: Why are building columns relatively wide?
A: Columns must:
- Support heavy loads (compressive stress)
- Resist side buckling
Width increases the second moment of area and improves bending resistance.
Q12: Is elasticity always reversible?
A: In the elastic region: Yes! Deformation is fully reversible.
In the plastic region: No! Deformation is permanent.
Q13: Why do tall buildings sway in strong wind?
A: Buildings experience wind torque and bend. Design allows controlled bending to absorb energy. The swaying represents the building's adaptive response.
Q14: Why is diamond (though very hard) brittle?
A: Diamond is very stiff (large Young's modulus) but brittle (no plastic region). Under sudden impact, it breaks without warning.
Q15: Where is shear stress greatest in a beam?
A: Shear stress is maximum at the center (farthest from neutral axis). It's zero at the surfaces.
Q16: If a beam is made of two different metals (steel and copper) welded together, what happens?
A: Each metal deforms differently (different Young's moduli). At the interface, there's high stress concentration. This can become a weak point.
Q17: Does temperature affect equilibrium?
A: Not directly. Equilibrium conditions (ΣF = 0, Στ = 0) are temperature-independent. But temperature causes thermal expansion, which can introduce stress.
Q18: If a ladder is very light, do the results change?
A: Yes! If the ladder's mass is negligible, its weight can be ignored. The torque equations become simpler.
Q19: What's the difference between static and kinetic friction in equilibrium problems?
A:
- Static: object is at rest; friction can be up to
μ_s × N. - Kinetic: object is moving; friction is constant
μ_k × N.
Equilibrium problems usually involve static friction.
Q20: Does Hooke's law (σ = Eε) apply to liquids?
A: No. Liquids have no shear resistance. Hooke's law applies only to elastic solids.
📚 Reference: Halliday Vol 1, Ch 12, Frequently Asked Questions. 🔗 Learn more: Sections 12.1–12.7 for detailed explanations of each answer.
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