Questions
5–8 MCQs per paper
Difficulty
Medium
Importance
High yield for HPCL/NTPC
Overview
Engineering Mechanics serves as the foundation for all mechanical and civil engineering disciplines, dealing with the behavior of physical bodies under force systems. Mastering this is critical for PSU exams because it provides the base for strength of materials and machine design questions. The core objective is to achieve equilibrium analysis and understand motion dynamics through systematic vector representation.
Free Body Diagrams and Equilibrium
A Free Body Diagram (FBD) is the essential tool for isolating a body from its environment by representing all applied forces and reactions. Equilibrium requires the sum of all forces and moments acting on a rigid body to be zero in a static state.
- Sum of forces in X and Y directions: ΣFx = 0, ΣFy = 0
- Sum of moments about any point: ΣM = 0
- Lami's Theorem for three concurrent coplanar forces: P/sin(alpha) = Q/sin(beta) = R/sin(gamma)
- Use local axes for inclined planes to simplify force components
Friction
Friction is a resistive force that opposes relative motion between two contact surfaces. PSU exams frequently focus on block-on-inclined-plane problems and ladder friction, requiring identification of the limiting state.
- Frictional force F = μN, where μ is coefficient of friction
- Angle of friction: phi = tan⁻¹(μ)
- Angle of repose equals angle of friction for a sliding body
- Always define the direction of impending motion to assign force signs correctly
Dynamics and Newton's Laws
Dynamics deals with the relationship between motion and the forces that cause it. Newton's second law is the cornerstone for solving problems involving accelerating bodies, including constrained motion and pulley systems.
- Newton's Second Law: F = ma or F = m(d²s/dt²)
- Work-Energy Principle: Work done = Change in kinetic energy
- Impulse-Momentum equation: Fdt = mdv
- Conservation of linear momentum: m1v1 + m2v2 = constant
- Centrifugal force: Fc = mv²/r
Virtual Work
The principle of virtual work offers a powerful alternative to FBDs, especially for complex mechanism linkage analysis. It states that the total work done by all forces during a virtual displacement is zero for a system in equilibrium.
- Virtual work principle: Σ(F_i * delta_s_i) = 0
- Ideal for determining support reactions in trusses or frames
- Eliminates internal forces/reactions from the calculation if they do no work
- Crucial for finding equilibrium configurations of interconnected members
Formula Sheet
ΣFx = 0, ΣFy = 0, ΣM = 0
P/sin(α) = Q/sin(β) = R/sin(γ)
F_max = μ_s * N
v = u + at
s = ut + 0.5at²
v² = u² + 2as
W = F * d
KE = 0.5 * m * v²
PE = mgh
Momentum = mv
Exam Tip
Always verify the direction of the friction force relative to the impending direction of motion before writing your equilibrium equations.
Common Mistakes
- Forgetting to include all reactive forces in the FBD, especially for internal pins or hinges.
- Confusing the coefficient of static friction with kinetic friction in threshold-motion problems.
- Incorrectly resolving force components on inclined planes by swapping sine and cosine terms.
More Revision Notes
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