Engineering Mechanics is the backbone of technical problem-solving for all branches of engineering in BCECE LE. With 50 questions carrying 200 marks, a solid conceptual grasp of Newtonian statics, friction, and dynamics guarantees a competitive edge over applicants relying on rote memorization.
1. Force Systems & Conditions of Equilibrium
Concurrent Coplanar Forces
Forces whose lines of action pass through a single common point in the same plane. For complete static equilibrium:
$$\sum F_x = 0 \quad \text{and} \quad \sum F_y = 0$$Lami's Theorem
If three concurrent, coplanar forces acting at a point keep a body in static equilibrium, each force is directly proportional to the sine of the angle between the other two forces:
$$\frac{P}{\sin(\alpha)} = \frac{Q}{\sin(\beta)} = \frac{R}{\sin(\gamma)}$$2. Free Body Diagram (FBD) — Step-by-Step Drawing Rules
- Isolate the body from all contacting surfaces, supports, ropes, or adjacent bodies.
- Represent Self-Weight ($W = mg$): Always acts vertically downward through the centre of gravity.
- Normal Reaction ($N$ or $R$): Always acts perpendicular (normal) to the surface of contact, directed toward the isolated body.
- Tension in Cable/String ($T$): Always pulls away from the body along the line of the string.
- Frictional Force ($f$): Always acts parallel to the contacting surface and strictly opposes the tendency of relative motion.
3. Laws of Dry Friction (Coulomb's Friction)
- Limiting Friction ($F_s$): The maximum frictional force developed when a body is on the verge of impending motion:
$$F_s = \mu_s \cdot N$$ - Kinetic Friction ($F_k$): The friction operating during steady relative sliding motion:
$$F_k = \mu_k \cdot N \quad (\text{where } \mu_k < \mu_s)$$ - Angle of Friction ($\phi$): $\tan(\phi) = \mu_s \implies \phi = \tan^{-1}(\mu_s)$
- Angle of Repose ($\theta$): $\theta = \phi = \tan^{-1}(\mu_s)$
4. Centroid & Moment of Inertia Formulas
| Shape / Section | Area ($A$) | Centroid ($\bar{y}$) | Moment of Inertia ($I_{xx}$) |
|---|---|---|---|
| Rectangle ($b \times d$) | $b \cdot d$ | $d / 2$ | $\frac{b d^3}{12}$ (about centroid) |
| Triangle (Base $b$, Height $h$) | $\frac{1}{2} b h$ | $h / 3$ (from base) | $\frac{b h^3}{36}$ (about centroid) |
| Circle (Diameter $d$) | $\frac{\pi d^2}{4}$ | $r$ | $\frac{\pi d^4}{64}$ |