Part II — Engineering Mechanics & Strength of Materials

Chapter 2: Force Systems and Mechanics of Materials

2.1 Basic Concepts of Engineering Mechanics

Force is a vector quantity (having both magnitude and direction) that changes or tends to change the state of rest or motion of a body. Newton's Laws of Motion form the foundation of mechanics: the First Law (a body remains at rest or in uniform motion unless acted upon by an external force — the law of inertia), the Second Law (F = ma, force equals mass times acceleration), and the Third Law (for every action, there is an equal and opposite reaction). A system of forces can be resolved into components, and multiple forces can be combined using the parallelogram law or triangle law of forces to determine a resultant.

2.2 Friction

Friction is the resistive force that opposes relative motion (or tendency of motion) between two surfaces in contact. Static friction acts on a body at rest and prevents motion up to a maximum limiting value; kinetic (dynamic) friction acts on a body already in relative motion, and is generally slightly less than the maximum static friction. The coefficient of friction (μ) is the ratio of limiting friction force to the normal reaction force between surfaces (μ = F/N).

2.3 Stress and Strain

Stress is internal resisting force per unit area (σ = P/A); strain is the ratio of deformation to original dimension (ε = δL/L). Hooke's Law states that, within the elastic limit, stress is directly proportional to strain: σ = Eε, where E is the Modulus of Elasticity (Young's Modulus). Steel has a Modulus of Elasticity of approximately 200 GPa (2×10⁵ N/mm²). The Poisson's Ratio (ν) is the ratio of lateral strain to longitudinal strain for a material under axial load, typically ranging from about 0.25 to 0.35 for common metals.

2.4 Types of Stress

Tensile stress (from a pulling/stretching force), compressive stress (from a pushing/squeezing force), and shear stress (from forces causing layers to slide relative to each other) are the three fundamental stress types. Factor of Safety (FoS) is the ratio of a material's ultimate (or yield) strength to the allowable/working stress used in design, providing a safety margin against uncertainties in loading, material properties, and workmanship.

2.5 Practice Set — Mechanics & Strength of Materials (16 MCQs)

1. Newton's First Law of Motion is also known as the law of:
   (a) Action-reaction (b) Inertia (c) Conservation of energy (d) Gravitation
2. Newton's Second Law of Motion is expressed as:
   (a) F = ma (b) F = m/a (c) F = m + a (d) F = a/m
3. Newton's Third Law states that for every action, there is:
   (a) No reaction (b) An equal and opposite reaction (c) A smaller, unequal reaction (d) A delayed reaction only
4. Static friction, compared to kinetic friction, is generally:
   (a) Always less than kinetic friction (b) Slightly greater than (or equal to, at the limiting point of) kinetic friction (c) Always exactly zero (d) Unrelated to kinetic friction
5. The coefficient of friction (μ) is defined as:
   (a) The ratio of limiting friction force to normal reaction (b) The ratio of normal reaction to friction force (c) The product of mass and acceleration (d) The ratio of stress to strain
6. Stress is defined as:
   (a) Force per unit volume (b) Force per unit area (c) Deformation per unit length (d) Energy per unit area
7. Hooke's Law states that, within the elastic limit:
   (a) Stress is inversely proportional to strain (b) Stress is directly proportional to strain (c) Stress is independent of strain (d) Strain is always zero
8. The Modulus of Elasticity of steel is approximately:
   (a) 2×10⁵ N/mm² (200 GPa) (b) 2×10³ N/mm² (c) 2×10⁷ N/mm² (d) 25–35 GPa
9. Poisson's Ratio is defined as the ratio of:
   (a) Longitudinal strain to lateral strain (b) Lateral strain to longitudinal strain (c) Stress to strain directly (d) Force to area
10. Poisson's Ratio for common metals typically ranges between:
    (a) 0.05–0.10 (b) 0.25–0.35 (c) 0.50–0.75 (d) 1.0–1.5
11. Tensile stress results from a force that:
    (a) Pulls/stretches a material (b) Pushes/squeezes a material (c) Causes layers to slide past each other (d) Causes rotation only
12. Shear stress results from forces that:
    (a) Pull a material apart uniformly (b) Cause layers to slide relative to each other (c) Compress a material uniformly (d) Have no effect on material layers
13. Factor of Safety (FoS) is defined as the ratio of:
    (a) Working stress to ultimate/yield strength (b) Ultimate/yield strength to allowable/working stress (c) Strain to stress (d) Force to velocity
14. A higher Factor of Safety generally indicates:
    (a) A smaller safety margin (b) A larger safety margin in design (c) No relation to safety margin (d) An error in calculation
15. The parallelogram law of forces is used to:
    (a) Determine the resultant of two forces acting at a point (b) Calculate stress directly (c) Determine the coefficient of friction (d) Calculate Poisson's ratio
16. Compressive stress results from a force that:
    (a) Pulls/stretches a material (b) Pushes/squeezes a material (c) Causes rotation only (d) Has no effect on the material

Answer Key

1.(b)

2.(a)

3.(b)

4.(b)

5.(a)

6.(b)

7.(b)

8.(a)

9.(b)

10.(b)

11.(a)

12.(b)

13.(b)

14.(b)

15.(a) 16.(b)