Lesson 2.1: Engineering Mechanics (Statics, Dynamics, Friction, Work & Energy)

Engineering Mechanics is the foundation of mechanical engineering. GATE and PSU exams frequently test statics, dynamics, friction, work-energy principles, and their applications in machines, structures, and mechanical systems.

🔹 1. Statics

• Definition: Study of bodies at rest or in equilibrium under applied forces.

• Equations of Equilibrium:

  • For 2D: ∑Fx=0,∑Fy=0,∑M=0\sum F_x = 0, \sum F_y = 0, \sum M = 0∑Fx​=0,∑Fy​=0,∑M=0

  • For 3D: ∑Fx=0,∑Fy=0,∑Fz=0,∑Mx=0,∑My=0,∑Mz=0\sum F_x = 0, \sum F_y = 0, \sum F_z = 0, \sum M_x = 0, \sum M_y = 0, \sum M_z = 0∑Fx​=0,∑Fy​=0,∑Fz​=0,∑Mx​=0,∑My​=0,∑Mz​=0

Applications:

• Trusses, beams, frames

• Static load analysis in structures

Example:
A 10 kN force acts at 30° on a pin joint. Find horizontal & vertical components:

Fx=10cos⁡30∘=8.66 kN,Fy=10sin⁡30∘=5 kNF_x = 10 \cos 30^\circ = 8.66 \text{ kN}, \quad F_y = 10 \sin 30^\circ = 5 \text{ kN}Fx​=10cos30∘=8.66 kN,Fy​=10sin30∘=5 kN

🔹 2. Dynamics

• Definition: Study of motion of bodies under forces.

• Equations of Motion (Newton’s 2nd Law):

F⃗=ma⃗\vec{F} = m \vec{a}F=ma

• Kinematics: Study of motion without considering forces.

• Kinetics: Study of motion with forces.

Applications:

• Mechanisms, machine elements

• Vehicle dynamics, robotic arms

Example:
A 5 kg block accelerates at 2 m/s². Force required: $F=ma=5\ast 2=10\text{ N}$

🔹 3. Friction

• Definition: Resistance to relative motion between contacting surfaces.

• Laws of Friction:

  1. Friction acts opposite to motion.

  2. Maximum static friction: Fmax=μsNF_{\text{max}} = \mu_s NFmax​=μs​N

  3. Kinetic friction: Fk=μkNF_k = \mu_k NFk​=μk​N

• Inclined Plane:
  $\text{Minimum force to move block}=W\sin \theta +\mu W\cos \theta$

Applications:

• Clutches, brakes, bolts, bearings

🔹 4. Work & Energy Principles

• Work Done by Force:

W=F⃗⋅d⃗=Fdcos⁡θW = \vec{F} \cdot \vec{d} = F d \cos \thetaW=F⋅d=Fdcosθ

• Kinetic Energy (KE):

KE=12mv2KE = \frac{1}{2} m v^2KE=21​mv2

• Potential Energy (PE):

$$PE=mgh$$

• Work-Energy Principle:

$$\text{Work done by all forces}=\Delta KE$$

• Conservation of Energy:

KE1+PE1+Wnon-conservative=KE2+PE2KE_1 + PE_1 + W_{\text{non-conservative}} = KE_2 + PE_2KE1​+PE1​+Wnon-conservative​=KE2​+PE2​

Applications:

• Mechanisms, vibrating systems, energy methods in structures

🔹 5. Solved Examples (PYQ Style)

Example 1 (GATE ME 2018):
A block of 10 kg rests on horizontal surface with μ=0.3. Find minimum horizontal force to move it.
👉 Solution: $F=\mu mg=0.3\ast 10\ast 9.81=29.43\text{ N}$

Example 2 (PSU Exam):
A 5 kg block is pushed with 20 N. Compute acceleration if μ=0.2.
👉 Solution: Friction = 0.259.81 = 9.81 N, Net F = 20-9.81 = 10.19 N, a = F/m = 10.19/5 ≈ 2.04 m/s²

🔹 6. Practice Exercises

1. A 50 N force acts at 45° on a block. Find horizontal & vertical components.

2. Compute work done by a 20 N force moving 3 m along the force direction.

3. Block of 10 kg on incline 30°, μ=0.25. Minimum force to move uphill?

4. A 2 kg mass moves from height 5 m to 2 m. Find change in potential & kinetic energy.

🔹 7. Summary

• Statics: Equilibrium of forces and moments.

• Dynamics: Motion under forces, Newton’s laws.

• Friction: Resistance to motion, static & kinetic friction.

• Work & Energy: Work done, KE, PE, work-energy principle.

• Applications: Structures, machines, vehicles, mechanical systems.