Mechanics
Subject: General Science — Physics | Topic: Mechanics Exam: AP Group 2 (APPSC) | Sources: NCERT Class IX-X, Lucent's GS
Introduction
Mechanics is the branch of physics dealing with motion, forces, and energy. For APPSC Group 2, expect 2-3 questions — typically on Newton's Laws, equations of motion, and simple machines. The formulas in this chapter are among the most directly testable in the entire science section.
Newton's Laws of Motion
Newton's three laws form the foundation of classical mechanics. Every APPSC paper has at least one question traceable to these laws.
First Law (Law of Inertia): A body at rest stays at rest, and a body in uniform motion continues in a straight line, unless acted upon by an external unbalanced force.
- Inertia is directly proportional to mass — heavier objects resist change more.
- Example: Passengers jerk forward when a bus suddenly stops.
Second Law: Force = Mass × Acceleration (F = ma). The rate of change of momentum is proportional to the applied force and occurs in its direction.
- SI unit of force: Newton (N). 1 N = 1 kg·m/s².
Third Law: To every action, there is an equal and opposite reaction. Action and reaction act on different bodies.
- Example: Rocket propulsion — exhaust gases push backward, rocket moves forward.
Momentum and Impulse
| Quantity | Formula | SI Unit |
|---|---|---|
| Momentum (p) | p = m × v | kg·m/s |
| Impulse | F × t = Δp | N·s |
Law of Conservation of Momentum: In an isolated system, total momentum before collision = total momentum after collision.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Gravitation
Newton's Law of Universal Gravitation:
F = G(m₁ × m₂) / r²
where G = 6.674 × 10⁻¹¹ N·m²/kg² (Universal Gravitational Constant)
| Fact | Value |
|---|---|
| Acceleration due to gravity (g) | 9.8 m/s² (≈10 m/s² for calculations) |
| Weight formula | W = m × g |
| Weight at Earth's centre | Zero |
| Free fall | All objects fall at same rate regardless of mass (in vacuum) |
Weight varies with location; mass is constant. Weight decreases with altitude and depth.
Kepler's Laws of Planetary Motion
| Law | Statement |
|---|---|
| First (Orbits) | Planets move in elliptical orbits with the Sun at one focus |
| Second (Areas) | A line joining a planet and the Sun sweeps equal areas in equal time intervals |
| Third (Periods) | T² ∝ a³ (square of period proportional to cube of semi-major axis) |
Work, Energy, and Power
| Quantity | Formula | SI Unit |
|---|---|---|
| Work | W = F × d × cos(θ) | Joule (J) |
| Kinetic Energy | KE = ½mv² | J |
| Potential Energy | PE = mgh | J |
| Power | P = W / t | Watt (W) |
Work-Energy Theorem: Net work done = change in kinetic energy.
Law of Conservation of Energy: Energy can neither be created nor destroyed, only transformed. Total energy in an isolated system remains constant.
1 Horsepower (HP) = 746 W.
Work is zero when force is perpendicular to displacement (e.g., carrying a bag horizontally — gravity acts downward).
Equations of Motion (Uniformly Accelerated)
| Equation | Formula |
|---|---|
| First | v = u + at |
| Second | s = ut + ½at² |
| Third | v² = u² + 2as |
Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.
Friction
- Friction opposes relative motion between two surfaces in contact.
- Order: Static friction > Sliding friction > Rolling friction.
- Friction depends on the nature of surfaces and normal force, NOT on area of contact.
- Friction is essential for walking, braking, and holding objects.
Simple Machines
Six types: Lever, Pulley, Inclined Plane, Wheel and Axle, Wedge, Screw.
Mechanical Advantage (MA) = Load / Effort. Machines make work easier, not less.
Lever Classes
| Class | Position of Fulcrum | Examples |
|---|---|---|
| Class 1 | Between load and effort | Scissors, see-saw |
| Class 2 | Load between fulcrum and effort | Wheelbarrow, nutcracker |
| Class 3 | Effort between fulcrum and load | Tongs, fishing rod |
Pulley: MA = number of supporting rope sections. Single fixed pulley has MA = 1 but changes direction.
Inclined Plane: F = W sin(θ). Reduces force needed but increases distance.
Pressure and Buoyancy
| Concept | Formula/Principle |
|---|---|
| Pressure | P = F / A. SI unit: Pascal (Pa). 1 atm = 101,325 Pa |
| Pascal's Law | Pressure on enclosed fluid transmitted equally in all directions (hydraulic machines) |
| Archimedes' Principle | Buoyant force = weight of fluid displaced |
| Floating condition | Object density < fluid density |
Centripetal Force
Centripetal force keeps objects moving in a circle, directed toward the centre.
F = mv² / r
Likely Exam Questions
-
Newton's First Law is also called the Law of: Ans: Inertia
-
The SI unit of momentum is: Ans: kg·m/s
-
The value of Universal Gravitational Constant (G) is: Ans: 6.674 × 10⁻¹¹ N·m²/kg²
-
According to Kepler's Third Law, T² is proportional to: Ans: a³ (cube of semi-major axis)
-
1 Horsepower equals: Ans: 746 Watts
-
Which type of friction is the least? Ans: Rolling friction
-
In a Class 2 lever, the ___ is between the fulcrum and effort: Ans: Load
-
Pascal's Law is the basis for: Ans: Hydraulic machines (hydraulic press, brakes)
-
An object floats when its density is: Ans: Less than the fluid density
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The equation v² = u² + 2as is the ___ equation of motion: Ans: Third