Applied Mechanics Made Easy
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color: white; border-radius: 20px; padding: 3px 12px; font-size: 0.8em; font-weight: 700; margin-left: 8px; vertical-align: middle; }⚙️ Engineering Mechanics
📚 Chapter 1 — Basics of Mechanics | Diploma Level | Complete Notes
🎯 Zero to Hero | Easy Language | Real Life Examples | Exam Ready
🧲 Forces | 🔺 Vectors | ⚖️ Equilibrium | 📐 Moments
🗺️ What You Will Learn in This Chapter
📌 What is Mechanics?
📌 Units & Measurements
📌 Scalar vs Vector
📌 Types of Forces
📌 Resolution of Forces
📌 Resultant of Forces
📌 Lami’s Theorem
📌 Moment of Force
📌 Couple
📌 Equilibrium
📌 Free Body Diagram
1.1 🤔 What is Mechanics?
🌍
Mechanics is the branch of science that deals with the effect of forces on bodies — whether the body moves or stays still.
Think of it this way: Every time you push a door, lift a bag, sit on a chair, or throw a ball — mechanics is at work!
🌳 Family Tree of Mechanics
⚙️ MECHANICS
|
┌───────────────┴───────────────┐
│ │
📐 STATICS 🏃 DYNAMICS
(Body at REST) (Body in MOTION)
│
┌───────────┴───────────┐
│ │
🔄 KINEMATICS ⚡ KINETICS
(study of motion) (motion + forces)
🧠 Simple Words:
- 📐 Statics = Body is NOT moving. Forces are balanced. Example: A book on a table.
- 🏃 Dynamics = Body IS moving. Example: A car running on a road.
- 🔄 Kinematics = HOW body moves (distance, speed, acceleration) — no force discussion.
- ⚡ Kinetics = WHY body moves (due to which force).
Remember: “Statics = Still” — Both start with S! If it’s still, it’s statics. If it’s moving, it’s dynamics!
1.2 📏 Units and Measurements
We use the SI System (International System of Units) in mechanics.
| Quantity | Symbol | SI Unit | Example |
|---|---|---|---|
| Length | L | metre (m) | Length of a table = 1.5 m |
| Mass | m | kilogram (kg) | Your weight bag = 5 kg |
| Time | t | second (s) | Time to run 100m = 15 s |
| Force | F | Newton (N) | Weight of 1 kg = ~10 N |
| Angle | θ | degree (°) or radian | Right angle = 90° |
1 kN = 1000 N and 1 MN = 10,00,000 N. In exam problems, always convert kN to N before solving!
🤔 What is Force?
Force is a push or pull that changes (or tries to change) the state of a body.
- 🏋️ Lifting a dumbbell = Force upward (you apply force against gravity)
- ⚽ Kicking a ball = Force that makes ball move
- 🌬️ Wind hitting a wall = Force on wall
Force is measured in Newtons (N).
1.3 🏹 Scalar vs Vector Quantities
| Feature | 📦 Scalar | 🏹 Vector |
|---|---|---|
| Definition | Only has Magnitude (size) | Has Magnitude + Direction |
| Example | Mass, Temperature, Time, Speed | Force, Velocity, Displacement |
| Representation | Just a number (e.g., 5 kg) | Number + direction (e.g., 5 N at 30°) |
| Drawn as? | — | Arrow ➡️ |
🍕 Real Life Example:
Imagine you order pizza 🍕
Imagine you order pizza 🍕
- Scalar: “The pizza is 500 grams” — Only size, no direction.
- Vector: “The pizza shop is 2 km to the North” — Size + Direction!
“Vector has a Velocity and a Variety (it tells you direction too!)”
1.4 🧘 Understanding X and Y Axes (with Yoga!)
🧘♀️ STAND UP AND LEARN!
Imagine you are standing straight in Tadasana (Mountain Pose)
🧘♀️
⬆️ Y-AXIS (Vertical)
Your BODY is Y-Axis — standing tall, pointing UP.
Think: Height, Vertical forces (like gravity pulling you DOWN, or you jumping UP)
Your BODY is Y-Axis — standing tall, pointing UP.
Think: Height, Vertical forces (like gravity pulling you DOWN, or you jumping UP)
➡️ X-AXIS (Horizontal)
Your ARMS spread horizontal = X-Axis — pointing LEFT and RIGHT.
Think: Horizontal forces, side push, wind from side
Your ARMS spread horizontal = X-Axis — pointing LEFT and RIGHT.
Think: Horizontal forces, side push, wind from side
🙏 Now do Virabhadrasana (Warrior Pose):
You lean at an angle θ (theta) — that’s how inclined forces work!
The angle between your body and the vertical = angle of force!
You lean at an angle θ (theta) — that’s how inclined forces work!
The angle between your body and the vertical = angle of force!
⬆ Y-axis (Vertical)
|
| 🎯 ← Force at angle θ
| /
| / θ
|/_______ ➡ X-axis (Horizontal)
O (Origin)
The force can be broken into:
↕️ Vertical Component = F × sin θ
↔️ Horizontal Component = F × cos θ
📐 Origin (O): The meeting point of X and Y axes is called ORIGIN. In your yoga pose, it’s your belly button / center of body! 🎯
1.5 💪 Types of Forces
A) Based on Area of Application
| Type | Explanation | Real Example |
|---|---|---|
| Point Force / Concentrated Force 📍 | Force acting at a single point | A nail hit by hammer |
| Distributed Force 📊 | Force spread over an area or length | Snow on a roof, books on a shelf |
| Body Force 🌍 | Force that acts on every particle | Gravity (Weight) |
B) Based on Direction
| Type | Direction | Example |
|---|---|---|
| Tensile Force 🔗 | Pulling away (stretching) | Rope being pulled from both ends |
| Compressive Force 🤜🤛 | Pushing inward (squeezing) | Column carrying a load above it |
| Shear Force ✂️ | Forces in opposite directions, side by side | Cutting paper with scissors |
🧸 Imagine a Rubber Band:
- 🔗 You stretch it — Tensile Force
- 🤜 You compress it between fingers — Compressive Force
- ✂️ You slide your fingers across — Shear Force
C) System of Forces (VERY IMPORTANT ⭐)
| System | Meaning | Diagram Hint |
|---|---|---|
| Collinear Forces | All forces act on SAME LINE | ← ●→ (along one line) |
| Concurrent Forces | All forces meet at ONE POINT | Like spokes of a wheel meeting at center |
| Coplanar Forces | All forces in the SAME PLANE | Forces drawn on same paper/flat surface |
| Parallel Forces | Forces are PARALLEL to each other | Two people lifting a table from both ends |
| Non-Concurrent, Non-Parallel | Forces don’t meet and aren’t parallel | General loading on a structure |
Remember Concurrent vs Collinear:
🎯 Con-current = Meeting at a POINT (think: currency comes to ONE wallet)
📏 Co-linear = On same LINE (think: linear = line)
🎯 Con-current = Meeting at a POINT (think: currency comes to ONE wallet)
📏 Co-linear = On same LINE (think: linear = line)
1.6 🔀 Resolution of Forces
📖 Definition: Breaking a single force into two components — one along X-axis and one along Y-axis — is called Resolution of a Force.
🤸 Yoga Example — Warrior Pose (Virabhadrasana)!
You are pushing against a wall at angle θ with force F.
🤸♂️
Your push has two effects:
- Horizontal effect = You push the wall sideways → This is Fx = F cos θ
- Vertical effect = You push the wall upward/downward → This is Fy = F sin θ
Fx = F × cos θ (Horizontal Component)
Fy = F × sin θ (Vertical Component)
F = √(Fx² + Fy²) (Resultant Magnitude)
tan θ = Fy / Fx (Direction of Resultant)
⬆ Y
| /← F (force at angle θ)
Fy ↕| /
| / θ
|/________➡ X
Fx
F at angle θ splits into:
Fx = F cos θ (horizontal)
Fy = F sin θ (vertical)
The most common exam question: “Find horizontal and vertical components of a force F at angle θ with horizontal.” Just apply Fx = F cosθ and Fy = F sinθ!
SOLVED EXAMPLE 1
A force of 100 N acts at 30° to the horizontal. Find its horizontal and vertical components.
Given: F = 100 N, θ = 30°
Horizontal Component:
Fx = F cos θ = 100 × cos 30° = 100 × 0.866 = 86.6 N
Fx = F cos θ = 100 × cos 30° = 100 × 0.866 = 86.6 N
Vertical Component:
Fy = F sin θ = 100 × sin 30° = 100 × 0.5 = 50 N
Fy = F sin θ = 100 × sin 30° = 100 × 0.5 = 50 N
Check: √(86.6² + 50²) = √(7499.56 + 2500) = √9999.56 ≈ 100 N ✅
🧮 SOH CAH TOA Trick:
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
In forces: Opposite = Fy, Adjacent = Fx, Hypotenuse = F
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
In forces: Opposite = Fy, Adjacent = Fx, Hypotenuse = F
1.7 ➕ Resultant of Forces
📖 Definition: A single force that produces the same effect as all the given forces together is called the Resultant Force.
🛒 Real Life Example — Supermarket Trolley!
You and your friend both push a shopping trolley 🛒:
- You push with 30 N to the East
- Your friend pushes with 40 N to the North
The trolley doesn’t go East OR North alone — it goes in a diagonal direction. That diagonal combined force is the RESULTANT!
Resultant = √(30² + 40²) = √(900 + 1600) = √2500 = 50 N
Method 1: Analytical Method (Most Used in Exams)
Resolve all forces into X-components (ΣFx)
Resolve all forces into Y-components (ΣFy)
Find Resultant: R = √((ΣFx)² + (ΣFy)²)
Find angle: θ = tan⁻¹(ΣFy / ΣFx)
R = √(ΣFx² + ΣFy²)
θ = tan⁻¹ (ΣFy / ΣFx)
Method 2: Parallelogram Law
📖 Law: If two forces acting at a point are represented by two adjacent sides of a parallelogram, then their resultant is represented by the diagonal of that parallelogram.
R = √(P² + Q² + 2PQ cos θ)
When θ = 0° (forces in SAME direction): R = P + Q (Maximum resultant) 🔼
When θ = 180° (forces OPPOSITE): R = |P – Q| (Minimum resultant) 🔽
When θ = 90° (forces at RIGHT ANGLE): R = √(P² + Q²)
When θ = 180° (forces OPPOSITE): R = |P – Q| (Minimum resultant) 🔽
When θ = 90° (forces at RIGHT ANGLE): R = √(P² + Q²)
SOLVED EXAMPLE 2
Two forces of 60 N and 80 N act at a point at 90° to each other. Find the resultant.
P = 60 N, Q = 80 N, θ = 90°
R = √(P² + Q²) = √(60² + 80²) = √(3600 + 6400) = √10000 = 100 N
Direction: tan α = 80/60 = 1.333 → α = 53.13° with 60 N force
Method 3: Triangle Law / Polygon Law
Triangle Law: If two forces are represented by two sides of a triangle taken in ORDER, then the third side (closing side) in REVERSE order represents the resultant.
B
/|
Q / |
/ |
/ | R (Resultant — closing side, opposite direction)
/ |
A_____C
P
Forces P and Q → Resultant R = closing side from A to C
Triangle Law Trick: “Draw forces TIP to TAIL → Join START to END = Resultant!” 🔺
1.8 🔺 Lami’s Theorem Important
📖 Statement: When THREE CONCURRENT FORCES are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
F1 / sin α = F2 / sin β = F3 / sin γ
Where α, β, γ are angles opposite to forces F1, F2, F3 respectively.
🎪 Real Life: 3-Rope Circus Trick!
Imagine a trapeze artist 🎪 hanging from two ropes attached to the ceiling, with gravity pulling them down:
- Rope 1 has tension T1 (going up-left)
- Rope 2 has tension T2 (going up-right)
- Weight W pulls straight down
These 3 concurrent forces at the artist’s hands are in equilibrium → Apply Lami’s Theorem! ✅
Lami’s Theorem is ONLY for exactly 3 concurrent forces in equilibrium. Don’t use it for 4+ forces!
SOLVED EXAMPLE 3 — Lami’s Theorem
Three concurrent forces are in equilibrium. F1 = 100 N, angle opposite to F1 = 120°, angle opposite to F2 = 150°. Find F2.
Using Lami’s Theorem: F1/sin α = F2/sin β
100/sin 120° = F2/sin 150°
100/0.866 = F2/0.5
F2 = (100 × 0.5) / 0.866 = 57.73 N
1.9 🌀 Moment of a Force Important
📖 Definition: Moment of a force about a point is the turning effect of that force about the point.
Moment = Force × Perpendicular Distance from the point to the line of action of force.
Moment = Force × Perpendicular Distance from the point to the line of action of force.
M = F × d
Unit: N·m (Newton-metre)
🔑 Real Life: Opening a Door!
Have you noticed that door handles are placed far from the hinge? 🚪
- Hinge = Point about which door rotates (pivot)
- Handle = Where you apply force
- Distance from hinge to handle = d
Moment = Force × d
Larger ‘d’ → Easier to open the door → Less effort needed!
That’s why it’s HARD to open a door by pushing near the hinge! 😅
🔧 Another Example: Spanner/Wrench
🔧
Using a long spanner = More moment = Nut turns easily.
Short spanner = Less moment = More effort needed.
That’s why mechanics always use LONG spanners!
Types of Moments:
| Type | Direction | Sign | Example |
|---|---|---|---|
| Clockwise Moment (CW) | Like clock hands 🕐 | Negative (−) | Tightening a screw |
| Anti-Clockwise Moment (ACW) | Opposite to clock | Positive (+) | Loosening a screw |
Varignon’s Theorem: “Moment of Resultant = Sum of Moments of Components”
So you can split a force, find moments of each part, and add them! Much easier! ✅
So you can split a force, find moments of each part, and add them! Much easier! ✅
1.10 💑 Couple
📖 Definition: Two equal, parallel, opposite forces acting on a body (but NOT on same line) form a Couple. A couple only produces rotation — no translation!
🚗 Real Life: Steering Wheel!
🎡
When you turn a steering wheel, you push one side UP and the other side DOWN with EQUAL force.
This is a COUPLE — it only rotates the wheel, it doesn’t move the entire car!
Same with turning a tap 🚿, or opening a bottle cap 🍾.
Moment of Couple (M) = F × d
Where d = perpendicular distance between the two forces (arm of couple)
Key Property: The moment of a couple is the same about any point — it doesn’t matter where you calculate it from!
1.11 ⚖️ Equilibrium Most Important
📖 Definition: A body is said to be in equilibrium when the net effect of all forces and moments on it is ZERO — it neither moves (translates) nor rotates.
Conditions of Equilibrium:
Condition 1: ΣFx = 0 (Sum of horizontal forces = Zero)
Condition 2: ΣFy = 0 (Sum of vertical forces = Zero)
Condition 3: ΣM = 0 (Sum of all moments = Zero)
🛺 Real Life: Auto-Rickshaw Parked on Road!
🛺
- Weight of rickshaw acts downward
- Reaction from road acts upward (R)
- W = R → ΣFy = 0 ✅
- No horizontal forces (parked on flat road) → ΣFx = 0 ✅
- No rotation → ΣM = 0 ✅
Result: Auto is in equilibrium!
Types of Equilibrium:
| Type | Meaning | Example |
|---|---|---|
| Stable Equilibrium ✅ | Returns to original position after disturbance | Rocking chair comes back to rest, Ball in a bowl 🥣 |
| Unstable Equilibrium ⚠️ | Moves further away after disturbance | Pencil balanced on its tip ✏️ |
| Neutral Equilibrium ➡️ | Stays in new position — neither returns nor moves further | Ball on flat surface ⚽ |
Memorize: S-U-N = Stable, Unstable, Neutral 🌞
Stable = Safe (comes back)
Unstable = Unsafe (falls further)
Neutral = Neutral (stays wherever you put it)
Stable = Safe (comes back)
Unstable = Unsafe (falls further)
Neutral = Neutral (stays wherever you put it)
1.12 📊 Free Body Diagram (FBD)
📖 Definition: A diagram showing a body isolated from its surroundings, with all forces acting ON it clearly shown as arrows, is called a Free Body Diagram (FBD).
🎒 Example: Your School Bag on a Table!
Actual situation: Bag is on a table, gravity pulls it down, table supports it up.
FBD of bag:
↑ N (Normal Reaction from Table)
|
_____|_____
| BAG 🎒 |
|_________|
|
↓ W (Weight of Bag = mg)
Since bag is at rest: N = W
ΣFy = N – W = 0 ✅
Steps to Draw FBD:
Identify the body you want to analyze
Isolate it (remove all supports, strings, walls)
Replace removed supports with REACTION FORCES (arrows)
Mark Weight always downward ↓
always downward ↓Mark all other external forces with arrows
Apply equilibrium equations to solve
In FBD — ALWAYS draw weight (W = mg) first! It’s the one force that’s ALWAYS there. Students often forget it and lose marks!
1.13 📐 Important Trigonometry Values (Cheat Sheet)
⚡ Quick Reference — Trig Values for Common Angles
| Angle (θ) | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 = 0.5 | √3/2 = 0.866 | 1/√3 = 0.577 |
| 45° | 1/√2 = 0.707 | 1/√2 = 0.707 | 1 |
| 60° | √3/2 = 0.866 | 1/2 = 0.5 | √3 = 1.732 |
| 90° | 1 | 0 | ∞ |
| 120° | 0.866 | -0.5 | -1.732 |
| 150° | 0.5 | -0.866 | -0.577 |
| 180° | 0 | -1 | 0 |
🔑 Tip: For 30° and 60°, sin and cos values just SWAP! (sin30 = cos60 = 0.5)
📋 Master Formula Cheat Sheet Print This!
🔥 All Formulas at One Glance
| Topic | Formula | Units |
|---|---|---|
| Force | F = m × a | N (Newton) |
| Weight | W = m × g (g = 9.81 m/s²) | N |
| Horizontal Component | Fx = F cos θ | N |
| Vertical Component | Fy = F sin θ | N |
| Resultant (2 forces at 90°) | R = √(Fx² + Fy²) | N |
| Resultant (2 forces at angle θ) | R = √(P² + Q² + 2PQ cosθ) | N |
| Direction of Resultant | tan α = ΣFy / ΣFx | degrees |
| Moment of Force | M = F × d | N·m |
| Moment of Couple | M = F × d | N·m |
| Lami’s Theorem | F1/sinα = F2/sinβ = F3/sinγ | N |
| Equilibrium (Force) | ΣFx = 0, ΣFy = 0 | — |
| Equilibrium (Moment) | ΣM = 0 | — |
📚 Important Terms (Key Definitions for Exam)
| Term | Definition |
|---|---|
| Force | A push or pull that changes or tends to change the state of a body. Unit: Newton (N) |
| Resultant | A single force that produces the same effect as all given forces combined |
| Equilibrant | A force equal and opposite to the resultant that brings a system to equilibrium |
| Resolution | Breaking a single force into two mutually perpendicular components |
| Moment | Turning effect of a force about a point = F × perpendicular distance |
| Couple | Two equal, opposite, parallel forces acting at different lines of action |
| Equilibrium | State of a body where net force and net moment are both zero |
| Free Body Diagram | Diagram of a body with all external forces shown, isolated from surroundings |
| Concurrent Forces | Forces whose lines of action meet at a single point |
| Coplanar Forces | Forces lying in the same plane |
| Varignon’s Theorem | Moment of resultant = Algebraic sum of moments of all component forces |
| Lami’s Theorem | For 3 concurrent forces in equilibrium: F/sinα = constant for all 3 |
📝 Previous Year Exam Questions Must Solve!
⭐ Short Answer Type Questions (2-3 Marks)
- Define force. State its SI unit. Repeated
- Differentiate between scalar and vector quantities with 3 examples each.
- State and explain the Parallelogram Law of Forces.
- What is Moment of a Force? State its unit.
- Define Couple. Give two examples from daily life.
- State the conditions of equilibrium of a rigid body.
- What is a Free Body Diagram? Why is it drawn?
- State Lami’s Theorem. When is it applied?
- Define Equilibrant. How is it different from Resultant?
- What is the difference between Statics and Dynamics?
⭐⭐ Long Answer / Numericals (5-8 Marks)
- Find the resultant of forces 40N (East), 30N (North), 20N (West) and 10N (South). Repeated
- Three concurrent forces of 100N, 150N and 200N are in equilibrium. Find the angles between them using Lami’s Theorem.
- A force of 200N acts at 45° to the horizontal. Resolve it into horizontal and vertical components.
- Two forces of 5 kN and 8 kN act at 60° to each other. Find their resultant using Parallelogram Law.
- A beam of 4m length carries loads. Draw FBD and find support reactions. Repeated
- Explain the types of forces with neat diagrams and examples.
- State and prove Varignon’s Theorem.
- A 500N weight is supported by two strings making angles 30° and 45° with the vertical. Find tensions using Lami’s Theorem.
🎯 Practice Questions with Hints
Q1: A 200N force acts at 30° to horizontal. Find components.
Answer: Fx = 200 × cos30° = 173.2 N | Fy = 200 × sin30° = 100 N
Q2: Two equal forces of 100N act at 90°. Find Resultant.
Answer: R = √(100² + 100²) = √20000 = 141.4 N at 45°
Q3: When is the resultant of two forces maximum and minimum?
Answer: Maximum when θ = 0° (same direction) → R = P+Q | Minimum when θ = 180° (opposite) → R = |P-Q|
Q4: A 10N force has moment of 50 N·m. What is the perpendicular distance?
Answer: M = F×d → 50 = 10×d → d = 5 m
🏆 Tips & Tricks for Exam Success
📌 Problem Solving Approach — Always Follow This!
READ the problem twice. Underline numbers and what’s asked.
DRAW a rough sketch / Free Body Diagram first.
MARK all forces with arrows and angles.
WRITE down what is given and what is to find.
CHOOSE the right formula.
SOLVE step by step, showing all work.
CHECK units and verify your answer makes sense.
⚠️ Common Mistakes Students Make
- ❌ Forgetting to convert kN to N (1 kN = 1000 N)
- ❌ Using sin where cos is needed (always ask: horizontal = cos, vertical = sin)
- ❌ Forgetting weight (W = mg) in FBD
- ❌ Applying Lami’s Theorem to more than 3 forces
- ❌ Not checking if moment is CW or ACW when finding ΣM
- ❌ Drawing forces without arrowheads (direction is EVERYTHING in vectors!)
- ❌ Not writing units in final answer
✅ Quick Recall Tricks Summary
- 🧘 Y-axis = Your BODY (vertical), X-axis = Your ARMS (horizontal)
- 📐 SOH-CAH-TOA for sin, cos, tan
- 🔺 Lami’s = 3 forces only
- 🌀 Moment = Force × PERPENDICULAR distance (not any distance!)
- ⚖️ Equilibrium = ΣFx=0, ΣFy=0, ΣM=0 — all THREE must be zero!
- 🚪 Door handle far from hinge = More moment = Easy opening
- 💑 Couple = Only ROTATION, no movement
- 🔁 Resultant max when θ=0, min when θ=180
- 📌 S for Statics = S for Still / Stationary
🔬 Full Solved Problem (Step-by-Step)
SOLVED EXAMPLE 4 — Equilibrium Problem (Typical Exam Question)
Problem: A body of weight 500 N is supported by two strings OA and OB. String OA makes an angle of 30° with the vertical, and OB makes an angle of 45° with the vertical. Find tensions T1 (in OA) and T2 (in OB).
A\ /B
\ /
T1 \ / T2
30° \ / 45°
\ /
O ← Joint (Concurrent point)
|
↓ W = 500 N
Draw FBD at point O: Three forces — T1 (30° from vertical), T2 (45° from vertical), W = 500N downward.
Find angles from horizontal:
T1 is at 90° – 30° = 60° from horizontal
T2 is at 90° – 45° = 45° from horizontal
T1 is at 90° – 30° = 60° from horizontal
T2 is at 90° – 45° = 45° from horizontal
Apply ΣFx = 0:
-T1 cos 60° + T2 cos 45° = 0
-T1 × 0.5 + T2 × 0.707 = 0
T1 = 1.414 × T2 … (i)
-T1 cos 60° + T2 cos 45° = 0
-T1 × 0.5 + T2 × 0.707 = 0
T1 = 1.414 × T2 … (i)
Apply ΣFy = 0:
T1 sin 60° + T2 sin 45° – 500 = 0
T1 × 0.866 + T2 × 0.707 = 500 … (ii)
T1 sin 60° + T2 sin 45° – 500 = 0
T1 × 0.866 + T2 × 0.707 = 500 … (ii)
Substitute (i) into (ii):
1.414 T2 × 0.866 + T2 × 0.707 = 500
1.225 T2 + 0.707 T2 = 500
1.932 T2 = 500
T2 = 258.8 N
1.414 T2 × 0.866 + T2 × 0.707 = 500
1.225 T2 + 0.707 T2 = 500
1.932 T2 = 500
T2 = 258.8 N
From (i):
T1 = 1.414 × 258.8 = 365.9 N
T1 = 1.414 × 258.8 = 365.9 N
Verification: ΣFy = 365.9 × 0.866 + 258.8 × 0.707 – 500 = 316.9 + 183 – 500 ≈ 0 ✅
🎯 Chapter 1 Summary — One Page Revision
- 🔵 Mechanics = study of forces on bodies → Statics (rest) + Dynamics (motion)
- 🔵 Force = push/pull, measured in Newtons (N)
- 🔵 Vector has direction, Scalar has only magnitude
- 🔵 X-axis = horizontal (arms), Y-axis = vertical (body) 🧘
- 🔵 Resolution: Fx = F cosθ, Fy = F sinθ
- 🔵 Resultant: R = √(ΣFx² + ΣFy²), direction = tan⁻¹(ΣFy/ΣFx)
- 🔵 Parallelogram Law: R = √(P² + Q² + 2PQ cosθ)
- 🔵 Lami’s Theorem: F1/sinα = F2/sinβ = F3/sinγ (for 3 forces only)
- 🔵 Moment = F × d (turning effect, unit = N·m)
- 🔵 Couple = two equal & opposite parallel forces → pure rotation
- 🔵 Equilibrium: ΣFx = 0, ΣFy = 0, ΣM = 0
- 🔵 FBD: isolate body, show all forces as arrows
🎓
You Got This! 💪
Mechanics is all about understanding how forces work in real life.
Keep practicing with real examples — push a door, lift a bag, turn a steering wheel —
you’re doing mechanics every day without knowing it! 🌟
📌 Mechanics Chapter 1 | Complete Diploma Notes | Easy Language
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