FORCE AND MOTION , NOTES , CLASS 10

NOTES OF FORCE AND MOTION

COMPLETE NOTES OF FORCE AND MOTION , CLASS-10

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GRAVITATION AND FREE FALL

Complete Study Notes

★ WHY DO WE STUDY GRAVITATION?

To understand the force that keeps planets in orbit and holds galaxies together
To analyze the motion of objects under gravitational influence
To predict and calculate physical phenomena in space and on Earth

Gravitation is one of the FOUR fundamental forces of nature

★ NEWTON’S LAW OF UNIVERSAL GRAVITATION

Every two objects in the universe attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F = G(m₁ × m₂) / r²

F = Gravitational force (Newtons)
G = Gravitational constant = 6.67 × 10⁻¹¹ N·m²/kg²
m₁, m₂ = Masses of the objects (kg)
r = Distance between centers (m)

✓ Gravitational force is always ATTRACTIVE in nature

★ ACCELERATION DUE TO GRAVITY (g)

The acceleration acquired by a body due to Earth’s gravitational attraction.

At Earth’s Surface: g = GM / R²

g ≈ 9.8 m/s² (or 10 m/s² approximately)
M = Mass of Earth = 5.97 × 10²⁴ kg
R = Radius of Earth = 6.37 × 10⁶ m

Variation from Center to Surface:

At Earth’s Center: g = 0 (zero!)
At Surface: g = 9.8 m/s²

At Height h Above Surface: g = GM / (R + h)²

✓ As you go UP from Earth, g DECREASES ↓

★ GRAVITATIONAL FORCE & WEIGHT

Weight is the gravitational force exerted on an object by a planetary body.

W = m × g

W = Weight (Newtons or kgf)
m = Mass of object (kg) [CONSTANT]
g = Acceleration due to gravity (m/s²) [VARIES]

MASS vs WEIGHT:

MASS: Amount of matter, Always CONSTANT, Not a force
WEIGHT: Gravitational force, VARIES with location, Force (Vector)

Example: A person with mass 60 kg

On Earth: W = 60 × 10 = 600 N
On Moon (g=1.6): W = 60 × 1.6 = 96 N

✓ Your MASS is same everywhere but your WEIGHT changes!

★ FREE FALL – INTRODUCTION

Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.

Conditions for Free Fall:

Only gravity acts on the object
Air resistance is NEGLECTED (or zero)
Object may be dropped, thrown up, or thrown down

Key Characteristics:

Acceleration = constant = g = 9.8 m/s²
Direction = DOWNWARD (toward Earth)
It is uniformly accelerated motion

In free fall, weight appears to be ZERO (weightlessness)

★ EQUATIONS OF MOTION IN FREE FALL

These are the three kinematic equations with acceleration = g:

Equation 1: v = u + gt

Equation 2: s = ut + ½gt²

Equation 3: v² = u² + 2gs

Where:

v = Final velocity (m/s)
u = Initial velocity (m/s)
g = 9.8 m/s² (take downward as positive)
t = Time (s)
s = Displacement (m)

✓ Use DOWNWARD as POSITIVE direction

★ SPECIAL CASES IN FREE FALL

Case 1: Object Dropped from Rest

u = 0

v = gt | s = ½gt² | v² = 2gs

Case 2: Object Thrown Upward

u = positive (upward)
At highest point: v = 0

Max height: h = u² / (2g)

Time to max height: t = u / g

Case 3: Object Thrown Downward

u = positive (downward)
All three equations apply directly

Case 4: Total Time of Flight (Vertical Throw)

T = 2u / g

✓ Time to go UP = Time to come DOWN

★ APPLICATIONS OF FREE FALL IN DAILY LIFE

Falling Objects & Building Drops: Calculating time for objects to fall from skyscrapers
Projectile Motion: Analyzing trajectories of balls, rockets, and bullets
Astronauts & Weightlessness: Objects in orbit undergo continuous free fall
Parachuting: Calculating fall time before parachute deployment
Water Fountains: Designing fountains using freefall calculations
Vehicle Safety: Airbag deployment and safety engineering
Sports Physics: Jump heights in basketball, volleyball, and high jump
Elevators: Analyzing motion when cables break

Free fall explains why astronauts feel WEIGHTLESS in space!

★ SOLVED PROBLEMS

Problem 1: Ball Dropped from Height

A ball is dropped from a height of 45 m. Find time taken and final velocity. (g = 10 m/s²)

Given: s = 45 m, u = 0, g = 10 m/s²

Solution:

Using s = ut + ½gt²

45 = 0 + ½(10)t²

45 = 5t² → t² = 9

t = 3 seconds ✓

Problem 2: Ball Thrown Upward

A ball is thrown upward with initial velocity 20 m/s. Find maximum height and total time of flight. (g = 10 m/s²)

Given: u = 20 m/s (upward), g = 10 m/s²

Solution:

Time to reach max height: t = u/g = 20/10 = 2 seconds

Maximum height: h = u²/(2g) = (20)²/(2×10) = 400/20 = 20 m ✓

Total time of flight: T = 2u/g = 2(20)/10 = 4 seconds ✓

Problem 3: Gravitational Force Calculation

Calculate gravitational force between Earth and a 5 kg object. (M = 5.97×10²⁴ kg, R = 6.37×10⁶ m)

Solution:

F = GMm/R² = (6.67×10⁻¹¹ × 5.97×10²⁴ × 5) / (6.37×10⁶)²

F ≈ 49 N ✓

★ KEY FORMULAS SUMMARY

Gravitational Force: F = G(m₁m₂)/r²
Acceleration due to Gravity: g = GM/R²
Weight: W = mg
Equations of Motion: v = u+gt, s = ut+½gt², v² = u²+2gs
Max Height (upward): h = u²/(2g)
Time of Flight: T = 2u/g

All the best for your exams!

NOTES OF FORCE AND MOTION

COMPLETE NOTES OF FORCE AND MOTION , CLASS-10

GET COMPLETE NOTES

GRAVITATION AND FREE FALL

Complete Study Notes

★ WHY DO WE STUDY GRAVITATION?

To understand the force that keeps planets in orbit and holds galaxies together

To analyze the motion of objects under gravitational influence

To predict and calculate physical phenomena in space and on Earth

Gravitation is one of the FOUR fundamental forces of nature

★ NEWTON’S LAW OF UNIVERSAL GRAVITATION

Every two objects in the universe attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

F = G(m₁ × m₂) / r²

F = Gravitational force (Newtons)

G = Gravitational constant = 6.67 × 10⁻¹¹ N·m²/kg²

m₁, m₂ = Masses of the objects (kg)

r = Distance between centers (m)

✓ Gravitational force is always ATTRACTIVE in nature

★ ACCELERATION DUE TO GRAVITY (g)

The acceleration acquired by a body due to Earth’s gravitational attraction.

At Earth’s Surface: g = GM / R²

g ≈ 9.8 m/s² (or 10 m/s² approximately)

M = Mass of Earth = 5.97 × 10²⁴ kg

R = Radius of Earth = 6.37 × 10⁶ m

Variation from Center to Surface:

At Earth’s Center: g = 0 (zero!)

At Surface: g = 9.8 m/s²

At Height h Above Surface: g = GM / (R + h)²

✓ As you go UP from Earth, g DECREASES ↓

★ GRAVITATIONAL FORCE & WEIGHT

Weight is the gravitational force exerted on an object by a planetary body.

W = m × g

W = Weight (Newtons or kgf)

m = Mass of object (kg) [CONSTANT]

g = Acceleration due to gravity (m/s²) [VARIES]

MASS vs WEIGHT:

MASS: Amount of matter, Always CONSTANT, Not a force

WEIGHT: Gravitational force, VARIES with location, Force (Vector)

Example: A person with mass 60 kg

On Earth: W = 60 × 10 = 600 N

On Moon (g=1.6): W = 60 × 1.6 = 96 N

✓ Your MASS is same everywhere but your WEIGHT changes!

★ FREE FALL – INTRODUCTION

Free fall is the motion of an object under the sole influence of gravity, with no other forces acting on it.

Conditions for Free Fall:

Only gravity acts on the object

Air resistance is NEGLECTED (or zero)

Object may be dropped, thrown up, or thrown down

Key Characteristics:

Acceleration = constant = g = 9.8 m/s²

Direction = DOWNWARD (toward Earth)

It is uniformly accelerated motion

In free fall, weight appears to be ZERO (weightlessness)

★ EQUATIONS OF MOTION IN FREE FALL

These are the three kinematic equations with acceleration = g:

Equation 1: v = u + gt

Equation 2: s = ut + ½gt²

Equation 3: v² = u² + 2gs

Where:

v = Final velocity (m/s)

u = Initial velocity (m/s)

g = 9.8 m/s² (take downward as positive)

t = Time (s)

s = Displacement (m)

✓ Use DOWNWARD as POSITIVE direction

★ SPECIAL CASES IN FREE FALL

Case 1: Object Dropped from Rest

u = 0

v = gt | s = ½gt² | v² = 2gs

Case 2: Object Thrown Upward

u = positive (upward)

At highest point: v = 0

Max height: h = u² / (2g)

Time to max height: t = u / g

Case 3: Object Thrown Downward

u = positive (downward)

All three equations apply directly

Case 4: Total Time of Flight (Vertical Throw)

T = 2u / g

✓ Time to go UP = Time to come DOWN