The Universal Law of Gravitation - Part 1 | Physics | Don't Memorise

Summary

This video explains the concept of gravitational force and how it acts between two objects. It clarifies that both the Earth and an apple apply equal gravitational force on each other, but due to the Earth's massive size, the apple accelerates toward it. The Universal Law of Gravitation is introduced, stating that gravitational force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. The formula for this force includes the Universal Gravitational Constant (G), whose value was discovered by Lord Henry Cavendish.

Takeaways

• 🌍 The gravitational force is an attractive force between any two objects with non-zero mass separated by a distance.
• 🍎 Both the Earth and the apple exert an equal gravitational force on each other, but the apple accelerates more due to its smaller mass.
• ⚖️ According to Newton's second law, acceleration is inversely proportional to mass, meaning objects with less mass accelerate more for the same force.
• 📏 The Universal Law of Gravitation states that every object attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• 🔢 The gravitational force (F) can be written as: F = G * (m1 * m2) / d², where G is the gravitational constant.
• 🧲 G is the Universal Gravitational Constant, which is experimentally determined to be 6.673 × 10⁻¹¹ N·m²/kg².
• 🧪 Lord Henry Cavendish discovered the value of G using a torsion balance experiment.
• 📐 The units for G are derived as N·m²/kg² based on the units of force (Newtons), distance (meters), and mass (kilograms).
• 🔗 As the distance between two objects increases, the gravitational force decreases due to the inverse-square relationship.
• 🚀 If the mass of either object increases, the gravitational force between them also increases.

Q & A

What is the gravitational force?

The gravitational force is the attractive force between any two objects with non-zero mass, separated by a distance.

Does the Earth move towards the apple or does the apple move towards the Earth?

Both the Earth and the apple apply an equal gravitational force on each other, but due to the much larger mass of the Earth, the apple accelerates more towards the Earth.

Why does the apple accelerate more than the Earth if both apply equal forces?

According to Newton's second law, acceleration is inversely proportional to mass. Since the Earth's mass is much greater than the apple's, the apple experiences much more acceleration.

What is the Universal Law of Gravitation?

The Universal Law of Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

How is the gravitational force between two objects calculated mathematically?

The gravitational force is calculated as F = G * (m1 * m2) / d², where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between their centers.

What is the value of the universal gravitational constant (G)?

The value of G is 6.673 × 10⁻¹¹ N·m²/kg².

How does the distance between two objects affect the gravitational force between them?

The gravitational force decreases as the distance between two objects increases, specifically, it is inversely proportional to the square of the distance.

Who determined the value of the universal gravitational constant?

The value of the universal gravitational constant was determined by Lord Henry Cavendish using a torsion balance.

What are the units of the gravitational constant (G)?

The units of G are N·m²/kg², where N is newtons, m is meters, and kg is kilograms.

What happens to the gravitational force if the mass of one object increases?

If the mass of one object increases, the gravitational force between the two objects also increases, as the force is directly proportional to the product of the masses.

Outlines

00:00

🍎 Why Does the Apple Fall and Not the Earth?

This paragraph explores the concept of gravitational force, questioning whether the apple falls towards the Earth, the Earth moves towards the apple, or both move towards each other. The key idea is that both exert an equal gravitational force on each other. However, based on Newton's second law, because the Earth’s mass is significantly larger, the apple experiences much greater acceleration. Thus, the apple falls towards the Earth, and not vice versa.

🌍 How Do We Measure Gravitational Force?

Here, the discussion shifts to the quantification of gravitational force. To explain this, the concept of the Universal Law of Gravitation is introduced. It explains that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The formula is also provided to mathematically express this relationship.

🔢 The Formula for Gravitational Force

This paragraph explains the mathematical formulation of the Universal Law of Gravitation. The gravitational force (F) is equal to G (the Universal Gravitational Constant) multiplied by the product of the two masses (m1 and m2), divided by the square of the distance between the objects (d²). It emphasizes that increasing mass strengthens gravitational force, while increasing distance weakens it.

🧮 Understanding the Universal Gravitational Constant (G)

The value of the Universal Gravitational Constant (G) is introduced here, explaining its historical discovery by Lord Henry Cavendish using a torsion balance. The paragraph gives the universally accepted value of G as 6.673 x 10⁻¹¹ and outlines the units for G based on force, distance, and mass. This constant is a crucial part of the gravitational force equation.

Keywords

💡Gravitational Force

Gravitational force is the attractive force between two objects with mass. In the script, it is used to explain why an apple falls toward the Earth and not the other way around. This force acts between any two objects, and the Earth and the apple are used as examples to show how this force operates in nature.

💡Newton’s Second Law

Newton’s Second Law states that force is the product of mass and acceleration. This concept is used in the video to explain why the apple accelerates towards the Earth instead of the Earth moving towards the apple, highlighting the inverse relationship between mass and acceleration.

💡Universal Law of Gravitation

The Universal Law of Gravitation explains that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This law is central to understanding how gravity operates at large scales, as illustrated in the script using objects A and B.

💡Mass

Mass refers to the amount of matter in an object. In the script, the masses of the apple and the Earth (or objects A and B) are discussed to show how gravitational force depends on the mass of the objects involved. The larger the mass, the stronger the gravitational force.

💡Distance

Distance refers to the separation between the centers of two objects. In the video, distance plays a critical role in determining the strength of the gravitational force, as force decreases with the square of the distance between two objects, according to the Universal Law of Gravitation.

💡Proportionality

Proportionality describes how one quantity changes in relation to another. In the video, gravitational force is described as directly proportional to the product of two objects' masses and inversely proportional to the square of the distance between them. This concept helps quantify how gravitational force behaves in different scenarios.

💡Gravitational Constant (G)

The Gravitational Constant (G) is a fundamental constant that quantifies the strength of the gravitational force between two objects. In the script, its value is given as 6.673 × 10⁻¹¹, and it serves as the constant of proportionality in the formula for gravitational force.

💡Acceleration

Acceleration refers to the rate at which an object’s velocity changes. In the context of the video, it explains why the apple accelerates toward the Earth, as the apple’s much smaller mass leads to a greater acceleration compared to the Earth.

💡Torsion Balance

A torsion balance is a scientific instrument used to measure small forces, such as gravitational forces between masses. In the script, it is mentioned as the tool used by Lord Henry Cavendish to calculate the value of the Gravitational Constant (G).

💡Inverse Square Law

The inverse square law refers to the fact that a physical quantity (such as gravitational force) decreases in proportion to the square of the distance from the source. In the script, this law is applied to the distance between two objects, explaining how the gravitational force weakens rapidly as distance increases.

Highlights

Gravitational force is an attractive force between any two objects with non-zero mass, separated by a distance.

Both the Earth and the apple apply an equal force to attract each other due to gravity.

Newton’s second law states that the force is the product of mass and acceleration.

Acceleration is inversely proportional to mass, meaning objects with larger mass accelerate less.

Since the mass of the Earth is much greater than the mass of the apple, the apple accelerates towards the Earth.

The Universal Law of Gravitation states that every object attracts every other object with a force directly proportional to the product of their masses.

The force is inversely proportional to the square of the distance between the two objects.

Mathematically, gravitational force can be written as F = G * (m1 * m2) / d^2, where G is the universal gravitational constant.

As the mass of an object increases, the gravitational force between the objects also increases.

As the distance between two objects increases, the gravitational force decreases.

The Universal Gravitational Constant (G) was determined by Lord Henry Cavendish using a torsion balance.

The value of the Universal Gravitational Constant is approximately 6.673 x 10^-11 N(m^2)/kg^2.

The units of G are derived from force in Newtons, distance in meters squared, and mass in kilograms.

Gravitational force can be quantified using the formula F = G * (m1 * m2) / d^2.

Gravitational forces are vital in understanding how masses interact over distances in the universe.

Transcripts

We saw that the gravitational force is the attractive

force between any two objects with non-zero mass

seperated by a distance.

So does the Apple fall towards the Earth

or does the Earth move towards the Apple?

Or do both move towards each other?

It’s actually simple logic!

This is the Earth, and say this minuscule object is an Apple.

Based on what we learnt about the gravitational force,

both apply an equal force to attract the other object towards itself.

So if the forces are equal which one will accelerate more?

Based on the Newton’s second law,

we know that the force applied is the product

of mass and acceleration.

So the acceleration will equal ‘Force over the mass’.

The acceleration is inversely proportional to the mass.

If the mass is more, the acceleration will be lesser.

As the mass of the Earth is MUCH MUCH MUCH more

than the mass of the Apple,

It is the Apple that accelerates towards the Earth

and not the other way around.

Hope that makes it clear.

Now the question is ‘how do we quantify this force?’

To understand this, we need to understand

a simple concept!

And this simple concept is called

the Universal law of Gravitation.

Say there are two objects A and B

separated by a distance ‘d’.

The distance between the centres is considered the

distance between the 2

objects and not this distance.

Assume that the mass of object A is ‘m1’

and that of object B is ‘m2’.

As object A is bigger, let’s assume

'm1' to be bigger than 'm2'.

The Universal law of gravitation says that,

‘Every object in the universe attracts every object

with a force which is DIRECTLY proportional

to the product of their masses and

INVERSELY proportional

to the SQUARE of the distance between them’.

Let me repeat.

The force is Directly proportional

to the PRODUCT of their masses

and INVERSELY proportional to the SQUARE of the

distance between them.

With this data, we can write it mathematically like this.

So if the mass of any of the objects increases,

the gravitational force will have more magnitude.

And more the distance between the two objects,

the lesser will the gravitational force!

Directly proportional to the product of the masses,

and inversely proportional

to the square of the distance between them.

This can be written as F equals G times m1 one times

m2 over 'd' squared.

‘G’ here is the Constant of proportionality and is called

the UNIVERSAL GRAVITAITONAL CONSTANT.

The equation can be modified and written as

G equals ‘F times d squared' over ‘m1 times m2’.

The value of ‘G’ was found out by

Lord Henry Cavendish using a Torsion Balance.

The universally accepted value of G is

‘six point six seven three’ times ‘ten raised to negative 11’.

What will be the units of G?

Force is Newtons.

As the distance is in meters, we have ‘meters squared’.

And as the mass is measured using kilograms,

we multiply this with ‘kilograms raised to negative 2’.

This is the value of the Universal gravitational constant!