CALCULATION OF GRAVITATIONAL FORCE: Basic Science E-Note J S 1

SUBJECT: BASIC SCIENCE

CLASS: J S S 1

TERM: 3RD TERM

REFERENCE

BASIC SCIENCE FOR JUNIOR SECONDARY SCHOOLS BOOK 1

Force is a fundamental concept in physics that describes an interaction that changes the motion of an object. It can cause an object with mass to change its velocity (to accelerate), which includes starting to move from a state of rest, stopping, or changing direction. CALCULATION OF GRAVITATIONAL FORCE: Basic Science E-Note J S 1

Force can also be defined as any influence that can change the position, speed, and state of an object. Force can also be defined as a push or pull.

The formula to describe force is given by Newton’s Second Law of Motion:

$F = m \cdot a$

where:

$F$ is the force applied to an object,
$M$ is the mass of the object,
$A$ is the acceleration produced by the force.

Units of Force

The unit of force in the International System of Units (SI) is the newton (N). One newton is defined as the amount of force required to accelerate a one-kilogram mass by one meter per second squared:

$1 N = 1 kg \cdot m / s^{2}$

CALCULATION OF GRAVITATIONAL FORCE: Basic Science E-Note J S 1

Types of Forces

There are various types of forces, including:

Gravitational Force: The attraction between two masses. For example, the force that the Earth exerts on objects to pull them toward its center.
Electromagnetic Force: Includes both electric forces (between charged particles) and magnetic forces (between magnetic poles).
Normal Force: The support force exerted upon an object that is in contact with another stable object (e.g., a book on a table).
Frictional Force: The force exerted by a surface as an object moves across it or makes an effort to move across it.
Tension Force: The force that is transmitted through a string, rope, cable, or wire when it is pulled tight by forces acting from opposite ends.
Applied Force: The force that is applied to an object by a person or another object.
Spring Force: The force exerted by a compressed or stretched spring upon any object that is attached to it.

Example Calculation

Let’s apply the concept with a simple example:

Suppose a 10 kg object is subjected to a force that accelerates it at $2 m/s^{2}$ .

Using the formula $F = m \cdot a$ :

$F = 10 kg \times 2 m/s^{2} = 20 N$

So, the force applied to the object is 20 newtons.

CALCULATION OF GRAVITATIONAL FORCE

WHAT IS GRAVITATIONAL FORCE

Gravitational force is a natural phenomenon by which all objects with mass are attracted toward one another. It is one of the four fundamental forces of nature, and it is described by Newton’s Law of Universal Gravitation.

Example:

Suppose you lift an object of mass 1kg from the ground to a height of 1m, the work done in lifting the abject is calculated by using the formula Mgh

Mgh = 1 x 1 x 9.8 joules (g = 9.8m 152) joule is the unit of work

To calculate the gravitational force between two masses, you can use Newton’s Law of Universal Gravitation. The formula is:

$F = G. m ^{1} m ^{2/r*2}$

Where:

$F$ is the gravitational force between the two masses,
$G$ is the gravitational constant ( $6.67430 \times 1 0^{-11} N \cdot m^{2} \cdot kg^{-2}$ ),
$m_{1}$ and $m_{2}$ are the masses of the two objects,
$r$ is the distance between the centers of the two masses.

Example Calculation

Let’s say we have two masses:

$m_{1} = 5 kg$

$m_{2} = 10 kg$

and they are 2 meters apart.

Using the formula, the gravitational force $F$ is:

$F = (6.67430 \times 1 0^{-11} N \cdot m^{2} \cdot kg^{-2}) ( 2 m ) ^{2} ( 5 kg ) ( 10 kg )$

Let’s calculate this step-by-step.

Multiply the masses: 5 kg×10 kg=50 kg25kg×10kg=50kg2

Square the distance: 2 m×2 m=4 m22m×2m=4m2

Divide the product of the masses by the square of the distance: 50 kg24 m2=12.5 kg2/m24m250kg2=12.5kg2/m2

Multiply by the gravitational constant: 6.67430×10−11 N⋅m2⋅kg−2×12.5 kg2/m2=8.342875×10−10 N6.67430×10−11N⋅m2⋅kg−2×12.5kg2/m2=8.342875×10−10N

So, the gravitational force $F$ is $8.342875 \times 1 0^{-10} N$ .

Properties of Gravitational Force

Attractive Nature: Gravitational force is always attractive. It always pulls masses toward each other.
Dependence on Mass and Distance: The force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them.
Weakest of the Fundamental Forces: Despite being the force that governs the motion of planets and stars, gravity is the weakest of the four fundamental forces (the others being electromagnetic, strong nuclear, and weak nuclear forces).
Universal: Every object in the universe exerts a gravitational force on every other object. This force is what gives weight to physical objects and causes the phenomena of tides, orbits, and free fall.