9.2.1 TO CALCULATE THE VALUE OF GRAVITY

Description

Quick Overview

This section discusses how to calculate the acceleration due to gravity, denoted as 'g', using the universal gravitational constant and other values.

Standard

In this section, we learn the formula for calculating the acceleration due to gravity 'g' by substituting known values like the universal gravitational constant (G), the mass of the Earth (M), and the radius of the Earth (R). It also explains the importance of understanding how 'g' varies in different locations.

Detailed

Detailed Summary

In this section, we delve into the calculation of gravitational acceleration, commonly referred to as g. Gravitational acceleration is a crucial concept in physics as it describes the rate at which objects accelerate towards the Earth due to gravitational attraction. The value of g is typically approximated as 9.8 m/s² near the Earth's surface, but it can vary based on geographical location (greater at the poles than the equator) and altitude.

To compute g, we utilize the equation derived from Newton's Law of Gravitation:

$$ g = \frac{G \times M}{R^2} $$

Where:
- G is the universal gravitational constant (approximately 6.67 × 10^-11 N m²/kg²),
- M is the mass of the Earth (6 × 10^24 kg), and
- R is the radius of the Earth (6.4 × 10^6 m).

By substituting these values into the equation, we arrive at the calculated value of g, which is approximately 9.8 m/s². This section emphasizes the universality of gravitational acceleration and its relevance to the motion of objects near the Earth's surface.

Key Concepts

  • Gravitational acceleration ('g') averages 9.8 m/s² near Earth's surface.

  • The formula for calculating 'g' is g = GM/R², where G is the gravitational constant.

  • The value of 'g' varies with altitude and location on Earth.

Memory Aids

🎵 Rhymes Time

  • When objects drop and don’t sway, g brings them down in a steady way.

📖 Fascinating Stories

  • Once there was a curious student who dropped a ball from a tower. To their surprise, it hit the ground in 9.8 seconds, teaching them about gravitational pull!

🧠 Other Memory Gems

  • GMR – Gravitational Mass Radius for remembering the formula for 'g'.

🎯 Super Acronyms

Remember 'GEM'

  • Gravitational constant
  • Earth’s mass
  • radius to calculate 'g'.

Examples

  • An object in free fall accelerates at approximately 9.8 m/s² until it reaches the ground.

  • Calculating 'g' from values of G, M, and R shows how gravitational force works.

Glossary of Terms

  • Term: Gravitational Constant (G)

    Definition:

    The universal constant that measures the strength of the gravitational force, approximately 6.67 × 10^-11 N m²/kg².

  • Term: Acceleration due to Gravity (g)

    Definition:

    The acceleration experienced by an object in free fall due to the Earth's gravitational pull, approximately 9.8 m/s².

  • Term: Mass (M)

    Definition:

    The quantity of matter in an object, measured in kilograms (kg).

  • Term: Radius of Earth (R)

    Definition:

    The average distance from the center of the Earth to its surface, approximately 6.4 × 10^6 m.