9.2.2 MOTION OF OBJECTS UNDER THE INFLUENCE OF GRAVITATIONAL FORCE OF THE EARTH

Description

Quick Overview

This section examines the effects of Earth's gravitational force on the motion of objects, demonstrating that acceleration due to gravity is constant regardless of mass.

Standard

The section discusses how objects in free fall exhibit the same acceleration due to gravity, independent of their mass. It includes experiments, key equations for motion under gravity, and examples illustrating these concepts.

Detailed

Detailed Summary

The motion of objects influenced by Earth's gravitational force can be understood through various experiments and equations. For instance, dropping a sheet of paper and a stone shows that the stone reaches the ground first due to air resistance affecting the paper more significantly. However, in a vacuum, both would fall at the same rate, demonstrating that gravitational acceleration (
g
) is constant and independent of mass. This conclusion aligns with Galileo's historic experiments conducted at the Leaning Tower of Pisa.

In the context of uniformly accelerated motion, gravitational acceleration replaces acceleration in equations, yielding three key equations:

  1. v = u + gt
  2. s = ut + (1/2)gt^2
  3. v^2 = u^2 + 2gs

These equations facilitate the calculation of velocity, displacement, and time under gravitational influence. For example, a car dropped from a ledge with an initial velocity of u = 0 and g = 10 m/s^2 will have a velocity of 5 m/s after 0.5 seconds and would have fallen from a height of 1.25 m.

Another example illustrates an object thrown upwards reaching a height of 10m. Using the equations, it can be determined that the initial throw velocity was approximately 14 m/s. This section solidifies understanding of how gravitational principles govern motion, emphasizing the universality of these laws.

Key Concepts

  • Gravitational Force: A fundamental force that attracts two bodies toward each other, causing objects to fall to Earth.

  • Equations of Motion: Mathematical formulas that describe the motion of objects under the influence of forces.

  • Free Fall: The condition under which an object falls solely due to gravitational pull without other forces affecting it.

Memory Aids

🎵 Rhymes Time

  • When things fall, don't fret or fuss, gravity's here to make it a must.

📖 Fascinating Stories

  • Imagine two friends, a feather and a rock, both dropped from a great height: one was light, and one was not. In a vacuum, they hit the ground just right – proving gravity cares not for size or height!

🧠 Other Memory Gems

  • To remember motion equations: SUVAT - S for displacement, U for initial velocity, V for final velocity, A for acceleration, and T for time.

🎯 Super Acronyms

Use **GRAVITY**

  • Gravitational force Regularly Accelerates Varying mass In Time yielding a consistent result.

Examples

  • A stone and a sheet of paper dropped simultaneously in air and in a vacuum.

  • A car dropped from a ledge, calculating its impact velocity and the height it fell.

  • An object thrown vertically upwards reaching a height of 10 meters.

Glossary of Terms

  • Term: Gravitational Acceleration (g)

    Definition:

    The acceleration experienced by an object due to Earth's gravitational force, approximately 9.8 m/s^2.

  • Term: Free Fall

    Definition:

    The motion of an object falling solely under the influence of gravity, with no other forces acting on it.

  • Term: Air Resistance

    Definition:

    The forces that oppose the motion of an object through the air, which affects lighter objects more than heavier ones.

  • Term: Displacement (s)

    Definition:

    The distance covered by an object in motion, typically measured in meters.

  • Term: Velocity (v)

    Definition:

    The speed of an object in a given direction.

  • Term: Initial Velocity (u)

    Definition:

    The velocity of an object at the beginning of its motion.