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Summary Acceleration due to Gravity vs Space-Time Continuum Curvature (General Relativity Vs. Newton)
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  • Physics
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  • Abacus College, Oxford

Acceleration due to Gravity vs Space-Time Continuum Curvature (General Relativity Vs. Newton) And problem solution document

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Document information

  • July 23, 2023
  • 19
  • 2022/2023
  • Summary

Subjects

  • general relativity
  • relativity
  • gravity
  • acceleration
  • acceleration due to gravity
  • general relativity field of study
  • curved space time in general relativity
  • general relativity vs special relativity theo

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  • Abacus College, Oxford
  • Unknown
  • Physics
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Acceleration due to Gravity & Space-Time Continuum
Curvature (General Relativity Vs. Newton)

Acceleration Due to Gravity
we will be discussing the acceleration due to gravity. We will also touch on
topics such as gravitational force and spacetime curvature. I want to
introduce these concepts to show you how exciting modern research in
physics can be. We will start by talking about what happens when you
drop an object and then delve into the modern thinking behind gravity
and its acceleration. Don't worry, we won't be diving too deep into the
math, but you will gain an appreciation for the theories that have been
developed by some of the greatest minds in the field.

Motion with Constant Acceleration
Before we get into the acceleration due to gravity, let's briefly talk about
motion with constant acceleration. This type of motion is the most
common and familiar to everyone. It is the motion that occurs during
freefall, such as when you drop something or when you fall down. Gravity
is the force acting on the object, causing it to accelerate. The acceleration
for any object in freefall is constant, which means it speeds up at the same
rate every second.

Acceleration Due to Gravity on Earth
The acceleration due to gravity on Earth is denoted by the lowercase "g"
and has a value of 9.8 meters per second squared. This means that every
second an object is falling, it gains 9.8 meters per second of speed in the
downward direction. Since gravity pulls objects down, we define the
positive direction as up and use a negative sign to indicate the downward
acceleration. It's worth noting that you may see slightly different values in
different sources, but 9.8 is generally accepted as the standard value to
use.

Acceleration Due to Gravity on the Moon and the Sun

,On the Moon, the acceleration due to gravity is much lower than on Earth,
with a value of 1.62 meters per second squared. This is because the Moon
has less mass than Earth, resulting in a weaker gravitational force. If you
were on the Moon, you would weigh around six times less than you do on
Earth. On the other hand, the acceleration due to gravity on the surface of
the Sun is much higher, approximately 274 meters per second squared.
This is because the Sun has significantly more mass than Earth. In fact, the
Sun is much more massive than the Earth, even though it appears smaller
in the sky.

Understanding Acceleration Due to Gravity
Now, let's focus on Earth and what the acceleration due to gravity means
in practice. When an object is dropped, its velocity in the downward
direction increases by 9.8 meters per second every second. This means
that the speed of the object keeps increasing as it falls. Heavier objects will
experience the same acceleration due to gravity, but the force acting on
them will be greater, leading to a faster increase in velocity.

One interesting phenomenon in physics is that any object, regardless of its
mass, will fall at the same rate when dropped. This rate is known as the
gravitational acceleration and is approximately 9.8 meters per second
squared on the surface of the Earth. This constant acceleration applies to
all objects in the Earth's gravitational field.

However, it's important to note that objects like feathers or bubbles may
not appear to fall at this rate due to air resistance. In a vacuum, where
there is no air resistance, even a feather will fall at the same rate as a
heavier object like a marker or pipe cutter. This was demonstrated by
astronauts on the moon, where there is no atmosphere to interfere with
the gravitational effect.

The acceleration due to gravity, denoted as "g," decreases as you move
farther away from the surface of the Earth. For example, at the top of
Mount Everest, the highest point on Earth, the acceleration of gravity is
approximately 9.77 meters per second squared, which is still very close to
the value at ground level.

, Regardless of the altitude or location, the constant 9.8 meters per second
squared is commonly used in physics problems involving free fall or
objects acted on by gravity. This simplifies calculations and allows for
consistent analysis.

It's worth mentioning that the constant acceleration of 9.8 meters per
second squared applies to all objects, regardless of their mass. Whether
it's a pipe cutter, a marker, a bowling ball, or even a car, they will all
accelerate downwards at the same rate when dropped.

Now, if you're interested, I'd like to take a moment to discuss one of the
most fascinating concepts in physics: relativity. This concept, first explored
by Albert Einstein, delves into the relationship between gravity and the
behavior of objects in motion. While this may not be directly related to our
discussion of gravitational acceleration, it's an intriguing field of study that
offers incredible insights into the nature of the universe.

Free Fall Motion Physics Problems (Gravitational
Acceleration), Part 1

Introduction to Free Fall Motion Problems
we will be discussing free-fall motion problems. Before we dive into the
problems, let's review some key concepts. Gravitational acceleration,
denoted as g, is equal to 9.8 meters per second squared and acts
downwards. We will be using the same equations of motion as before but
with a few modifications.

Equation Modifications

 Acceleration (a) will be replaced with negative g (-9.8 m/s^2) to account
for downward motion.
 Position (x) will be replaced with position (y) to represent vertical
motion.

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