Enrol to start learning
Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.
7.5. Acceleration Due to Gravity of the Earth
Interactive Audio Lesson
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free account
Today we're diving into how gravity operates around and inside the Earth. Can anyone tell me what gravity does?
It pulls objects toward the Earth!
Excellent! Gravity pulls objects toward the center of the Earth. This is why when you throw something up, it eventually comes back down. Now, imagine if we could picture the Earth as consisting of concentric shells. What do you think happens to gravitational force as you move away from the Earth's surface?
It should decrease, right?
You're on the right track! As you go upward, gravity does decrease. The formula we use for gravitational force when at a height h is: g(h) = g(1 - (h/R_E)) where g is the gravity at the surface. Can anyone guess what R_E stands for?
That's Earth's radius!
Great job! So, as you rise above the Earth, the gravitational acceleration does decrease slightly.
But what happens if we dig down? Do we get heavier?
Interesting question! Let's discuss that next. As you go below the surface, the acceleration due to gravity also decreases. This is captured by the formula g(d) = g(1 - (d/R_E)) but why do you think that is?
Because there’s less mass below us?
Exactly! Only the mass below you exerts gravitational force. Great understanding! To wrap up, why is knowing how gravity changes important?
It helps us understand how things will fall or float!
Precisely! Understanding how gravity works in different conditions helps in various practical applications. Well done, everyone!
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free account
Now, let’s apply these concepts using some formulas. The gravitational acceleration at the surface of the Earth can be expressed as g = (GM_E) / R_E². Who knows what the variables mean?
Um, G is the gravitational constant, right?
Correct! And M_E is Earth’s mass while R_E is its radius. This equation allows us to calculate the 9.8 m/s² gravity we experience. Can someone tell me why this number is significant?
It’s used everywhere in physics!
Spot on! This value is essential for calculations in physics. Now, let’s consider height. If an object is 10 km above the Earth’s surface, what would you do to find the new gravitational pull?
We’d use g(h), right?
Exactly! And remember, as height increases, gravitational pull decreases. Can anyone summarize what we did today?
We talked about gravity, how it changes with height and depth, and the equations for calculating it.
Great recap! Keep practicing these equations, and think about how they apply in real life!
Unlock the classroom podcast
The transcript is above and free to read. A free account plays the conversation back.
Create a free accountLet’s explore how the changes in gravity we discussed could impact different scenarios, like construction at high elevations. Who can tell me how gravity at a higher elevation may affect construction?
Weights would be less, so construction materials might not behave the same?
Exactly! We need to consider gravity when planning structures. What else might change if we were on another planet with a different gravity?
Things would weigh different, but how would that feel?
That’s a fantastic question! It could feel like we are lighter, or even heavier depending on the planet. Can anyone think of a planet with low gravity?
Mars!
Correct! And knowing these different gravitational pulls helps in space missions. Why do you think astronauts train so much?
So they can adapt to being in lower gravity!
Exactly! They need to be prepared for changes in their physical abilities. Outstanding discussion today!
Overview
Short Summary
This section details how the acceleration due to gravity is determined by the Earth's mass and radius, both on the surface and at varying heights or depths.
Medium Summary
The section explains the concept of gravitational force exerted by Earth, how it varies based on distance (height above the surface and depth below it), and includes equations that relate the acceleration due to gravity to Earth's mass and radius.
Detailed Summary
Acceleration Due to Gravity of the Earth
The concept of gravitational acceleration is integral in physics, representing how objects are influenced by Earth’s mass. The earth can be conceptualized as a series of concentric spherical shells, which allow us to understand how gravity operates at different distances—both above and below the surface.
Key Points:
-
For points located outside the Earth, all mass can be considered to be concentrated at the center, allowing the use of Newton's law of gravitation to determine gravitational force.
-
The force experienced by an object inside the Earth varies; shells outside it contribute no force.
-
The formula for gravitational force on an object of mass m, at a distance r from the center of the Earth, can be expressed as:
F = (GMm) / r²,
where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth.
-
At the surface, the acceleration due to gravity, denoted by g, is determined as:
g = (GM_E) / R_E²,
where R_E is Earth’s radius. The value of g is approximately 9.8 m/s².
-
The gravitational force changes with height and depth:
- At height h above the Earth’s surface, the acceleration due to gravity is:
g(h) = g(1 - (h/R_E)) for heights much smaller than the radius of the Earth.
-
At depth d below the Earth’s surface, gravitational force is:
g(d) = g(1 - (d/R_E)), allowing the conclusion that gravitational acceleration decreases as one approaches the center of the Earth.
This section highlights the relationship between gravity and Earth's dimensions, showcasing how gravitational acceleration is a fundamental principle that varies with one's position relative to the center of Earth. It elucidates the nature of gravitational force, encouraging a deeper understanding of universal gravitation concepts.
Reference YouTube Videos
Key Concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
Gravitational acceleration (g) varies with height and depth.
Gravitational force follows the inverse square law.
The formulas for gravitational force involve Earth's radius and mass.
Acceleration due to gravity decreases with increasing height and depth.
Examples
Memory Aids
Interactive tools to help you remember key concepts
Stories
Memory Tools
Flash Cards
Glossary
Acceleration due to gravity (g)
The acceleration experienced by an object due to the gravitational force exerted by the Earth, approximately 9.8 m/s² at Earth's surface.
Gravitational constant (G)
A fundamental constant used in the calculation of gravitational force, approximately equal to 6.67×10^-11 N m²/kg².
Radius of the Earth (R_E)
The average distance from the center to the surface of the Earth, approximately 6,371 km.
Mass of Earth (M_E)
The total mass of the Earth, roughly 5.97 × 10^24 kg.
Height (h)
The vertical distance above the Earth's surface where acceleration due to gravity is calculated.
Depth (d)
The vertical distance below the Earth's surface where gravitational force is determined.