Universal Gravitation

In summary: However, as you move away from the center, the gravitational field will increase and so will your weight.In summary, the conversation discusses a question proposed by a professor regarding the acceleration of an object located at 10% of the Earth's radius. The conversation explores how this question relates to Newton's law of universal gravitation and the formula for force. The participants suggest considering the Earth's density and being inside the Earth as factors that may affect the calculation. They also discuss the concept of weight and how it differs from mass.
  • #1
kiwikahuna
61
0

Homework Statement


My prof proposed a question for us. He gave us this information: if your body is inside an object (earth) and is located at 10% of the Earth's radius, what is the acceleration? We are currently learning about Newton's law of universal gravitation but I'm not sure I see how this question is related to the formula

Homework Equations


force = gravity * Mass of Earth * mass of object / (radius^2) = mg



The Attempt at a Solution


I've tried plugging the numbers into the equation above but my problem is that the mass of the object is unknown. I'm assuming that since he didn't give us a specific mass, mass would not be an important part of the problem and should be a constant? Could I perhaps use a kinematics equation to solve for acceleration? Please help if you know of any way to figure this out! Thank you.
 
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  • #2
I assume that the problem assumes that you are in some hollowed out area located at the point in question.

Try assuming that the Earth's density is uniform and see if that helps.

You won't be able to just plug into the formula; you'll have to do some thinking.
 
  • #3
if density is constant, would that mean that there is no gravitational acceleration at all? I'm still not sure i get the idea of what's happening.
 
  • #4
No. But that fact that you are inside the Earth is significant. What part of the Earth's mass pulls on you?
 
  • #5
do you mean the center of the Earth's mass pulls on you?
 
  • #6
I mean there will be some mass below you and some mass above you.

When you are standing on the surface, things are simple: All the mass is below you (below = closer to the center). But when you are inside the earth, that's not true. Does it matter?

What if you were in a hollowed out space exactly at the center of the earth? What would be your "weight" then?
 
  • #7
wouldn't your weight be the same thing as your mass because if you are that close to the center, there would be no gravitational force pulling you towards the center?
 
  • #8
kiwikahuna said:
wouldn't your weight be the same thing as your mass
Weight (a force) is never the same thing as mass--they are two different kinds of things. Your weight is the gravitational force that the Earth exerts on you.
because if you are that close to the center, there would be no gravitational force pulling you towards the center?
It is true that at the center of the Earth your weight would be zero, since the gravitational field of the Earth cancels out at that point.
 

1. What is the concept of Universal Gravitation?

Universal gravitation is a physical law that states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. Who discovered the concept of Universal Gravitation?

The concept of Universal Gravitation was first proposed by Sir Isaac Newton in his famous work "Philosophiæ Naturalis Principia Mathematica" in 1687.

3. How does Universal Gravitation affect the motion of objects?

Universal Gravitation plays a major role in the motion of objects in the universe. It causes objects to move towards each other and is responsible for the formation of celestial bodies like planets, stars, and galaxies.

4. Can Universal Gravitation be explained by Einstein's theory of relativity?

Yes, Einstein's theory of relativity provides a more accurate and comprehensive explanation of Universal Gravitation. It explains gravity as the curvature of space-time caused by the presence of massive objects.

5. How is the strength of the gravitational force affected by the distance between two objects?

The strength of the gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases.

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