How Does Gravity Affect Acceleration at 10% of Earth's Radius?

[kiwikahuna]

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.

 

[Doc Al]

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.

 

[kiwikahuna]

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.

 

[Doc Al]

No. But that fact that you are inside the Earth is significant. What part of the Earth's mass pulls on you?

 

[kiwikahuna]

do you mean the center of the Earth's mass pulls on you?

 

[Doc Al]

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?

 

[kiwikahuna]

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?

 

[Doc Al]

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.