Mass and weight differences on earth

[mmfoley]

Hello,

How do the mass and weight of an object at the Earth's center compare with their values at the Earth's surface? My textbook is pretty terrible for the non-physics major. I think they answer this question in eqations rather than plain English, so I'm having a hard time with this. Basically, I'm trying to figure out if I dug a hole down to the center of the Earth and dropped a rock down the hole, how would its mass and weight change from the surface of the Earth to the center of the earth.

Thanks!

mmfoley

 

[Jimmy]

The mass will remain constant but as the rock fell toward the center of the earth, it's weight would decrease. At the center of the earth, the rock would be weightless. The net gravitational force would be zero since the Earth's mass is surrounding the rock. The gravitational force of the Earth on one side of the rock will cancel out the force on the other side.

note: actually the rock would be weightless at the gravitational center of the Earth which doesn't exactly coincide with its geometrical center due to irregularities in the density of the earth. It's probably pretty close so for a simplified case it's OK to assume that the geometrical and gravitational centers are the same.

 

[turin]

Originally posted by mmfoley
... I'm trying to figure out if I dug a hole down to the center of the Earth and dropped a rock down the hole, how would its mass and weight change from the surface of the Earth to the center of the earth.

The mass won't change (excluding inconsistent relativistic termonology). Weight is defined as the force of gravity exerted on an object at rest (more or less). Approximating the Earth as a perfect solid sphere, the wieght would decrease linearly with depth until it reached zero at the center (At the center of the earth, there is no pull of gravity in this model. The weight would be directly proportional to the distance from the center).

The significance of the mass not changing is that the object would remain just as difficult to push, even though its weigth would decrease.

 

[mmfoley]

thank you

thank you both!