The Force of Gravity at Different Heights above the Earth

[oisalex]

I use a vacuum container and drop an object within the container from A (the top) to B (the bottom) and measure the speed and acceleration of its fall under gravity.

How will the speed and acceleration differ, if at all, if I conduct this experiment at, say, 20,000 feet. 5,000 feet, at ground level and below ground level?

Alex M

[scotstone]

The fact that the object is in a vacuum will make no difference to the acceleration due to gravity. However the speed will be greater due to the lack of air resistance. The acceleration will alter due to the altitude as the force of gravity is dependent upon the distance from the centre of the Earth to the object being acted upon.

[Peter Pedant]

Gravity varies inversely with the square of the distance from the ce of the earth
This follows from F= G mm/r2

As you climb up the mountain, g gets less (see above).

Below the surface -
more complicated - do you remember the proof that the electrostatic field inside a charged sphere is nil ? The proof starts off with considering a circle and a point inside. same inverse square law. This by integration can be extended to a shell (surface of a sphere).
This means tha the force of gravity inside the earth is less,because the shell above it does not contribute to the attraction.

Read your chapter again.

Somewhere there, also should be the proof that if that if you drill a chord straight hole through the earth but not through its centre then a ball will execute simpe harmoinc motion

goodluck anyway

[mibn2cweus]

If we ignore variations in mass density as well as variations in the radial distance from the center of gravity to the surface, (mountains, equatorial bulge etc.), and external forces such as the gravity of the Moon and Sun, then:

From anywhere on or above the Earth�s surface, gravity can be considered a point source at its center, equivalent to the entire mass of the Earth and the sphere of the Earth�s surface is the radial distance of maximum gravitational acceleration . . . However . . .

Beneath the surface of a sphere, gravity plays a different kind of ball game.

As Peter Pedant pointed out we do not consider the mass in overlying spheres (above the radius from which we are determining gravitational acceleration) because the mass of the spheres above this radius �attract� from all directions equally and effectively cancel each other out.

A spheres volume increases with the cube of the radius. Therefore, comparing two solid spheres of equal density, a sphere of twice the size would have eight times the mass. Remember that gravity varies inversely to the radius squared, consequently, doubling the radius doubles the gravitational acceleration. The result is that below the surface gravitational acceleration should diminish linearly as we approach the Earth�s center.

But the Earth has another curve ball to throw our way.

Beneath the Earth�s surface mass density increases as we approach the core. The Earth�s core has a mass density five to six times that of surface material. The net effect of this is that gravitational acceleration actually increases below the Earth�s surface reaching 10.7 m/s� at the core-mantle boundary before declining to zero at its center. Go figure!