Chapter 12
Gravitational Force Near the Surface of the Earth, First Brush with Newton’s 2nd Law
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12
Gravitational Force Near the Surface of the Earth, First
Brush with Newton’s 2
nd
Law
Some folks think that every object near the surface of the earth has an
acceleration of
9
.
8 m/s
2
downward relative to the surface of the earth.
That just
isn’t so.
In fact, as I look around the room in which I write this sentence, all the
objects I see have zero acceleration relative to the surface of the earth.
Only
when it is in freefall, that is, only when nothing is touching or pushing or pulling
on the object except
for the gravitational field of the earth, will an object
experience an acceleration of 9
.
8 m/s
2
downward relative to the surface of the
earth.
Gravitational Force near the Surface of the Earth
We all live in the invisible gravitational field of the earth.
Mass is always accompanied by a
surrounding gravitational field.
Any object that has mass, including the earth, is surrounded by a
gravitational field.
The greater the mass of the object, the stronger the field is.
The earth has a
huge mass; hence, it creates a strong gravitational field in the region of space around it.
The
gravitational field is a force-per-mass at each and every point in the region around the object,
always ready and able to exert a force on any particle that finds itself in the gravitational field.
The earth’s gravitational field exists everywhere around the earth, not only everywhere in the air,
but out beyond the atmosphere in outer space, and inside the earth as well.
The effect of the
gravitational field is to exert a force on any particle, any “victim,” that finds itself in the field.
The force on the victim depends on both a property of the victim itself, namely its mass, and on a
property of the point in space at which the particle finds itself, the force-per-mass of the
gravitational field at that point.
The force exerted on the victim by the gravitational field is just
the mass of the victim times the force-per-mass value of the gravitational field at the location of
the victim.
Hold a rock in the palm of your hand.
You can feel that something is pulling the rock
downward.
It causes the rock to make a temporary indentation in the palm of your hand and you
can tell that you have to press upward on the bottom of the rock to hold it up against that
downward pull.
The “something” is the field that we have been talking about.
It is called the
gravitational field of the earth
.
It has both magnitude and direction so we use a vector variable,
the symbol
g
h
to represent it.
In general, the magnitude and the direction of a gravitational field
both vary from point to point in the region of space where the gravitational field exists.
The
gravitational field of the earth, near the surface of the earth is however, to a very good
approximation, much simpler than that.
To a very good approximation, the gravitational field of
the earth has the same value at all points near the surface of the earth, and it always points