1. A __________ is an idea used to explain how
objects can ________________ on each another
without touching ("at a _____________" forces)
even if separated by a ____________:
field
exert forces
distance
vacuum
the 2 fields
____________
with each other
interact
object 1
object 2
field of 1
field of 2
Examples of fields:
__________________
_________________
electric
All fields are _________
because they represent
____________ .
vectors
magnetic
gravitational
forces

2. The force of ______________ is explained by saying
gravity, Fg
The force of ______________ is explained by saying
that a gravitational ___________ exists around
every______________ . Here is how it works:
field, g
mass, m
To study the field, put a
______ mass m in it, and
measure the gravitational
________ Fg pulling on it:
test
force
Suppose there is
a _______ somewhere
near here (not shown).
Because of that,
there must be a
________________
field all around it.
mass m Fg
gravitational

3. Then the ____________ (magnitude) of the field g
is given by the force _______ mass:
strength
per
g =
Fg / m
same as Fg
direction of g: ____________________
units of g:
[g] =
[ ] / [ ] Fg m
[g] = N / kg
And since 1 N = __________ , these units can be
written:
kgm/s2
[g] =
kgm/s2 / kg =
m/s2
N/kg
derived _________ = __________  fundamental
m/s2

5. Ex: A 5.0 kg mass experiences a gravitational
force of N when placed at the position shown
here.
5.0 kg
30 N
Determine the strength (magnitude) and direction
of the gravitational field at the point shown.
strength: g = =
Fg / m
30.0 N / 5.0 kg
6.0 N/kg
6.0 m/s2 Fg
direction:
Same direction as_____

6. When Fg is due to a planet, we call it _________. So you can write:
weight
g =  same as  g =
Fg/m
w/m
Ex: What will a 0.10 kg stick of butter weigh
when placed in the gravitational field shown?
g = =
w/m
g = 8.2
N/kg
w/ 0.10 kg
8.2 N/kg w
0.82 N
planet Butterway
What is the force of gravity acting on the butter?
0.82 N

7. Ex: To find the shape of the g field around a
"point" mass m, use a “test” mass mt.
> Fg
strong m mt
one
_____ field
line in the
circle out here
_____ field
lines in the
circle in here
two
weak
force lines
The force arrows are connected into ____________ .

8. The lines are ___________ to the forces. They are
Notes:
The lines are ___________ to the forces. They are
“__________________ " that act on a test mass m.
2. Closer lines  _____________ field ________
the mass. Also, the lines ________________
because then one point
would have _______________
3. The arrows show______________ by pointing
in towards the mass. We say g is directed
_______________________ .
tangent
lines of force
stronger
near
never cross F?
two forces F?
attraction
radially inward

9. Closer ____________ to Earth, As seen from far the lines don’t spread
away, Earth's field
is very similar to
a __________ mass.
The g field lines
are ______________
to the surface.
____________ to Earth,
the lines don’t spread
out as much:
point
perpendicular
surface
> E
Coming even closer,
________ spreading
less
surface

10. Close to the surface, the lines appear __________
spaced and ___________ .
equally
>
parallel
surface
g at Earth's surface is ___________ because on
the surface you remain the same ___________ from
Earth's center (one Earth _____________ ).
In fact, g is simply the _________________ due
to gravity. Its value is ____________ near Earth's
surface. This means that an easy way to find g
would be to __________ an object and measure
its ____________________ in free fall.
constant
distance
radius
acceleration
9.81 m/s2
drop
acceleration

11. (Note: For any planet, use: gp = )
The field g around Earth (or a point mass) is
proportional to ________ because _______ is .
1/r2 Fg
g = /m Fg
> E
GMem r2
g = ( )/m
GMe r2 r2 1
g = ~
GMe
Re2 Re
At the surface, r = ___ , so g = =
But at greater r's, g will be _________ .
(Note: For any planet, use: gp = )
9.81 m/s2
less
GMp
Rp2

12. Ex. g as a function of distance from Earth's center:
9.81
g = ____ /42 = _____
0.61
4Re
9.81
g = ____ /32 = _____
1.09
3Re
> E
g = ____ /22 = _____
9.81
2.45
2Re
1Re
g = ____
9.81
9.8
inverse
square g r
1Re
2Re
3Re
4Re
Compare:
Big G = ________________________ never changes!
6.67 x Nm2/kg2

13. In sum: g = the gravitational ____________
= the ________________ due to gravity
direction: _____________________________
units of g: derived: ______________
fundamental: ______________
How to find g:
Take a mass and weigh it (find Fg):
 Calculate: g = =
Drop an object and find its _________________ .
For a planet of mass Mp and radius Rp:
 Calculate: g =
field
acceleration
same as gravity
N/kg
m/s2
w/m
Fg/m
acceleration
GMp
Rp2

14. Ex: Astronauts experiencing “g forces”
0 g  weightless
1 g =  what you feel on Earth
2 g =  when your acceleration upwards
is 9.8 m/s2, you feel twice as heavy
3 g = when your acceleration upwards
is 2 x (9.8 m/s2), you feel three times as heavy
etc
Highest survived g forces…..

15. Ex. To experience “artificial gravity” on earth,
use a centrifuge to accelerate:
ac = v2 r
Higher v  more a  more “gravity”
Centrifuges are used
in biology and chemistry
to separate out
substances according
to their densities.