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gravitational
attraction |
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inverse square law |
the attraction between two objects is = G(m1m2)/r2
thererfore... |
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CHANGES IN THE DISTANCE |
|
double the distance (2 x)...
| new
force |
vs |
old force |
|
G(m1m2) |
|
------------ |
|
(2r)2
|
|
vs |
|
| |
|
|
|
1 x
G(m1m2) |
|
------------ |
|
(2r)x(2r)
|
|
vs |
|
1 x
G(m1m2) |
|
----------- |
|
1r2 |
|
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1/4 to 1 |
and the new force = 1/4 x the old
force, or 4 times smaller |
triple the distance (3 x)...
| new
force |
vs |
old force |
|
G(m1m2) |
|
------------ |
|
(3r)2
|
|
vs |
|
| |
|
|
|
1 x
G(m1m2) |
|
------------ |
|
(3r)x(3r)
|
|
vs |
|
1 x
G(m1m2) |
|
----------- |
|
1r2 |
|
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1/9 to 1 |
and the new force = 1/9 x the old
force, or 9 times smaller |
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quadruple
the distance (4 x) and the
new force is 16 times smaller |
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5x , 25 times smaller and so on. |
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halve the distance (.5 x) ...
| new
force |
vs |
old force |
|
G(m1m2) |
|
------------ |
|
(r/2)2
|
|
vs |
|
| |
|
|
|
1 x
G(m1m2) |
|
------------ |
|
(1 x
r/2)x(1
x r/2)
|
|
vs |
|
1 x
G(m1m2) |
|
----------- |
|
1r2 |
|
|
4 to 1 |
and the new force = 4 times the
old force, or 4 times bigger |
make the distance 3 times less
(1/3 x) ...and the
new force = 9 times the old force, or 9 times bigger
make the distance by 4 times
less (1/4 x) ...and
the new force = 16 times the old force, or 16 times
greater
divide distance by 5, force
increases by 25 times
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CHANGES TO THE MASSES |
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double either one of the masses
(2 x)
| new
force |
vs |
old force |
|
G(2m1m2) |
|
------------ |
|
(r)2
|
|
vs |
|
| |
|
|
|
|
vs |
|
1 x
G(m1m2) |
|
----------- |
|
1r2 |
|
|
2 to 1 |
and the new force = 2 times the
old force
|
double both of the masses
| new
force |
vs |
old force |
|
G(2m12m2) |
|
------------ |
|
(r)2
|
|
vs |
|
| |
|
|
|
G(2m1
x 2m2) |
|
------------ |
|
1 r2 |
|
vs |
|
1 x
G(m1m2) |
|
----------- |
|
1r2 |
|
|
4 to 1 |
and the new force = 4 times the
old force |
| |
triple either one and the force
will be 3 times greater, and so on... Triple both of the
masses and the new force will be 9 times greater |
| |
The table below is provided for reference, do not try to
memorize it. Make one yourself to help understand how to figure a new
combination out. |
| |
| change what... |
multiplier |
m1 |
m2 |
r |
r2 |
Fnew/Fold |
increase
distance
byand
force
decreases |
1 |
1 |
1 |
1 |
1 |
1 |
| 2 |
1 |
1 |
2 |
4 |
1/4 |
| 3 |
1 |
1 |
3 |
9 |
1/9 |
| 4 |
1 |
1 |
4 |
16 |
1/16 |
| 6 |
1 |
1 |
6 |
36 |
1/36 |
| 9 |
1 |
1 |
9 |
81 |
1/81 |
| 10 |
1 |
1 |
10 |
100 |
1/100 |
| change what... |
multiplier |
m1 |
m2 |
r |
r2 |
Fnew/Fold |
|
decrease
(divide)
distance
by __
and
force
increases
by
the
square |
1 |
1 |
1 |
1 |
1/1 |
1 |
|
| 2 |
1 |
1 |
1/2 |
1/4 |
4 |
|
| 4 |
1 |
1 |
1/4 |
1/16 |
16 |
|
| 5 |
1 |
1 |
1/5 |
1/25 |
25 |
|
| 6 |
1 |
1 |
1/6 |
1/36 |
36 |
|
| 9 |
1 |
1 |
1/9 |
1/81 |
81 |
|
| 10 |
1 |
1 |
1/10 |
1/100 |
100 |
|
| change what... |
multiplier |
m1 |
m2 |
r |
r2 |
Fnew/Fold |
|
change
one
mass
by
____
and the
force
increases
by the
same
factor |
1 x |
1 |
1 |
1 |
1 |
1 |
|
| 2 x |
2 |
1 |
1 |
1 |
2 |
|
| 1 |
2 |
1 |
1 |
2 |
|
| 3 x |
3 |
1 |
1 |
1 |
3 |
|
| 3 |
1 |
1 |
1 |
3 |
|
| 4 x |
4 |
1 |
1 |
|
4 |
|
| 1 |
4 |
1 |
1 |
4 |
|
| 5 x |
5 |
1 |
1 |
1 |
5 |
|
| 10 x |
1 |
10 |
1 |
1 |
10 |
|
| change what... |
multiplier |
m1 |
m2 |
r |
r2 |
Fnew/Fold |
|
change
both
masses
by ____
and the
force
increases
by the
square
of the factor |
| 2 x |
2 |
2 |
1 |
1 |
4 |
|
| 3 x |
3 |
3 |
1 |
1 |
9 |
|
| 4 x |
4 |
4 |
1 |
1 |
16 |
|
| 5 x |
5 |
5 |
1 |
1 |
25 |
|
| 6 x |
6 |
6 |
1 |
1 |
36 |
|
| 9 x |
9 |
9 |
1 |
1 |
81 |
|
| 10 x |
10 |
10 |
1 |
1 |
100 |
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