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Lesson 30: Gravitational Field Strength
In the last lesson we were able to combine our two formulas for force due to gravity to get a new formula.
F
g
=
F
g
m
test
g
=
Gm
test
M
e
r
2
g
=
GM
e
r
2
●
The great news is that the mass (shown above as the mass of the Earth “M
e
”) can actually be any
mass. It could be the mass of the moon, Mars, an asteroid, whatever!
●
In fact, we should replace
mass of the Earth
in the formula with just
mass
, since it can be any
mass.
g
=
Gm
r
2
g = gravitational field strength (m/s
2
)
G = Universal Gravitational Constant
m = mass of object producing the field (kg)
r = distance from centre of mass (m)
●
This formula lets you calculate the the gravitational field strength (the acceleration due to gravity)
caused by that mass ata specific distance from its centre.
Example 1
: The planet Mars has a mass of 6.42e23 kg and a radius (from its centre to the surface) of
3.38e6 m.
a)
Determine
how much a 60.0 kg person would weigh on Mars.
b)
Compare
it to his weight on Earth.
c)
Determine
how heavy the 60.0 kg person would “feel” as an
apparent
mass in kilograms on
Mars.
a) To determine someone's weight, we first need to know the acceleration due to gravity
on Mars.
g
=
Gm
r
2
g
=
6.67e11
6.42e23
3.38e6
2
g
=
3.75
m
/
s
2
So the person's weight will be.
..
F
g
=
mg
F
g
=
60.0
3.75
F
g
=
225
N
7/6/2007
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Page 1 of 4 / Section 4.3
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View Full Documentb) On Earth the person has a weight of…
F
g
=
mg
F
g
=
60.0
9.81
F
g
=
589
N
Probably the easiest way to compare the person's weight on Mars and the Earth is to find
the ratio of the two.
F
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 Fall '08
 Staff
 Force, Gravity, Mass

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