A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight. (a) Calculate the mass of the
1 answer:
Answer:
a) M = 2,939 10¹⁷ kg
, b) / M = 2 10⁷
Explanation:
a) The equation for gravitational force is
F = G m M / r²
Where G is the gravitational constant that is worth 6.67 10⁻¹¹ N m² / kg², m the mass epa person. M the mass of the Mountain and r the distance between them.
The value of this force is 2% of the person's weight
F = 0.02 W = 0.02 mg
we replace
0.02 mg = G m M / r²
M = 0.02 g r² / G
r = 10 km = 10 10³ m = 1.0 10⁴ m
M = 0.02 9.8 (10⁴)² / 6.67 10⁻¹¹
M = 2,939 10¹⁷ kg
b) to compare the masses we find their relationship
/ M = 5.98 1024 / 2,939 1017
/ M = 2 10⁷
c) treating the mountain as a point object
d) The mountain is not spherical so the distance changes depending on the height of the mountain
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, assuming that
and
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Explanation:
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Find the first and second derivative of with respect to
. (Note that
.)
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Second derivative:
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The value of the coulomb constant is greater than
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with respect to
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.
would be convex over all
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By the convexity of with respect to
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that globally maximizes
. The first derivative of
with respect to
should be
for that particular
. In other words:
<em>.</em>
.
.
In other words, the force between the two point charges would be maximized when the charge is evenly split:
.