P22_011.PDF

(56 KB) Pobierz
11. (a) The magnitudes of the gravitational and electrical forces must be the same:
mM
1
q
2
=
G
2
4πε
0
r
2
r
where
q
is the charge on either body,
r
is the center-to-center separation of Earth and Moon,
G
is
the universal gravitational constant,
M
is the mass of Earth, and
m
is the mass of the Moon. We
solve for
q:
q
= 4πε
0
GmM .
According to Appendix C of the text,
M
= 5.98
×
10
24
kg, and
m
= 7.36
×
10
22
kg, so (using
4πε
0
= 1/k) the charge is
q
=
(6.67
×
10
−11
N
·
m
2
/kg
)(7.36
×
10
22
kg)(5.98
×
10
24
kg)
8.99
×
10
9
N
·
2
m
2
/C
2
= 5.7
×
10
13
C
.
We note that the distance
r
cancels because both the electric and gravitational forces are propor-
tional to 1/r
2
.
(b) The charge on a hydrogen ion is
e
= 1.60
×
10
−19
C, so there must be
q
5.7
×
10
13
C
=
= 3.6
×
10
32
ions
.
−19
C
e
1.6
×
10
Each ion has a mass of 1.67
×
10
−27
kg, so the total mass needed is
(3.6
×
10
32
)(1.67
×
10
−27
kg) = 6.0
×
10
5
kg
.

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin