example 1: kg and m example 1 - physics · 2019. 12. 4. · gravitation 1 example 1: a.)what is the...
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Gravitation 1
Example 1:a.) What is the acceleration due to gravity at
the surface of Venus?(MV = 4.88 x 1024 kg and RV = 6.07 x 106 m)
b.) What is the escape velocity for an objecton the surface of Venus?
c.) What is the total energy of a satellite witha mass of 15,000 kg orbiting in a circularorbit 200 km above the surface of Venus?
!
MV = 4.88"1024 kg and RV = 6.07"106 m
a.) gV = ?
!
Fg =GMV mRV
2
!
= mgV
!
gV =G MV
RV2
!
= 6.67"10#11 N $m2
kg2
%
& '
(
) *
4.88"1024 kg( )6.07"106 m( )2
!
gV = 8.83 ms2
b.) ve = ?
!
K = "U
!
so 12mve
2 =GMVmRV
!
ve = 2GMVRV
!
= 2 6.67"10#11 N $m2
kg2
%
& '
(
) *
4.88"1024 kg( )6.07"106 m( )
!
ve = 10,356 ms
Example 1:
!
MV = 4.88"1024 kg, RV = 6.07"106 m, m = 15,000 kg, and d = 200 km
c.) E = ?
!
Fg =GMV mr2
!
E = K +U
!
=12mv2 "GMVm
r
!
= m v2
r
!
= mac
!
so v = GMV r
!
E =12m GMV
r"
# $
%
& '
2
(GMVmr
!
=12GMVm
r"GMVm
r
!
E = "12
6.67#10"11 N $m2
kg2
%
& '
(
) *
4.88#1024 kg( ) 15,000 kg( )6.07#106 m + 2.0#105 m( )
!
E = "3.9#1011J
!
E = "12GMVm
r
!
RV
!
d
!
r = RV + d
!
= "12G MVmRV + d
Example 1:
Gravitation 4
Example 2:What is the weight of 85 kg person on the surfaceof Pluto?(MP = 1.2 x 1022 kg and RP = 1.15 x 106 m)
!
MP = 1.2"1022 kg, RP = 1.15"106 m, and m = 85 kg
Fg = ?
!
Fg =GMP mRP
2
!
Fg = 6.67"10#11 N $m2
kg2
%
& '
(
) *
1.2"1022 kg( ) 85 kg( )
1.15"106 m( )2
!
Fg = 51.4 N
!
gP =G MP
RP2
!
= 6.67"10#11 N $m2
kg2
%
& '
(
) *
1.2"1022 kg( )1.15"106 m( )2
!
gP = 0.61 ms2
!
Fg = mgP
!
= 85 kg( ) 0.61 ms2
" # $
% & '
!
Fg = 51.4 N
Example 2:
Gravitation 6
Gravitation 7
Example 3:Find the speed of a satellite that would orbit Mars200 km above its surface.(MM = 6.42 x 1023 kg and RM = 3.38 x 106 m)
!
MM = 6.42"1023 kg , RM = 3.38"106 m, and d = 200 km
v = ?
!
Fg =GMM mr2
!
= m v2
r
!
= mac
!
v = GMM r
!
RM
!
d
!
r = RM + d
!
v = G MM RM + d
!
v = 6.67"10#11 N $m2
kg2
%
& '
(
) *
6.42"1023 kg( )3.38"106 m + 2.0"105 m( )
!
v = 3459 ms
Example 3:
Gravitation 9
Example 4:How many minutes would it take a satellite toorbit Earth 150 km above its surface?(ME = 5.98 x 1024 kg and RE = 6.37 x 106 m)
!
ME = 5.98"1024 kg , RE = 6.37"106 m, and d = 150 km
T = ?
!
Fg =GME mr2
!
= m v2
r
!
= mac
!
v = GME r
!
RE
!
d
!
r = RE + d
!
T = 2"6.37#106 m +1.5#105 m( )3
6.67#10$11 N %m2
kg2
&
' (
)
* + 5.98#1024 kg( )
!
T = 5238 s
!
=2"rT
!
T = 2"r r GME
!
= 2" r 3 GME
!
T = 2" RE + d( )3 GME
!
= 87.3 min
Example 4:
The Law of Gravity 11
Example 5:A spaceship is fired from the Earth’s surfacewith an initial speed of 2.00 x 104 m/s. Whatwill be its speed when it is very far awayfrom the Earth? (Neglect friction)
(ME = 5.98 x 1024 kg and RE = 6.37 x 106 m)
12
!
M = ME = 5.98"1024 kg, v1 = 2.00"104 ms
, r1 = RE = 6.37"106 m, r2 =#, v2 = ?
Example 5:
!
K1 +U1 = K2 +U2
!
12mv1
2 "G Mmr1
=12mv2
2 "G Mmr2
!
v2 = 1.66"104 ms
!
r2 ="
!
v2 = v12 " 2G M
r1
!
v2 = 2.00"104 ms
# $ %
& ' (
2) 2 6.67"10)11 N *m2
kg2
#
$ %
&
' (
5.98"1024 kg( )6.37"106 m( )