Practice QuestionVIII
Gravitational Interactions
Level : Physics I
Date :
Name :
Teacher : Kim
Fg =
G=6.67×10-11N·m2/kg2
You must show your work~ !! difficulty level ; * = Moderate
** = Challenging!
*** = Are you crazy!!
*1. The center-to-center distance between the Earth and the Moon 384400km. The moon completes an
orbit in 27.3 days. Determine the Moon's orbital speed. Use
.
(remember to convert days into seconds and 1km=1000m)
a) 8.32×103m/s
b) 5.67×103m/s
c) 1.02×103m/s
d) 9.22×102m/s
2. A m1=200kg mass and a m2=500kg mass are separated by r =0.4m.
m1
*(i) Find the net-gravitational force(=∑F) exerted by these
masses on a 50kg mass placed midway between them and
the direction. F1 is the force acting on the 50kg mass due to
m1, . F2 is the force acting on the 50kg mass due to m2.
a) 2.5×10-5N toward 200kg
b) 2.5×10-5N toward 500kg
-5
c) 1.5×10 N toward 200kg
d) 1.5×10-5N toward 500kg
r
F1
m2
F2
50kg!
**(ii) Find the time it takes for the 50kg mass before it collides with that mass
(use ∑F=ma & d=vit + ½at2)
a) 894s
b) 545s
c) 204s
***(iii) At what position (other than infinitely remote ones)
can the 50kg mass be placed so as to experience a net force
of zero?
d) 45s
m1
r
m2
50kg!
Fg =
G=6.67×10-11N·m2/kg2
3. A satellite with a mass of 200kg is placed in Earth's orbit at a height of 200km above the surface.
*i) Assuming circular orbit, how long, in hours, does the satellite take to complete one orbit? (Mass and
radius of Earth Me=6×1024kg, Re= 6.38×106m, 1km=1000m)
a) 1.47hrs
b) 3.45hrs
c) 5.72hrs
d) 8.97hrs
*ii) What is the satellite's speed?
a) 23×103m/s
b) 5.1×103m/s
c) 7.8×103m/s
d) 9.4×103m/s
***4. Two objects attract each other with a gravitational force of 1×10-8N when separated by 0.2m. If the
total mass of the two objects is 5kg, what is the mass of each?
a) 1.3kg & 3.7kg
b) 2kg & 3kg
c) 2.5kg & 2.5kg
d) 3.8kg & 1.2kg
**5. Three uniform spheres of masses m1=6kg, m2=4kg and
m3=2kg are placed at corners of a right triangle. Calculate the
resultant gravitational force on m2. (hint : use Pythagorean theorem
r2=x2 + y2)
a) 1.16×10-10N b) 4.54×10-10N c) 7.22×10-10N d) 9.54×10-10N
(0, 3)m
m3
F32
m1
m2
F12
(–4, 0)m
(0,0)
Fg =
G=6.67×10-11N·m2/kg2
6. A spacecraft in the shape of a long
cylinder length of 100m, and its mass with
occupants is 1000kg. It has strayed too
close to a 1m radius black hole have a mass
100 times that of our Sun. The nose of the
spacecraft is pointing toward the center of
100m
the black hole, and the distance between
the nose and the black hole is 10km.
(1km=1000m, MSUN=2×1030kg)
*i) Determine the gravitational force acting on the spacecraft.
a) 1.32×1017N
b) 4.55×1017N
c) 7.76×1017N
Black hole
10km
d) 9.29×1017N
*ii) Find speed necessary to escape from the gravitational pull of the black hole at that position.
a) 8.36×109m/s
b) 5.21×109m/s
c) 3.74×109m/s
d) 1.63×109m/s
*iii) Based on your escape speed you obtained from above, how many times greater is it than the escape
speed of Earth's gravity, which is ve=1.12×104m/s ?
a) 8.34×104 times greater b) 1.45×105 times greater c) 4.22×105 times greater d) 8.16×105 times greater
**7. As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off,
walking always ahead, and find yourself returning to your spacecraft from the opposite side after
completing a lap of 25km. If the mass of the planet M=7.79×1014kg, what is the speed necessary to
escape the planet? (1km=1000m, hint: you need to find the radius of the planet based on the information
given in the question)
a) 24.5m/s
b) 19.8m/s
c) 12.1m/s
d) 5.1m/s
Fg =
G=6.67×10-11N·m2/kg2
*8. If the earth had twice its present mass, the earth's orbital period around the sun(at our present distance
from the sun) would be
a)
years
b) 1 year
c) year
d) 0.5 year
*9. If the sun had twice its present mass, the it's orbital period around the sun(at our present distance from
the sun) would be
a) 2 years
b)
year
c) year
d) 0.5 year
**10. When two point masses are a distance D apart, each exerts a gravitational attraction F on the other
mass. To reduce this force to F, you would have to separate the masses to a distance of
a) D
b) 3D
c) 9D
d) D
**11. If a planet is ever discovered orbiting midway between the earth and the sun, its orbital period will
be closest to
a) 2.0 years
*~ use
b) 0.5 years
c) 0.35 years
d) 0.25 years