Physics P
Review
4
Review 4: Gravitation and Two-Dimensional Motion
Gravitation and Two-Dimensional
Motion
d  at
1
2
Fg  G
1.
v2
ac 
r
Fnet  ma
2
m1m2
r2
A busy waitress slides a plate of apple pie
along a counter to a hungry customer
sitting near the end of the counter. The

customeris not paying attention, and the
plate slides off the counter horizontally at
0.84 m/s. The counter is 1.38 m high.
a.
How long does it take the plate to
fall to the floor?
b.
How far from the base of the
counter does the plate hit the floor?
G  6.67  1011 Nm
kg2
2
5.
A marble rolls
 off the edge of a table that
is 0.734 m high. The marble is moving at
a speed of 0.122 m/s at the moment that it
leaves the edge of the table. How far from
the table does the marble land?
6.
A car moving at 12.67 m/s rounds a bend
in the road. The bend is semicircular and
has a radius of 60 m. What is the
centripetal acceleration of the car?
7.
A town has a large clock on the hall in the
town square. The clock has hands that
show the hours, minutes, and seconds. A
fly is sitting on the tip of the hand that
shows the seconds. If the length of the
hand is 1.2 m, what is the fly’s centripetal
acceleration?
2.
The Moon revolves around Earth in a
circular orbit with a radius of
3.84  108 m. It takes 27.3 days for the
Moon to complete one orbit around Earth.
What is the centripetal acceleration of the
Moon?
3.
A clown rides a small car at a speed of
15 km/h along a circular path with a
radius of 3.5 m.
a.
What is the magnitude of the
centripetal force on a 0.18–kg ball
held by the clown?
b.
At the point where the car is headed
due north, the clown throws the ball
vertically upward with a speed of
5 m/s relative to the moving car. To
where must a second clown run to
catch the ball the same distance
above the ground as it was thrown?
8.
A rock is tied to a string and spun in a
horizontal circle. The string is 1.8 m long
and the rock has an acceleration of
3.4 m/s2. What is the tangential velocity of
the rock?
9.
The mass of Earth is 5.97  1024 kg, the
mass of the Moon is 7.35  1022 kg, and
the mean distance of the Moon from the
center of Earth is 3.84  105 km. Use these
data to calculate the magnitude of the
gravitational force exerted by Earth on the
Moon.
A 0.45–kg ball is attached to the end of a
cord of length 1.4 m. The ball is whirled
in a circular path in a horizontal plane.
The cord can withstand a maximum
tension of 57.0 N before it breaks. What is
the maximum speed the ball can have
without the cord breaking?
10.
Two identical bowling balls are placed
1.00 m apart. The gravitational force
between the bowling balls is 3.1  10–9 N.
Find the mass of a bowling ball.
4.
Physics P
11.
A plane drops a rescue capsule from an
altitude of 8500 m.
a.
How long does it take for the
capsule to fall to Earth, assuming air
resistance is negligible?
b.
If the plane is traveling with a
horizontal speed of 483 km/h when
the capsule is released, what is the
horizontal distance between the
point at which the capsule is
released and the point at which the
capsule strikes the ground?
12.
A satellite is placed in a circular orbit
100 km above Earth’s surface. Earth’s
mass is 5.97  1024 kg and its average
radius is 6.38  106 m.
a.
What is the speed of the satellite?
b.
How many minutes does it take the
satellite to complete one orbit?
13.
The asteroid Vesta has a mass of
3.0  1020 kg and an average radius of
510 km.
a.
What is the acceleration due to
gravity at its surface?
b.
How much would a 95–kg astronaut
weigh at the surface of Vesta?
Review 4: Gravitation and Two-Dimensional Motion
14.
The mass of Earth is 5.98  1024 kg and
the mass of the Sun is 330,000 times
greater than the mass of Earth. If the
center of Earth is, on average,
1.495  1011 m from the center of the Sun,
calculate
the
magnitude
of
the
gravitational force the Sun exerts on
Earth.
15.
Two metal spheres, each weighing 24 kg
are placed 0.05 m apart. Calculate the
magnitude of the gravitational force the
two spheres exert on each other.
16.
A car and a truck are traveling side by side
on the highway. The car has a mass of
1.37  103 kg and the truck has a mass of
9.92  103 kg. If the cars are separated by
2.1 m, find the force of gravitational
attraction between the car and the truck.
17.
A 5–kg mass weighs 8.1 N on the surface
of the Moon. If the radius of the Moon is
1737 km, what is the mass of the Moon?
19.
Acceleration due to gravity on Earth’s
surface is 9.80 m/s2. Thus, a 1.00–kg mass
weighs 9.80 N on the surface of Earth. If
the radius of Earth was cut exactly in half
but the mass of Earth remained
unchanged, how much would a 1.00–kg
mass weigh on the surface of Earth?
Physics P
1a.
Review 4: Gravitation and Two-Dimensional Motion
4.
2h
Dt =
g
2 (1.38 m )
9.8 m/s 2
Dt = 0.53 s
Dt =
1b.
Dd = vDt
Dd = 0.45 m
5.
a=
a=
2 ( 0.734 m )
9.8 m/s2
Dt = 0.39 s
Dd = ( 0.122 m/s) ( 0.39 s)
)
Dd = 0.047 m
6.
v2
r
2
0.18 kg) ( 4.17 m/s)
(
F=
3.5 m
7.
It will take 1 s for the ball to return so it
will go 4.17 m.
(12.67 m/s)2
Dd
Dt
2p r
v=
Dt
2p (1.2 m )
v=
60 s
v = 0.126 m/s
v=
F = 0.89 N
3b.
v2
r
60 m
a = 2.7 m/s2
8
mv 2
r
a=
a=
(1022 m/s)2
15 km/h = 4.17 m/s
F=
2h
g
Dd = vDt
3.84 ´10 m
a = 0.0027 m/s2
3a.
Dt =
Dt =
v=
(
0.45 kg
v = 13.3 m/s
27.3 days = 2 358 720 s
Dd
Dt
2p r
v=
Dt
2p 3.84 ´108m
v=
2 358 720 s
v = 1022 m/s
( 57 N ) (1.4 m )
v=
Dd = ( 0.84 m/s) ( 0.53 s)
2.
mv 2
F=
r
Fr
v=
m
a=
v2
r
2
0.126 m/s)
(
a=
1.2 m
a = 0.013 m/s2
Physics P
8.
Review 4: Gravitation and Two-Dimensional Motion
v2
a=
r
v = ar
v=
12a.
mv 2 GMm
= 2
r
r
GM
v=
r
(3.4 m/s ) (1.8 m )
2
v = 2.5 m/s
9.
(
F= 6.67´10-11N×m 2 /kg2
10.
20
)(
)(
5.97´1024 kg 7.35´10 22 kg
(3.84´108m)
2
)
12b.
N
Fr 2
G
(3.1´10 N ) (1.00 m )
2
G
m = 6.8 kg
13a.
11a.
Dt =
2h
g
2 (8500 m )
9.8 m/s2
Dt = 41.6 s
g=
GM
r2
G 3.0 ´10 20 kg
(
( 510 000 m )
)
)
2
g = 0.077 m/s2
13b.
483 km/h = 134 m/s
Fg = mg
(
Fg = ( 95 kg) 0.077 m/s2
Dd = vDt
)
Fg = 7.3 N
Dd = (134 m/s) ( 41.6 m/s)
Dd = 5588 m
Dd
Dt
Dd
Dt =
v
2p r
Dt =
v
2p 6.38 ´10 6 m + 100 000 m
Dt =
7840 m/s
Dt = 5190 s
Dt = 86 min
v=
g=
Dt =
11b.
6
(
-9
m=
)
6.38 ´10 m + 100 000 m
v = 7840 m/s
mm
F =G 1 2
r2
m=
(
G 5.97 ´10 24 kg
v=
m1m2
F =G 2
r
F = 1.98 ´ 10
Fc = FG
14.
F = G
m1m2
r2
(
F= 6.67´10-11N×m 2 /kg2
F = 3.5 ´ 10
22
N
)(
)
(
2
(1.49´1011m)
5.97´1024 kg ( 330 000) 5.97´10 24 kg
)
Physics P
15.
Review 4: Gravitation and Two-Dimensional Motion
mm
F =G 1 2
r2
( 24 kg) ( 24 kg)
F =G
0.05 m 2
(
)
F = 1.5 ´10 N
-5
16.
mm
F =G 1 2
r2
(1370 kg) ( 9920 kg)
F =G
2.1 m 2
(
)
F = 2.1´10 -4 N
17.
mm
F =G 1 2
r2
Fr 2
M=
Gm
2
8.1 N ) (1 737 000 m )
(
M=
G ( 5 kg )
M = 7.33 ´10 22 kg
18.
If the radius was half, the force would
increase by a factor of 4, thus a 1.00–kg
mass would weigh 39.2 N